TRANSLATION 


OF  THIS 


SURYA-SIDDHANTA, 

A TEXT-BOOK  OF  HINDU  ASTRONOMY; 

WITH  NOTES,  AND  AN  APPENDIX, 

CONTAINING  ADDITIONAL  NOTE8  AND  TABLES,  CALCULATIONS  OF 
ECLIPSES,  A STELLAR  MAP,  AND  INDEXES. 


By  Rev,  E.BENEZER  BURGESS, 

■ FORMERLY.'  MISSIONARY  OF  TUB  A.  B.  C.  F.  M.  IN  IXTHA 

ASSISTED  BY  TTIE 

COM MITTKJ5  OF  PUBLICATION  OF  THU  AMERICAN  ORIENTAL  SOCIETY. 


[Vkom  the  Journal  of  the  American  Oriental  Society,  Vol.  yi,  1800.J 


NEW  HAYE.N: 

FOR  THE  AMERICAN  ORIENTAL  SOCIETY, 

l'KIH  rfiU  IT  E*  IUra,  pRIKTSR  TO  ViL|  GdUloI 
XDOOOLE, 

BO£D  BY  TUB  society's  agents: 

NEW  YORK  : JOE(N  WItEY,  50  WALKER  OT. : 

LONDON:  TKijBNEI* & CCS  ; PARIS:  BKNJ*  DUFRAT; 
LEIPZIG:  F.  A BSOCKKAUB. 


COMMITTEE  OF  PUBLICATION. 


or  THE 

AMERICAN  ORIENTAL  SOCIETY, 

Foil  THIS  YEARS  1858-60. 


Edward  E.  Salisbury, 
WillAm  D.  Whitney' 
James  Hadley, 

Ezra  Abbot, 

William  W.  Turner, 


New  Ha vcd. 

a 

u 

Cambridge. 

Washington. 


Eotarad  according  to  Aqt  of  Congrua,  in  the  year  1660,  by  tli* 
Ankuoah  Oubntao  Booiett, 
in  the  Clark'*  Offica/oT  tha  'District  Court  of  Connecticut. 


TRANSLATION 


OF  TD 

SffRYA-SIDDHiHTA, 

WITH  NOTES,  AND  AN  APPENDIX. 


[Communicated  to  the  American  Oriental  Society  May  17, 1858,  and  published  in. 
the  Sixth  Volume  of  its  Journal.] 


Introductory  Note. 

Soon  after  my  entrance  upon  the  mission  ary  field,  in  the  Mar&tha 
country  of  western  India,  in  the  year  1830,  my  attention  was  directed 
to  the.  preparation,  in  the  Mar&thi  language,  of  an  astronomical  text- 
book for  schools.  I was  thus  led  to  a study  of  JJie  Hindu  science  of 
astronomy,  ns  exhibited  in  the  native  text-books,  and  to  an  examination 
of  what  had  been  written  respecting  it  by  European  scholars.  I at 
once  found  myself,  on  the  one  hand,  highly  interested  by  the  snhject 
itself,  and,  on  the  other,  somewhat  embarrassed  for  want  of  a satisfactory 
introduction  to  it.  A comprehensive  exhibition  of  the  Hindu  system  had 
nowhere  been.  made.  The  Astronomic  Indicnnc  of  Bbilly,  the  first  ex- 
tended work  upoxi  its  subject,  had  long  been  acknowledged  to  he  founded 
upon  insufficient  data,  to  contain  a greatly  exaggerated  estimate  of  the 
antiquity  and  value  of  the  Hindu  astronomy,  and  to  have  been  written 
for  the  purpose  of  supporting  an  untenable  theory.  The  articles  in  the 
Asiatic  Researches,  by  Davis,  Colebrooke,  and  llenticy,  which  were  the 
first,  as  they  still  remain  the  most  important,  sources  of  knowledge  re- 
specting the  matters  with  vthich  they  deni,  relate  only  to  particular 
points,  in  the  Rystem,  of  especial  prominence  and  interest.  Bentley’s 
volume  on  Hindn  astronomy  is  mainly  occupicd  witli  an  endeavor  to 
ascertain  the  age  of  the  principal  astrononjical  treatises*  and  the  epochs 
of  astronomical  discovery  and  progress,  ajid  Is,  moreover,  even  in  these 
respects,  an  exceedingly  unsafe  guide. , The  freatment'of  the  subject  .by, 
Delambrc,  in  his  History  of  Ancient  Astronomy,  being  fonndc#*Snly 
upon  Bailly  and  the  earliest  of  jthe. essays  in  the  Asiatic  Researches,, 
partakes,  of  .course,  of  the  iii^mpletenesa  of  his  authorities.  Works 
^of  value  have  been  published  in  India,  also,  into  which  more  or  lf»  of. 
""Hindu  astronomy  enters,  as  ^Rfarren’s  KAla  Sankalita,  Jervis’s  Weights 
Measures  and  Coins  of  Indi^  ^HoisiQgton’s  , Oriental  Astronomer,  sad 


11 


the  like ; but  these,  too,  give,  for  the  most  part-,  hardly 'foore  than  the 
practical  processes  employed  in  parts  of  the  system,  and  they  arc,  like 
many  of  the  authorities  already  mentioned,  only  with  difficulty  accessi- 
ble. Tn  short,  there  was  nothing  in  existence  which  showed  Die  world 
how  much  aud  how  little  the  Hindus  know  of  astronomy,  as  also  their 
mode  of  presenting  the  subject  in  its  totality,  the  intermixture  in  tlicir 
/science  of  old  ideas  with  new,  of  astronomy  with  astrology,  of  observa- 
tion and  mathematical  deduction  with  arbitrary  theory,  mythology, 
cosmogony,  and  pure-  imagination.  It  seemed  to  me  that  nothing  would 
so  well  supply  the  deficiency  os  the  translation  and  detailed  explication 
of  a complete  treatise  of  llindu  astronomy : utul  this  work  1 accord- 
ingly undertook  to  execute. 

Among  the  different  Siddliantas,  or  text-books  of  astronomy,  existing 
in  India  in  the  Sanskrit  language,  none  appeared  better  suited  to  my 
purpose  than  the  Sfirya-Siddhanla.  That  it  is  one  of  the  most  highly 
esteemed,  best  known,  and  most  frequently  employed,  of  all,  must  be 
evident  to  any  one.  who  has  noticed  now  much  ofLcner  Ilian  any  other 
it  is  referred  to  as  authority  in  the  \arious  papers  on  the  Hindu  astron- 
omy. In  fact,  the  science  as  practised  in  modern  India  is  in  the  greater 
part  founded  upon  its  data  and  processes.  In  the  lists  of  Siddhfintas 
given  by  native  authorities  ii  is  almost  invariably  mentioned  second,  the 
Hrahma-Siddlianla  being  placed  first : the  latter  enjoys  this  preniinence. 
perhaps,  mainly  on  account  of  its  name ; it  is,  at  any  rate,  compara- 
tively rare  ami  little  known.  For  completeness,  simplicity,  ami  concise- 
ness combined,  the  Kuryn-Siddliiinta  is  believed  not  to  be  surpassed  by 
any  oilier.  It  h aUo  more  easily  obtainable.  In  general,  it  is  difficult-, 
without  official  influence  or  exorbitant  pay,  to  gain  possession  of  texts 
an  liioh  arc  rare  and  held  in  high  esteem.  I Miring  my  stay  in  India,  l 
was  able  to  procure  copies  of  only  three  astronomical  1 realises  besides 
the  Siina-Siddhiuna;  the  (aikalya-Sanhila  of  the  Hrahmu-Siddliaiitu, 
the  Kiddliuntnd'iroinuni  of  Bhaskani,  and  the  Cmha-Laghava,  of  which 
the  lw<»  latter  I^a\e  also  been  punted  at  Calcutta.  Of  the  Surva- 
Siddliuuta  i obtained  throe  copies,  two  of  them  giving  the  text  alone, 
and  the  In  ini  also  the  comment  an  entitled  Oiidharthaprakaraka,  l»v 
Uanganathn,  of  which  the  date  is  unknown  to  me.  The  hitter  manu- 
script agrees  in  all  respects  with  the  edition  of  the  Surya-Siddlmnta. 
accompanied  by  the  same  commentary,  of  which  the  publication,  in  the 
series  entitled  Bibliotheca  Indira,  has  been  commenced  in  India  by 
an  American  scholar,  and  a member  of  this  Society,  Prof.  Fitz- Edward 
Hall  of  Benares;  to  this  I have  also  had  access,  although  not  until  inv 
work  wax  nearly  completed. 

My  first  rough  draft  of  the  translation  aiul  notes  wits  made  while  l 
was  still  in  India,  with  the  aid  of  Brahmans  who  were  familiar  with  the 
Sanskrit  and  well  versed  in  Hindu  astronomical  science,  in  a few  points 
received  help  from  the  native  Professor  of  Mathematics  in  the 
Sanskiit  College  at  Puna.  But  notwithstanding  this,  there  remained 
not  a few  obscure  and  difficult  poirtts,  connected  with  the  demonstration 
and  application  of  the  processes  taught  in  the  text,  in  the  solution  of 
these?  I have  received  very  important  assistance  from  the  Committee  of 
Publication  of  the  Society.  They  have  also — the  main  share  of  the 


m 


IV  ...  ' ' 

Vork  falling  to  Frets  Whitney — enriched  the  notes  'with  mnch  additional 
matter  of  value.  My  whole  collected  material,  in  fact;  was  placed  in 
their  hands  for  revision,  expansion,  and  reduction  to  the  form  beat 
answering  to  the  requirements  of  modern  (scholars,  my  own  engrossing  ' 
occupations,  and  distance  from  the  place  of  publication,  as  well  as  my 
confidence  in  their  ability  and  judgment,  leading  me  to  prefer  to  intrust 
this  work  to  them  rather  than  to  undertake  its  execution  myself.  ^ 

We  have  also  to  express  our  acknowledgments  to  Mr.  Hubert  A. 
Newton,  Professor  of  Mathematics  in  Yale  College,  for  valuable  aid  ren- 
dered ns  in  the  more  difficult  demonstrations,  and  in  the  comparison  of 
the  ilindiL  and  Greek  astronomies,  as  well  as  for  his  constant  advice  and 
suggesting  which  add  not  a little  to  the  value  of  the  work. 

The  Sftrya-Siddhftnta,  like  the  larger  portion  of  the  Sanskrit  litera- 
ture; is  written  in  the  verse  commonly  called  the  floka,  or  in  stanzas  of 
Iwo  lilies,  each  line  being  composed  of  two  halves,  or  p&dn, »,  of  eight 
syllables  each.  With  its  metrical  form  arc  connected  one  or  two  pecu- 
liarities which  call  for  notice.  In  the  first  place,  for  the  terms  used 
there  arc  often  many  synonyms,  which  are  employed  according  to  the 
exigencies  of  the  verso:  thus,  the  snn  has  twelve  different  names,  Mam 
six,  the  divisions  of  time  two  or  throe  each,  radius  six  or  right,  and  so 
on.  Again,  the  method  of  expressing  numbers,  large  or  small,  is  by 
naming  the  figures  which  compose  them,  beginning  with  the  last  and 
going  backward ; using  for  each  figure  not  only  its  own  proper  name, 
but  that  of  any  object  associated  in  the  Hindu  mind  with  the  number  it 
represents.  Thus,  the  number  1,377,017,828  (i.  37)  is  thus  given: 
Yawi  (a  class  of  deities,  eight  in  number)  -two-eight  mountain  (the  seven 
mythical  chains  of  mountains)  -form-figure  (the  nine  digits)  -seven-moun- 
tain-lunar  days  (of  which  there  are  fifteen  in  the  half-month).  Once 
more,  the  style  of  expression  of  the  treatise  is,  in  general,  excessively 
concise  and  elliptical,  often  to  a degree,  that  would  make  its  meaning 
entirely  unintelligible  without  a commentary,  the  exposition  of  a native 
teacher,  or  such  a knowledge  of  the  subject  treated  of  as  should  show- 
what  the  text  must  bo  meant  to  say.  Some  striking  instances  are 
pointed  out  in  the  notes.  This  over-conciseness,  however,  is  not  wholly 
due  to  the  metrical  form  of  the  treatise : it  is  characteristic  of  mnch  of 
the  Hindu  scientific  literature,  in  its  various  branches ; its  text-books  are 
wont  to  he  intended  as  only  the  text  for  written  comment  or  oral  expli- 
cation, and  hint  rather  than  fully  express,  the  meaning  they  contain. 

In  our  translation,  we  have  not  thought  it  worth  while  to  iiulicate,  by 
parentheses  or  otherwise,  the  words  and  phrases  introduced  by  ns  to 
make  the  meaning  of  the  text  evident : such  a course  would  occasion 
the  reader  much  more  embarrassment  than  satisfaction.  Our  endeavor 
is,  in  all  cases,  to  hit  the  true  mean  between  uninUtligibility  and  diffuse 
ness,  altering  the  phraseology  and  construction  of  the  original  on(j-*So^ 
far  as  is  necessary.  In  both  the  translation  and  the  notes,  moreover 
we  keep  steadily  in  view  the  interests  of  the  two  classes  of  readers  for 
whose  benefit  the  work  is  undertaken  : those  who  arc  orientalists  with- 
out being  astronomers,  and  those  who  arc  astronomers  without  being 
orientalists.  For  the  sakcof  the  former,  our  explanations  and  demon- 


IV 


fttiatioTift  are  made  more  elementary  and  full  than  would  be  neocssaiy, 
were  we  addressing  mathematicians  only : for  the  sake  of  the  latter,  we 
cast  the  whole  into  a form  as  occidental  as  may  be,  translating  every 
technical  term  which  admits  of  translation : since  to  compel  all  those  who 
may  desire  to  inform  themselves  respecting  the  scientific  content  of  the 
Hindu  astronomv  to  learn  the  Sanskrit  technical  language  would  be 
highly  unreasonable.  To  furnish  no  ground  of  complaint,  however,  to 
those  who  arc  familiar  with  and  attached  to  these  terms,  wc  insert  them 
liberally  in  the  translation,  in  connection  with  their  English  equivalents. 
The  derivation  and  literal  signification  of  the  greater  part  of  the  tech- 
nical terms  employed  in  the  treatise  arc  also  given  in  the  notes,  since 
such  an  explanation  of  the  history  of  a term  is  often  cssAtial  to  its 
full  comprehension,  and  throws  valuable  light  upon  the  conceptions  of 
those  by  whom  it  was  originally  applied. 

We  adopt,  as  the  text  of  our  translation,  the  published  edition  of  the 
Siddhltnta,  referred  to  above,  following  its  readings  and  its  order  of  ar- 
rangement, wherever  they  differ,  as  they  do  in  many  places,  from  those 
of  the  manuscripts  without  commentary  in  our  possession.  The  dis- 
cordances of  the  two  versions,  when  they  are  of  sufficient  consequence 
to  be  worth  notice,  arc  mentioned  in  the  notes. 

As  regards  the  transcription  of  Sanskrit  words  in  Roman  letters,  wc 
need  only  specify  that  c represents  the  sound  of  the  English  rh  in 
11  church,”  Italian  c before  e and  i : that  j is  the  English  j : that-  r pro- 
nounced like  the  English  sh,  German  sch,  French  ch , while  sh  is  a sound 
nearly  resembling  it,  but  uttered  with  the  tip  of  the  tongue  turned  back 
into  the  top  of  the  mouth,  as  arc  the  other  lingunl  letters,  /,  r/,  n : 
finally,  that  the  Sanskrit  r used  as  a vowel  (which  value  it.  has  also  ii: 
some  of  the  Slavonic  dialects)  is  written  with  a dot  underneath,  us  r. 

The  demonstrations  of  principles  and  processes  given  by  the  native 
commentary  are  made  without  the  help  of  figures.  The  figures  which 
wc  introduce  arc  for  the  most  part  our  own,  although  a lew  of  them 
were  suggested  by  those  of  a set  obtained  in  India,  from  native  mathe- 
maticians. 

For  the  discussion  of  such  general  questions  relating  to  this  Siddli&nta 
as  its  age,  its  authorship,  the  alterations  which  it  may  have  undergone 
before  being  brought  into  its  present  form,  the  stage  which  it  represents 
in  the  progress  of  Hindu  mathematical  science,  the  extent  and  character 
of  the  mathematical  and  astronomical  knowledge  displayed  in  it,  and 
the  relation  of  the  same  to  that  of  other  ancient  nations,  especially  of 
the  Greeks,  the  reader  is  referred  to  the  notes  upon  the  text.  The  form 
in  which  our  publication  is  made  does  not  allow  us  to  sum  up  here,  in 
a preface,  the  final  results  of  our  investigations  into  these  and  kindred 
topics.  It  may  perhaps  be  found  advisable  to  present  such  a sun  injury 
at  the  end  of  the  article,  in  connection  with  the  additional  notes  and 
~ frier  matters  to  he  there  given. 


sObya-siddhanta 


CHAPTER  I. 

OP  THE  MEAN  MOTIONS  OF  THE  PI/ANETS. 

Cottemts: — 1,  homage  to  the  Deity  j 2-9,  revelation  of  the  present  treatise;  10-11. 
inodes  of  dividing  time  ; 11-12,  subdivisions  of  n day;  12-14,  of  a year;  14-17, 
of  the  Ages;  18-19,  of  an  J5on ; 20-21,  of  Brahma’s  life;  21-23,  part  of  it 
already  elapsed ; 24,  time  oerupied  in  the  work  of  creation ; 26-27,  general 
account  of  the  movements  of  the  planets  ; 28,  subdivisions  of  the  circle;  29-83, 
number  of  revolutions  of  the  planets,  and  of  the  moon's  apsis  and  node,  in  an 
Age ; 34-39,  number  of  days  and  months,  of  different  kinds,  in  an  Age  ; 40,  in  an 
TEon  ; 41-44,  number  of  revolutions,  in  an  iEon,  of  the  apsides  and  nodes  of  the 
planets  ; 46-17.  time  elapsed  from  the  end  of  creatiun  to  that  of  the  Golden  Age ; 
48-51,  rule  for  the  reduction  to  civil  days  of  the  wliple  time 'since  the  creation; 
51-52,  method  of  finding  the  lords  of  the  day,  the  month,  and  the  year ; 63-54, 
rule  for  finding  the  mean  place  of  a planet,  mid  of  its  apsis  and  node  ; 55,  to  find 
the  current  year  of  the  cycle  of  Jupiter  ; 56,  simplification  of  the  above  calcula- 
tions; 57-58,  situation  of  the  planets,  and  of  the  moon's  apsis  and  node,  at  the 
end  of  the  Golden  Age ; 59-60,  dimensions  of  the  earth ; GO-61,  correction,  for 
difference  of  longitude,  of  the  mean  place  of  a planet  as  found  ; 62,  situation  of 
the  principal  meridian ; 63-65,  ascertainment  of  difference  of  longitude  by  differ- 
ence between  observed  and  computed  time  of  a lunar  eclipse ; 66,  difference  of 
time  owing  to  difference  of  lougitude  ; 67,  to  find  the  mean  place  of  a planet  for 
any  required  hour  of  the  day;  6S-70,  inclination  of  the  orbits  of  the  planets. 

1.  To  him  whose  shape  is  inconceivable  and  unmanifested, 
who  is  unaffected  by  the  qualities,  .whose  nature  is  quality, 
whose  form  is  the  support  of  the  entire  creation — to  Brahma  De 
homage  1 

The  usual  propitiatory  expression  of  homage  to  some  deity,  with 
which  Hindu  works  arc  wont  to  commence. 

2.  When  but  little  of  the  Golden  Age  ( lc  mla  yuga)  was  left,  a 

great  demon  (asuru\  named  Maya,  being  desirous  to  know 
mysterious,  supreme,  pure,  and  exalted  science,  * 

3.  That  chief  auxiliary  of  the  scripture  (i veddngq),  in  its  en- 
tirety— the  cuuse,  namely,  of  the  motion  of  the  heavenly  bodies 
( jyotis ),  performed,  in  propitiation  of  the  Suu,  very  severe  re- 
ligious austerities. 


1 


2 


FKLrya-Siddhdnta,  [i.  3- 

Acconling  to  this,  the  Stirya-SiddliAnta  was  tyvealcd  more  than 
2,164,960  years  ago,  that  amount  of  time  having  elapsed,  according  to 
Hindu  reckoning,  since  the  end  of  the  Golden  Age ; see  below,  under 
verse  48,  for  the  computation  of  the  period.  As  regards  the  actual 
date  of  the  treatise,  it  is,  like  all  dates  in  Hindu  history  and  the  history 
of  Hindu  literature,  exceedingly  difficult  to  ascertain.  It  is  the  more 
'difficulty  because,  unlike  most,  or  all,  of  the  astronomical  treatises,  the 
SArva-Siddlianta  attaches  itself  to  the  name,  of  no  individual  as  its 
author,  but  professes  to  bo  a direct  revelation  from  the  Sun  ( sitrya ).  A 
treatise  of  this  name,  however,  is  confessedly  among  the  earliest  text- 
books of  the  Indian  science.  It  was  one  of  the  live  earlier  works  upon 
which  was  founded  the  Vanca-siddhantika,  Compendium  of  Five  As- 
tronomies, of  Varaha-inihira,  one  of  the  earliest  astronomers  whose  works 
have  been,  in  part,  preserved  to  us,  and  who  is  supposed  to  have,  lived 
about  the  beginning  of  the  sixth  century  of  our  era.  A Surva-fciddlifinta 
is  also  referred  to  by  .Brahmagupta,  who  is  assigned  to  the  close  of  the 
same  century  and  the  commencement  of  the  one.  following.  The  argu- 
ments by  which  Mr.  Bentley  (Hindu  Astronomy,  p.  158,  etc.)  attempts 
to  pro\e  Varaha-mihira  to  have  lived  in  the  sixteenth  century,  and  his 

Fwofesscd  works  to  be  forgeries  anil  impositions,  are  sufficiently  refuted 
iy  the  testimony  of  al-Hinmi  (the  same  person  as  the  Abu-r-Uiiiluin,  so 
often  quoted  in  the.  first  article  of  this  volume),  who  visited  India  under 
Mnhin&d  of  Ghnznn,  and  wrote  in  A.l).  3051  an  account  of  the  coun- 
try: lie  speaks  pf  Ynrahn-miliira  and  of  his  ]\nilca-siddhuntika,  assign- 
ing to  both  nearly  the  same  age  i\*  is  attributed  to  them  by  the.  modern 
Hindus  (see  Iteinaud  in  tlu  Journal  Asiatiquc  for  Scpt.-Oet.  1844.  ivnl« 
S6rie,  iv.  2Stf ; and  also  his  Memoire-  sur  l'lndc).  He.  also  speaks  of  the 
Surva-Siddhanta  itself,  and  ascribes  its  authorship  to  Lat&  (Memoire  sur 
Tlnde,  jip.  551,  552),  whom  Weber  (Vorlesungcn  iiber  Indische  Lit-era- 
tn.rgijschiehte,  p.  220)  eonjecfii rally  identifies  with  a L&dha  w'ho  is  cited 
by  Brahmagupta.  Bentley  1ms  endeavored  to  show  by  internal  evi- 
dence that  the.  iSftrya-Siddliunta  belongs  to  the  end  of  the  eleventh 
century:  see  below,  under  v«*rses  29-34,  where  his  method  ami  results 
are  explained,  and  their  ^alue  estimated. 

Of  the  six  Ycdangas,  u limbs  of  the  Veda,”  sciences  auxiliary  to  the 
sacred  scriptures,  astronomy  is  claimed  to  be  the  first  and  chief,  as  rep- 
resenting the  cyea ; grammar  being  the  mouth,  ceremonial  the  hands, 
prosody  the  feet,  etc.  (sec  Siddhunta-£Jiroinaui,  i.  12-14).  The  import- 
ance of  astronomy  to  the  system  of  religious  observance  lies  in  tlio  fact 
that  by  it  are  determined  the  proper  times  of  sacrifice  and  the  like.. 
There  is  a special  treatise,  the  Jyot-jsha  of  Lagadha,  or  Lagatn,  which, 
attaching  itself  to  the  Yci'lic  texts,  and  representing  a more  primitive 
phase  of  iliudu  science,  claims  to  be  the  astronomical  Ved&nga;  but  it 
is  said  to  be  of  late  date  and  of  small  importance. 

word  jyoti.%  “ heavenly  body,”  literally  “ light.”  although  the 
current  names  for  astronomy  and  astronomers  are  derived  from  it,  does 
- not  elsewhere  occur  in  this  treatise. 

4*.  Gratified  by  these  austerities,  and  rendered  propitious,  the 
Sun  himself  delivered  unto  that  Maya,  who  besought  a boon, 
the  system  of  the  planets. 


Translation  and  Notes . 


8 


i.  0.] 

The  blessed  Son  spoke : 

5.  Thine  intent  is  known  to  me;  I am  gratified  by  thine  aus- 
terities ; I will  give  thee  the  science  upon  which  time  is  founded, 
the  grand  system  of  the  planets. 

6.  N*>  one  iS  able  to  endure  my  brilliancy ; for  communication 
I have  no  leisure;  this  person,  who  is  a part  of  me,  shall  relate 
to  thee  the  whole. 

The  manuscripts  without  commentary  insert  here  the  following  verse : 

“Go  therefore  to  Romaka-city,  thine  own  residence;  there,  under- 
going incarnation  as  a barbarian,  owing  to  a curse  of  Eralmia,  I will 
impart  to  thee  this  science.” 

if  this  verse  really  formed  a part  of  the  test,  it  would  ho  as  clear 
an  acknowledgment  as  the  author  could  well  convey  indirectly,  that 
the  science  displayed  in  his  treatise  was  derived  from  the  Greeks. 
Romaka-city  is  Koine,  the  great  metropolis  of  the  West;  its  situation  is 
given  in  a following  chapter  (sec  xii.  39)  as  upon  the  equator,  ninety 
degrees  to  the  west  of  India.  The  incarnation  of  the  sun  there  us  a 
barbarian,  for  the  purpose  of  revealiug  astronomy  to  a demon  of  the 
Hindu  Pantheon,  is  but  ^transparent  artilicc  for  referring  the  foreign 
science,  after  all,  to  a Jl^B^prigin.  But  the  verse  is  clear!}  out  of 
place  here;  it  is  imof^^^Pwitli  the  other  verses  among  which  it 
occurs,  which  give  a (fflPrat  version  of  the  method  of  revelation. 
How  comes  it  here  then  1 It  can  hardly  have  been  gratuitously  devised 
and  introduced.  The  verse  itself  is  found  in  many  of  the  manuscripts 
of  this  Siddh&nta;  and  the  incarnation  of  The  Sun  at  Ruin  aka-city, 
among  tlje  Yavanas,  or  Greeks,  and  his  revelation  of  the  science  of 
astronomy  there,  are  variously  alluded  to  iu  later  works;  as,  for  instance, 
in  the  Jnana-bhuskura  (see  Weber's  Catalogue  of  the  Berlin  Sanskrit 
Manuscripts,  p.  287,  etc.),  where  lie  is  asserted,  to  have  revealed  also  the 
Romuka-Siddh&nta.  Is  this  verse,  then,  a fragment  of  a different,  and 
perhaps  more  ancient,  account  of  the  origin,  of  the  treatise,  fol*  which, 
as  conveying  too  ingenuous  a confession  of  the  source  of  the  Hindu 
astronomy,  another  has  been  substituted  later  i Such  a supposition, 
certainly,  does  not  lack  plausibility.  There  is  something  wliicli  looks 
the  same  way  in  the  selection  of  a demon,  an  A sura,  to  be  the  medium 
of  the  sun's  revelation  ; as  if,  while  the  essential  truth  and  value  of  the 
system  was  acknowledged,  it  were  sought  to  affix  a stigma  to  the  source 
wlieucc  the  Hindus  derived  it.  Weber  (Ind.  Stud.  ii.  243;  liul.  Lit.  p. 
22.r>)v  noticing  that  the  name  of  the  Egyptian  sovereign  Ptolcmaios 
occurs  in  Indian  inscriptions  in  the  form  Ttirumaya,  conjectures  that 
AsuraMaya  is  an  alteration  of  that  name,  and  that  the  demon  Muja  ac- 
cordingly represents  the  author  of  the  Almagest  himself;  and  the  conjec- 
ture is  ]towerfu]]v  supported  by  the  fact  that  al- Uirftni  (sec  Rciuaud.  as 
abuve)  ascribes  the  Pnuli^a-Siddh&iita,  which  the  later  Hindus  at^Xrtlft 
to  a Pullen,  to  Paulus  al-Yuu&iil,  Paulus  the  Greek,  and  that  another  of  the 
astronomical  treatises,  alluded  to  above,  is  called  the  Romaku-Siddh&ntu* 

It  would  he  premature  to  discuss  hero  the  relation  of  the  Hindu 
astronomy  to  the  Greek ; we  propose  to  sum  up,  at  {lie  end  df  this 
work,  the  evidence  upon  the  subject  which  it  contains. 


4 S&rya-Siddh&ntcL  [i.7- 

7.  Thus  having  spoken,  the  god  disappeared,  having  given 
directions  unto  the  part  of  himselfi  This  latter  person  thus  ad: 
dressed  Maya,  as  he  stood  bowed  forward,  his  hands  suppliantly 
joined  before  him : 

8.  Listen  with  concentrated  attention  to  the  ancient  and  exalted 
science,  which  has  been  spoken,  in  each  successive  Age,  to  the 

•’■"Great  Sages  (maharshi)}  by  the  Sun  himself. 

9.  This  is  that  very  same  original  text-book  which  the  Sun  of 
old  promulgated : only,  by  reason  of  the  revolution  of  the  Ages, 
there  is  here  a difference  of  times. 

According  to  the  commentary,  tlio  meaning  of  these  lost  verses  is 
that)  in  the  successive  Great  Ages,  or  periods  of  4,320,000  years  (Bee 
below,  under  vv.  15-17),  there  are  slight  differences  in  the  motions  of 
the  heavenly  bodies,  which  render  necessary  a new  revelation  from  time 
to  time  on  the  part  of  the  Sun,  suitod  to  the  altered  conditions  of  things ; 
and  that  when,  moreover,  even  during  the  continuance  of  the  Baltic  Age, 
differences  of  motion  are  noticed,  owing  to  a difference  of  period,  it  is 
customary  to  apply  to  the  data  given  a correction,  which  is  called  btja. 
All  this  is  very  suitable  for  the  commentato^o  say,  but  it  seems  not  a 
little  curious  to  find  the  Sun's  superhum^B^resentative  himself  in- 
sisting that  this  his  revelation  is  the  as  had  formerly  been 

made  by  the  Sun,  only  with  different  data^^^  cannot  help  suspecting 
in  the  ninth  vene,  rather,  a virtual  confession  on  the  part  of  the  promul- 
gators of  this  treatise,  that  there  was  another,  or  that  there  wore  others, 
in  existence,  claiming  to  be  the  buii’b  revelation,  or  else  that  the  data 
presented  in  this  were  different  from  those  which  had  been  previously 
current  as  revealed  by  the  Sun.  We  shall  have  more  to  say  hereafter 
(see  below,  under  vv.  20-34)  of  the  probable  existence  of  more  than 
one  version  of  the  Sftrya-Siddh&nta,  of  the  correction  called  Afj'a,  and 
of  its  incorporation  into  the  text  of  the  treatise  itself.  The  repeated 
revelation  of  the  system  in  each  successive  Great  Age,  as  stated  in  verse 
8,  presents  no  difficulty.  It  is  the  Puranic  doctrine  (sec  Wilson's  Vishnu 
Fur&na,  p.  260,  etc.)  that  during  the  Iron  Age  the  source*  of  knowledge 
become  either  corrupted  or  lost,  so  that  a new  revelation  of  scripture, 
law,  and  science  becomes  necessary  during  the  Age  succeeding. 

10.  Time  is  the  destroyer  of  the  worlds ; another  Tio|p  has 
for  its  nature  to  bring  to  pass.  This  latter,  according  a*  it  is 
cross  or  minute,  is  called  bv  two  names,  real  (miirta)  and  unreal 
JflrrvCurta)* 

There  is  in  this  verse  a curious  mingling  together  of  the  poetical,  the 
theoretical,  and  the  practical.  To  the  Hindus,  &<%  to  us,  Time  is,  in  a 
EisfcQphorical  sense,  the  great  destroyer  of  all  things;  as  such,  he  is 
identified  with  Death,  and  with  Yavna,  the  ruler  of  the  dead.  Time, 
.again,  in  the  ordinary  acceptation  of  the  word,  has  both  its  imaginary, 
and  its  appreciable  and  practically  useful  divisions : the  former  arc  called 
■ real  {mvrta,  literally  “embodied"”),  the  latter  unreal  (amitrta,  literally 
11  unembodied”).  The  following  verse  explains  these  divisions  more  fully. 


5 


i.  12.]  Tnnato&hn  And  Notes! 

The  epithet  htiarfltmaka,  applied  to  actnai  time  in  the  first  half  of 
the  verse,  is  not  easy  of  interpretation  Hie  commentary  translates  it 
“is  an  object  of  knowledge,  is  capable  of  being  .known,”  which  does  not 
seem  satisfactory.  It  evidently  contains  a suggested  etymology  (k&la, 

« time,”  from  kalana),  and  in  translating  it  as  above  we  have  seen  in  it 
also  an  antithesis  to  the  epithet  bestowed  upon  Time  the  divinity. 
Perhaps  it  should  be  rather  “ has  for  its  office  enumeration*”  ' 

11.  That  which  begins  with  respirations  (prAqa)  is  called  real ; 
that  which.begins  with  atoms  (fra*/)  is  called  unreal.  Six  respi- 
rations make  a vin&di,  sixty  of  these  a nudi  ; 

12,  And  sixty  nadis  make  a sidereal  day  and  night.  . . . 

The  manuscripts  without  commentary  insert,  as  the  first  half  of  v.  11, 
the  usual  definition  of  the  length  of  a respiration  : “ the  time  occupied 
ill  pronouncing  ten  long  syllables  is  called  a respiration.” 

The  table  of  tlie  divisions  of  sidereal  time  is  tlieii  as  follows : 

io  long  syllables  (gurvakthara)  = i respiration  (prana,  period  of  four  seconds) ; 

6 respirations  =s  i vinftdi  (period  of  twenty-four  seconds); 

6o  vin&dia  =s  i n&di  (period  of  twenty-four  minutes) ; 

6o  n&dw  =s=  i day. 

This  is  the  method  of  division  usually  adopted  in  the  astronomical 
text-books:  it  possesses  the  convenient  property  that  its  lowest  sub- 
division. the  respiration,  is  the  saute  part  of  the  day  as  the  minute  is  of 
the  circle,  that  a respiration  of  time  is  equivalent  to  a minute  of 
revolution  of  the  heavenly  bodies  about  the  earth.  The  respiration  is 
much  more  frequently  called  asu , in  the  text  botli  of  this  and  of  the 
other  Siddh&ntas.  The  vin&di  is  practically  of  small  consequence,  and 
is  only  two  or  three  times  made  use  of  in  the  treatise : its  usual  modern 
name  is  pala , but  as  this  term  nowhere  occurs  in  our  text,  wc  have  not 
felt  justified  in  substituting  it  for  vin&di.  For  nacli  also,  the  more 
common  name  is  danda , but  this,  too,  the  b&rya-Siddh&nta  nowhere 
employs,  although  it  uses  instead  of  nudi,  and  quite  as  often,  nddikd  and 
ghoLtikd*  We  shall  uniformly  make  use  in  our  translation  of  the  terms 
presented  above,  since  there  are  no  English  equivalents  which  admit  of 
being  substituted  for  them. 

The  ordinary  Puranic  division  of  the  day  is  slightly  different  from  the 
astronomical,  viz : 

1 5 twinklings  (nimevha)  = i bit  (kds/ithd) ; 

3o  bits  = i minute  (kafd) ; 

3o  minutes  = i hour  (muhurta);' 

3o  hours  = x day. 

Maim  (i.  64)  gives  the  same,  excepting  that  Ik1  makes  the  bit  to  con- 
sist of  18  twinklings.  Other  authorities  assign  lifferent  values  to  the 
■ lesser  measures  of  time,  but  all  agree  in  the  main  fact  of  the  divigiutT  oT 
the  day  into  thirty  hours,  which,  being  perhaps  ail  imitation  of  the 
division  of  the  mouth  into  thirty  days,  is  unquestionably  the  ancient  and 
original  Hindu  method  of  reckoning  time.  * @ 

The  Surya-Siddh&uta,  with  commendable  moderation,  refrains*firom 
giving  the  imaginary  subdivisions  of  the  respiration  which  make  up 


6 


JSCirya-Siddh&nta. 


p.  12- 


“ unreal 11  time.  They  arc  thus  stated  in  Bh&skara’^Siddh&nta-^iromani 
(i.  19,  20),  along  with  the  other,  the  astronomical,  table : 


toq  atoms  (trufi) 
3o  specks 
iB  twinklings 
3o  bits 
3o  minutes 
a half-hours 
3o  hours 


r=  r speck  (tatpara) ; 

= i twinkling  (nimesha) ; 
= i bit  (kdihthd) ; 

= i minute  (kald) ; 

= i half-hour  (ghatikd)  \ 
= i hour  (kthaiyi) ; 

= i day. 


This  makes  the  atom  equal  to  rrdvinnnrti1  of  a day,  or  TrVjvth 
of  a second.  Some  of  the  Pur&nas  (sue  Wilson's  Vish.  Pur.  p.  22)  give 
a different  division,  which  makes  the  atom  about  y^u-th  of  a second ; 
but  they  carry  the  division  three  steps  farther,  to  the  subtilissima 
(paramanu),  which  equals  troth  of  a day,  or  very  nearly 

ot  a second. 

We  have  introduced  here  a statement  of  these  minute  subdivisions, 
because  they  form  a natural  counterpart  to  the  immense  periods  which  wo 
shall  soon  have  to  consider,  and  are,  with  the  letter,  curiously  illustrative 
of  a fundamental  trait  of  Hindu  character  : a fantastic  imaginativeness, 
which  delights  itself  with  arbitrary  theorizings,  and  is  unrestrained  by, 
and  careless  nf,  actual  realities.  Thus,  having  no  instruments  by  which 
they  could  measure  even  seconds  with  any  tolerable  precision,  they  vied 
with  one  another  in  dividing  the  second  down  to  the  farthest  conceivable 
limit  of  minuteness;  thus,  socking  infinity  in  the  other  direction  also, 
while,  they  were  almost  destitute  of  a chronology  or  a history,  and  could 
hardly  fix  with  accuracy  the  date  of  any  event  boyornl  the  memory  of 
the  living  generation,  they  devised,  and  pul  forth  as  actual,  a frame- 
work of  chronology  reaching  for  millions  of  millions  of  years  back  into 
the  past  and  forward  into  tlic  future. 


12.  . . . Of  thirty  of  these  sidereal  days  is  composed  a month  ; 
a civil  (sduana)  month  consists  of  as  many  sunrises ; 

13.  A lunar  mouth,  of  as  many  lunar  days  (liihi) ; a solar 
(sdura)  month  is  determined  by  the  entrance  of  the  sun  into  a 
sign  of  the  zodiac : twelve  months  make  a year.  ... 

We  have  here  described  days  of  throe  different  kinds,  and  months 
and  years  of  four;  since,  according  to  the  commentary,  the  last  clause 
translated  means  that  twelve  months  of  each  denomination  make  up  a 
year  of  the  same  denomination.  Of  some  of  these,  the  practical  use 
and  value  will  be  made  to  appear  later;  but  as  others  arc  not  elsewhere 
referred  to  in  this  treatise,  and  as  several  are  merely  arbitrary  division's 
of  time,  of  which,  so  far  as  we  can  discover,  no  use  has  ever  been  made, 
it  may  not  be  amiss  briefly  to  characterize  them  here. 
w ,Of  the  measures  of  time  referred  to  in  the  twelfth  verse,  the  day  is 
evidently  the  starting-point  and  standard.  The  sidereal  day  is  the  time' 
of  the  earth's  revolution  on  its  axis;  data  for  determining  its  length  are 
given  below,  in  v.  34,  but  it  does  not  enter  as  an  element  into  the  later 
processes.  Ner  is  a sidereal  month  of  thirty  sidereal  days,  or  a sidereal 
year  of  three  hundred  and  sixty  such  days  (being  less  than  the  true 
sidereal  year  by  about  six  and  a quarter  sidereal  days),  elsewhere  men- 


i.  13.]  Dranalalum  and  Notea,  7 

tioned  in  this  work)  or,  so  far  as  wc  know,  made  account  of  in  any 
Hindu  method  of  reckoning  time.  The  civil  (t&vana)  day  is  the  natural 
day : it  is  counted,  in  India,  from  sunrise  to  sunrise  (sec  below,  v.  30), 
and  is  accordingly  of  variable  length  : it  is,  of  course,  an  important 
element  in  all  computations  of  time.  A month  of  thirty,  and  9 year  of 
three  hundred  and  sixty,  such  days,  arc  supposed  to  have  formed  tl)e 
basis  of  the  earliest  Hindu  chronology,  an  intercalary  month  being  added* 
once  in  five  years.  This  method  is  long  since  out  of  use,  however,  and 
the  month  and  year  referred  to  here  in  the  text,  of  thirty  and  three 
hundred  and  sixty  natural  days  respectively,  without  intercalations,  are 
elsewhere  assumed  and  made  use  of  only  in  determining,  for  astrological 
purposes,  the  lords  of  the  month  and  year  (see  below,  v.  52). 

The  standard  of  the  lunar  measure  of  time,  is  the  lunar  mopth,  the 
period  of  the  moon’s  synodical  revolution.  It  is  reckoned  cither  from 
new-moon  to  new-moon,  or  from  full-moon  to  full-moon ; generally,  the 
former  is  called  mukhya,  “ primary,”  and  the  latter  ydwiia, M secondary  ” : 
hut,  according  to  our  commentator,  either  of  them  maybe  denominated 
primary,  although  in  AuL  in  this  treatise,  only  the  find  of  them  is  so 
regarded ; and  the  secondary  lunar  month  is  that  which  is  reckoned 
from  any  giver,  lunar  day  to  the  next  of  the  same  name.  This  natural 
mouth,  containing  about  twenty-nine  and  a half  days,  mean  solar  time, 
is  then  divided  into  thirty  lunar  days  ( tithi ),  ancl  this  division,  although 
of  so  unnatural  and  arbitrary  a character,  the  lunar  days  beginning  and 
ending  at  any  moment  of  the  natural  day  and  night,  is,  to  the  Hindu, 
of  the  most-  prominent  practical  importance,  since  by  it  arc  regulated 
the  performance  of  many  religious  ceremonies  (see  below,  xiv.  ]3j,  and 
upon  it  depend  the  chief  considerations  of  propitious  and  unpropitious 
times,  and  the  like.  Of  the  lunar  year  of  twelve,  lunar  months,  how- 
ever, wo  know  of  no  use  made  in  India,  either  formerly  or  now,  except 
as  it  has  been  introduc'd  and  employed  by  the  Mohammedans. 

Finally,  the  year  last  mentioned,  the  solar  year,  is  that  by  which  time 
is  ordinarily  reckoned  in  India.  It  is,  however,  not.  the  tropical  solar 
year,  which  tu*  employ,  but  the  sidereal,  no  account  being  made  of  the 
precession  of  the  equinoxes.  The  solar  month  is  measured  by  the  con- 
tinuance of  the  sun  in  each  successive  sign,  and  varies,  according  to  the 
rapidity  of  bis  motion,  from  about  twenty-nine  and  a third,  to  a little 
more  than  thirty-one  and  a half,  days.  There  is  no  day  corresponding 
to  this  measure  of  the  month  and  of  the  year. 

In  the  ordinary  reckoning  of  time,  these  elements  are  variously  com- 
bined. Throughout  Southern  India  (sec  Warren's  lvala  Sankalita, 
Madras:  1625,  p.  4,  etc.),  the  year  and  month,  made  use  of  arc  the 
solar,  and  the  (lav  the  civil ; the  beginning  of  each  month  and  year 
being  counted,  in  practice,  from  the  sunrise  nearest  to  the  moment  of 
their  actual  commencement.  In  all  Northern  ndia  the  year  is  luni- 
solar ; the  month  is  lunar,  and  is  divided  into  both  lunar  and  civil  da)  s ; 
the  year  is  composed  of  a variable  number  of  months,  either  twelve  or 
thirteen,  beginning  always  with  the  lunar  month  of  which  the  com- 
mencement next  precedes  the  true  commencement  of  the  sidereal  year. 
But,  underneath  this  division,  the  division  of  the  actual  sidereal*year 
into  twelve  solar  months  is  likewise  kept  up,  and  to  maintain  the  con- 


8 


Mrya'8uMh/fa{to,>  p.  13- 

currence  of  (the  civil  and  lunar  days,  and  the  lunar  and 'tolar  montli*,  is 
a process  of  great- complexity,  into  the  details  of  which  we  need  not 
enter  here  (tatf  Wgtren,  as  above,  p.  57,  etch  It  will  be  seen  later  in 
this  chapter  (vv.  46-51)  that  the  Shrya-Sidali&nta  reckons  time  by  this. . 
latter  syitfam,  by  the  combination  of  civil,  lunar,  and  sidereal  elements* 

. 18. . . . This  is  called  a day  of  the  gods. 

14.  The  day  and  niglit  of  the  gods  and  of  the  demons  are 
mutually  opposed  to  ono-ajtother.  Six  times  sixty  of  them  are 
a year  of  the  gods,  and  likewise  of  the  demons. 

“This  is  called,*  etc. : that  is*  as  the  commentary  explains,  the  jrear 
composted  of  twelve  solar  months,  ns  being  those  last  mentioned ; die 
sidereal  -year.  It  appears  to  us  very  questionable  whether,  in  the  first 
instance,  anything  more  was  meant  bv  calling  the  year  fl  day  of  the 
gods  than  to  intimate  that  those  beings  of  a higher  order  reckoned  time 
upon  grander  scale  : just  as  the  month  was  said  to  be  a day  of  the 
Fathers,  or  Manes  (xiv.  14),  the  Patriarchate  (v.  T8),  a clay  of  the 
Patriarchs  (xiv.  21),  and  the  .Koli  (v.  20),  a d#f  of  Brahma;  all  these 
being  familiar  Puranic  designations.  Iji  th  astronomical  reconstruction 
of  the  Puranic  system,  however,  a physical  meailing  has  been  given  to 
this  day  of  the  gods  ? the  gods  arc  made  to  reside  at  the  north  pole,  and 
the  demons  at  the  south ; mid  then,  of  course,  during  the  naif-year 
when  the  sun  is  north  of  the  equator,  it  is  day  to  the  gods  and  night  to 
the  demons ; and  during  the  other  half-year,  the  contrary.  The  subject 
is  dwelt  upon  at  some  length  in  the  twelfth  chapter  (xii.  45,  etc.). 
To  make  such  a division  accurate,  the  year  ought  to  be  the  tropical,  and 
not  the  sidereal ; but  the  author  of  the  Sfirya-Siddh&nta  has  not  yet 
begun  to  take  into  account  the  precession.  See  what  is  said  upon  this 
subject  in  the  third  chapter  (vv.  9-10). 

The  year  of  the  gods,  or  the  divine  year,  is  employed  only  in.  des- 
cribing the  immense  periods  of  which  the  statement  now  follows. 

15.  Twelve  thousand  of  these  divine  years  are  denominated^ 
a Quadruple  Age  (caturyug a) ; of  ten  thousand  times  four  hun- 
dred and  thirty-two  solar  years 

16.  Is  composed  that  Quadruple  Age,  with  its  dawn  and  twi- 
light. The  difference  of  the  Golden  and  the  other  Ages,  as 
measured  by  the  difference  in  the  number  of  the  feet  of  Virtue 
in  each,  is  as  follows : 

17.  The  tenth  part  of  an  Age,,  multiplied  successively  by  four, 
three,  two,  and  one,  gives  the  length  of  the  Golden,  and  the  other 
Ages,  in  order : the  sixth  part  of  each  belongs  to  its  dawn  and 
twilight. 

' Thq.  period  of  4,320,000  years  is  ordinarily  staled  Great  Age  (ma- 
• h&yuga)  or,  as  above  in  two  instances,  Quadruple  Age  (caturyuga). 
In  the.Sfirya-Siddh&nta,  however,  the  former  term  ia  not  once  found, 
and  the  latter  qccurs  only  in  these  verses ; elsewhere,  Age  (yuga)  alpue 
is  employed  to  denote  it;  and  always  denotes  it,  unless  expressly  waited 
by  the  name  of  the  Golden  {kr to)  Age. 


9 


i.  if.]  ZVanrfationQnel  Kota. 


The  composition  of  the  Age;  or 

Great  Age,  is  then  m follows : 

Divine  jean. 

- ' 'itV  tfiiifetyri. 

Diiwn, 

4oo 

Golden  Age  (krta  yuga). 

4ooo 

i,44q,ooo ' 

Twilight, 

4oo 

144,000 

Total  duration  of  the  Golden  Age, 

~~  4,8oo 

1,728^00 

Dawn, 

3oo 

1 08,000 

Silver  Age  (tretd  yuga\ 

3ooo 

1 1,080,000 

Twilight, 

3oo 

100,000 

Total  duration  of  the  Silver  Age, 

~ 3,600 

1,296,000 

Dawn, 

200 

72,000 

Brazen  Age  (dudpara  yuga )( 

2000 

720,000 

Twilight, 

200 

72,000 

Total  duration  of  the  Brazen  Age, 

2,400 

864,000 

Dawn, 

100 

36fooo 

Iron  Age  {kali  yuga). 

1000 

36o.ooo 

Twilight, 

100 

36ooo 

Total  duration  of  the  Iron  Age; 

1,200 

. 43 2, OUO 

Total  duration  of  a Great  Age,  12,000  4, 3 20,000 


Neither  of  the  names  of  the  last  three  ages  is  once  mentioned  in  the 
Shrya-Siddh&nta.  The  first  and  last  of  the  four  are  derived  from  the 
game  of  dice : Arte,  “ made,  won,”  is  the  side  of  the  die  marked  with 
four  dots— the  lucky,  or  winning  one ; kali  is  the  side  marked  with  one 
dot  only — the  unfortunate,  the  losing  one.  I11  the  other  names,  of 
which  w'e  do  not  know  the  origiuul  and  proper  meaning,  the  numerals 
ire,  44 three,”  and  dv&,  “two,”  are  plainly  recognizable.  The  relation 
of  the  numbers  fonr,  three,  two,  and  one,  to  the  length  of  the  several 
periods,  as  expressed  in  divine  years,  and  also  as  compared  with  one 
another,  is  not  less  clearly  apparent.  The  character  attached  to  the 
different  Ages  by  the  Hindu  mythological  and  legendary  history  so 
closely  resembles  that  which  is  attributed  to  the  Golden,  Silver,  Brazen, 
and  Iron  Ages,  that  wc  have  not  hesitated  to  transfer  to  them  the  latter 
appellations.  An  accouut  of  this  character  is  given  in  Manu  i.  81-86. 
During^  the  Golden  Age,  Virtue  stands  firm  upon  fonr  feet,  truth  and 
justice  abound,  And  the  life  of  man  is  four  centuries ; in  each  following 
Age  Virtue  loses  a foot,  and  the  length  of  life  is  reduced  by  a century, 
so  that  in  the  present,  the  Iron  Age,  she  has  but  one  left  to  hobble 
upon,  while  the  extreme  age  attained  by  mortal*  is  but  a hundred  years. 
Sec  also  Wilson’s  Vishnu  Fur&nn,  p.  622,  etc.,  fo  * a description  of  the 
vices  of  the  Iron  Age. 

This  system  of  periods  is  not  of  astronomical  origin,  although  the 
fixing  of  the  commencement  of  the  Iron  Age,  the  only  possibly  his- 
torical point  in  it,  is,"  as1  we  shall  see  hereafter,  the  result  of  astro- 
nomical computation.  Its  arbitrary  and  artificial  character  is  apparent. 
It  is  tigs  system  of  the  Pur&nas  and  of  Manu,  a part  of  the  received 
Hindu -cosmogony,  to  which  astronomy  was  compelled  to  adapt  itself. 

3 


We  ought  to  remark,  however,  that  in  the  text  hsejf  of'  Mann  (i.  68-71) 
the  duration  of  the  Great  Age,  called  by  him  Divine  Age,  ia  given  as 
twelve  thousand 'years  simply,  and  that  it  is  his  commentator  who,  by 
asserting  these  to  be  divine  years,  brings  Manu’s  cosmogony  to  an  agree- 
ment with  that  of  the  Purfijias.  This  is  a strong  indication  that  the 
divine  year  is  an  afterthought,  and  that  the  period  of  4,320*000  years 
is  an  expansion  of  an  earlier  one  of  12,000.  Vast  as  this  period  is, 
however,  it  is  far  from  satjgg^ng  the  Hindu  craving  after  infinity.  We 
are  next  called  upon  to  M^paftruct  a new  period  by  multiplying  it  by  a 
thousand. 

13.  One  and  seventy  Ages  are  styled  here  a Patriarchate 
(manvantara)  ; at  its  end  is  said  to  be  a twilight  which  has  the 
number  of  years  of  a Golden  Age,  and  which  is  a deluge. 

, 19.  In  an  ASon  (kalpa)  aTe  reckoned  fourteen  such  Patriarchs 
(manu)  with,  their  respective  twilights ; at  the  commencement  of 
the  A3on  is  a fifteenth  dawn,  having  the  length  of  a Golden 
Ago.  t. 

The  A&on  is  accordingly  thus  composed : 


Divine  years.  Solar  years. 


The  introductory  dawn, 

4,8oo 

1,738,000 

Seventy-one  Great  Ages, 

852,000 

3o6,7  20,000 

A twilight, 

4,8oo 

1,728,000 

Duration  of  one  Patriarchate,  856, 8oo 

306,448.000 

PourftMMjatriart-liates, 

ii.995.aoo 

4,318,373,000 

Total  duration  of  on  ^Eon, 

12,000,000 

4,320,000,000 

Why  the  factors  fourteen  and  seventy-one  were  thus  used  in  making 
np  the  ^Eon  is  not  obvious ; unless,  indeed,  in  the  division  by  fourteen 
is  to  be  recognized  the  influence  of  the  number  seven,  while  at  the 
same  time  such  a division  furnished  the  equal  twilights,  or  interme- 
diate periods  of  transition,  which  the  Hindu  theory  demanded.  The 
system,  however,  is  still  that  of  the  Pur&nas  (see  Wilson’s  Vish.  Pur.  p. 
24,  etc.) ; and  Mann  (i.  72,  79)  presents  virtually  the  same,  although  he 
has  not  the  term  ASon  (Au/jni),  but  states  simply  that  a thousand  Divine 
Ages  make  up  a day  of  Brahma,  and  seventy-one  & Patriarchate.  The 
term  manvantara,  u patriarchate,”  means  literally  “ another  Menu,”  or, 

“ the  interval  of  a Manu.”  Manu,  a word  identical  in  origin  and  mean- 
ing with  our  “ man,”  became  to  the  Hindus  the  name  of  a being  pep? 
sonified  as  son  of  the  Sun  ( Vivasvant)  and  progenitor  of  the  human,, 
race.  In  each  Patriarchate  there  arises  a new  Manu,  who  becomes  for': 
his  own  period  the  progenitor  of  mankind  (see  Wilson’s  Vish.  Pur.  p. 
24). 

20.  The  A !on,  thus  composed  of  a thousand  Ages,  and  which 
brings  about  the  destruction  of  all  that  exists,  is  styled  a day  of 
Brahma ; his  night  is  of  the  Bame  length. 

21.  His  extreme  age  is  a hundred,  according  to  this  valuation 
of  a day  and  a night. . . . 


11 


i..  23.]  Tfonilation  and  Note*. 

Wo  have  already*  IHiid' indications  of  an  *%ksnmed  destruction  of 
existing  tilings  at  tne  tcnninstion  of  the'  lessor  peridot  celled  the  Age 
and  the  Patriarchate,  in  the  necessity  of  a newreifelaiiotfof  virtue  and 
knowledge  for  every  Age,  and  of  a new  father' of  the  hmgan'raee  for 
every  Patriarchate.  These  are  loft,  it  should  sfeera,  to  show  ns  how  the 
system  of’coemicol  periods  grew  to  lSreerand  huger  dimensions.  The 
loll  development  of  it,  as  exhibited  in  tne  Pprlntfs  .and. here,  admits  only 
two  kinds  of  destruction : the  one  occnxijijfer.pt  the  end  of  each  JSon, 
.or  day  Of  Brahma,  when  all  creature^  althflSir  not  the  substance  of  the 
world,  undergo  dissolution,  and  remain  bnrifed  in  chaos  dnring  his  night, 
to  be  created  anew  when  his  day  begins  again ; the  other  taking  place 
at  the  end  of  Brahma's  lifo,  when  all  matter  even  is  resolved  into#!* 
ultimate  source. 

According  to  the  commentary,  the  “ hundred”  in  verse  21  means  a hun- 
dred years,  each  composed  of  three  hundred  and  sixty  days  and  nighty  ‘ 
and  not  a hundred  days  and  nights  only,  as  the  text  might  be  understood 
to  signify;  since,  in  all  statements  respecting  age,  yean  are  necessarily 
nndentood  to  be  intended.  The  length  of  Brahma’s  life  would  be, 
then,  864,000,000,000  divine  years,  or  311,040,000,000,000  solar  yean. 
This  period  is  also  called  in  the  Puranns  a para,  “ extreme  period,*'  and 
its  half  a jxurardha  (see  Wilson’s  Vish.  Pur.  p.  23)  ;.  although  the  latter 
term  lias  obtained  also  an  independent  use,  an  signifying  a period  still 
more  enormons  (ibid.  p.  630).  It  is  curious  that  the  commeutator  does 
not  seem  to  recognize  the  affinity  with  this  period  of  the  expression 
used  in  the  text,  param  uyuh.  “ extreme  age,”  hut-  gives  two  different 
explanations  of  it;  both  of  which  arc  forced  and  unnatural. 

The  anthor  of  the  work  before  iis  is  modestly  content-  with  the  number 
of  yean  thns  placed  at  his  disposal,  and  attempts  nothing  farther.  So 
is  it  also  with  the  Pur&nas  in  general : although  some  of  them,  as  the 
Vishnu  (Wilson,  p.  63<)«assert  that  two  of  the  greater  parardhat  con- 
stitute only  a day  of  Vishnu,  and  others  (ibid.  p.  23)  that  Brahma’s 
whole  lifo  is  but  a twinkling  of  the  eye  of  Krshga  or  of  £ivn. 

21. . . . The  half  of  his  life  is  past ; of  the  remainder,  this  is 
the  first  Aton.  * 

22.  And  of  this  Alton,  six  Patriarchs  (manu)  are  past,  with 
their  respective  twilights;  and  of  the  Patriarch  Mann  son  of 
Vivaavant,  twenty-seven  Ages  are  post; 

23.  Of  the  present^  the  twenty-eighth,  Age,  this  Golden  Age 
is  past : from  this  point,  reckoning  up  the  timo,  one  should  com- 
pute together  the  whole  number. 

The  designation  of  the  part  already  elapsed  of  this  immense  period 
seems  to  be  altogether  arbitrary.  It  ngree#  in  general  with  that  given 
in  the  Pur&nae,  and,  so  far  as  the  Patriarchs  and  their  periods  are  con- 
cerned, with  Manu  a|pow  The  name  of  ihe  present  Aion  is  VarAha, 
“ that  of  the  hoar,”  because  Brahma,  in  performing  anew  at  its  corn- 
ineiiQcuient  the  act  of  creation,  put  ou  the  form  of  th»t  animal  (see 
'Wilson’s  Visit.  Pur.  p.  27,  etc.).  Tne  one  preceding  is  called  the  Paama% 
"that  of  the  lotus.  This  nomondatura,  however,  is  not  universally 


12  S&rya-Siddhdn ia, ' [i.  23- 

*■  A. 

accepted  ; under  the  wdrd  kalpa,  in  the  Lexiotiplf  JBtthtlingk  and  Roth, 
may  be  found  another  system  of  names  for  these  periods.  Manu  (i.*fllf 
02)  gives  the  . names  of  the  Patriarchs  of  the  past  Patriarchates ; the 
Puritans  add  other  particulars  respecting  them,  and  also  respecting  those 
which  are  still  to  come  (see  Wilson's  Vish.  Pur.  p.  259,  etc.). 

The  end  of  the  Golden  Age  of  the  current  Great  Age  is  the-. time  at 
which  the  S&rya-Siddh&nta  claims  to  have  been  revealed,  and  tita  epoch 
from  which  its  calculation^mrofess  to  commence.  We  will,  according, 
as  the  Sun  directs,  comput^the  number  of  years  which  are  supposed  to 
have  elapsed  before  that  period. 


Dawn  of  current  JSou, 
Six' Patriarchates. 
Twenty-seven  Great  Ages, 


Divine  years. 
4,8oo 
5,140.800 
324,000 


Solar  yean. 

1,738,000 
1.850,668.000 
1 16,640,000 


Total  till  commencement  of  present  Great  Age, 
Golden  Age  of  present  Great  Age, 

Total  time  elapeed  of  current  JEo n, 

Half  Brahma's  life, 


5,469.600 

4,8oo 


5.474,400 

433,000,000,000 


1,969,056,000 
. 1,728,000 

1 55,530, oo6^oo[ooo 


Total  time  elapsed  from  beginning  of  Brah- 
ma's life  to  end  of  last  Golden  Ago, 


43?, oo5, 474,4oo  155,521,970,784.000 


As  the  existing  creation  dates  from  the  commencement  of  the  current 
Ax>n,  the  second  of  the  above  totals  is  the  only  011c  with  which  the 
SArya-Siddh&nta  henceforth  has  any  thing  to  do. 

Wo  are  next  informed  that  the  present  order  of  things  virtually  began 
at  a period  less  distant  than  the  commencement  of  the  A£on. 


21.  One  hundred  times  four  hundred  and  seventy-four  divine 
j'ears  passed  while  the  All-wise  was  employed  in  creating  the 
animate  and  inanimate  creation,  plants,  stars,  gods,  demons,  and 
the  rest. 


That  is  to  say : 

Divlnr  years. 

From  the  total  above  given,  5,474,4oo 

deduct  the  time  occupied  in  creation.  <fr4oo 


Solar  year*. 
•.970,784.000 
*7,064000 


the  remainder  ia 


5^37,000  1,953,730,000 


This,  then,  is  the  time  elapsed  from  the  true  commencement  of  the  ex- 
isting order  of  things  to  the  epoch  of  this  work.  Tim  deduction  of  this 
period  as  spent  by  the  Deity  in  the  work  of  creation  is  a peculiar  fcatnra 
of  the  Shrya-Siddh&nta.  We  shall  revert  to  it  later  (see  below,  under 
vv.  20-34),  as  its  significance  cannot  be  shown  until  other  data  are 
before  us. 


25.  The  planets,  moving  westward  with  exceeding  velocity, 
but  constantly  beaten  by  the  oaterisms,  fall  behind,  at  a rate 
precisely,  equal,  proceeding  each  in  its  own  path. 

26.  Hence  they  have  an  eastward  motion.  From  the  number 
of  their  revolutions  is  derived  thek  .daily  motion,  which  is  dif- 
ferent according  to  the  Bize  of  their  (put*-,  in  proportion^  this 
' daily  motion  they  pass  through  the  Bsterisms. 


i.  27.]  Zkwufatwn  and  Nates.  13  * 

27.  One  which  jnOves  swiftly  passes  through  them  in  a short 
time ; one  which  moves  slowly,  in  a long  time,  By  their  move- 
ment, the  revolution  is  accounted  complete  the  end  of  the 
aaterism  Revatf. 

We  bate  here  presented  a part  of  the  physical  theory  of  the  planetary 
motions,  that  which1  accounts  for  the  mean  motions : the  theory  is  sup- 
plemented by  the  emanation  given  in  the  lutt  chapter  of  the  disturbing 
forces  which  give  rise  to  the  irregularities  dpinoveineut.  The  earth  is  a 
sphere,  and  sustained  immovable  in  the  centre  of  the  universe  (xii.  32), 
while  all  the  heavenly  bodies,  impelled  by  winds,  or  vortices,  called  pro- 
vectors (ii.  3),  revolve  about  it  from  east  to  west  In  this  general  west- 
ward movement,  the  planets,  as  the  commentary  explains  it  are,  ©is||g| 
to  their  weight  and  tne  weakness  of  their  vortices,  beaten  by  the  afflF 
isms  (i nakshatra  or  bha,  the  groups  of  stars  constituting  the  lunar  man- 
sions [see,  below,  chapter  viii],  and  used  here,  as  in  various  other  places; 
to  designate  the  whole  firmament  of  fixed  stars),  and  accordingly  fall 
behind (larnban te =labuntur,  delabuntur ),  as  if  from  shame:  and  this  is 
the  explanation  of  their  eastward  motion,  which  is  only  apparent  and  rela- 
tive, although  wont  to  be  regarded  as  real  by  those  who  do  not  under- 
stand the  true  causes  of  tilings.  Hut  now  a new  element  is  introduced 
into  the  theory,  which  does  not  seem  entirely  consistent  with  this  view  of 
the  merely  relative  character  of  the  eastward  motion.  It  is  asserted  that 
the  planets  lag  behind  equally,  or  that  each,  moving  in  its  own  orbit, 
loses  an  equal  amount  daily,  as  compared  with  the  asterisma  And  we 
shall  find  farther  on  (xii.  73-30)  that  the  dimensions  of  the  planetary 
orbits  are  constructed  upon  this  sole  principle,  of  making  the  mean  daily 
motion  of  each  planet  eastward  to  be  the  same  in  amonnt,  namely 
11,858.717  yojanas:  the  amount  of  westward  motion  being  equal,  in 
each  case,  to  the  difference  between  this  amount  and  the  whole  orbit  of 
the  planet.  Now  if  the  Hindu  idea  of  the  symmetry  and  harmony  of  the 
universe  demanded  that  the  movements  of  the  planets  should  be  equal,  it 
was  certainly  a very  awkward  and  unsatisfactory  way  of  complying  with 
that  demand  to  make  the  relative  motions  alone,  as  compared  with  the 
fixed  stars,  equal,  and  the  real  motions  sovaslly  different  from  one  an- 
other. We  should  rather  expect  that  soni{pnotliod  would  have  been  tie- 
vised  for  making  the  latter  come  out  alike,  and  the  former  unlike,  and  the 
result  of  differences  in  tho  weights  of  the  planets  and  the  forces  of  the 
impelling  currents.  It  looks  as  if  this  principle,  and  the  conformity  to  it 
of  the  dimensions  of/tho  orbits,  might  have  come  from  those  who  regarded 
the  apparent  daily  motion  as  tho  real  motion.  Hut  we  know  that  Arva-  \ 
bliatta  held  the  opinion  that  tho  earth  revolved  upon  its  axis,  causing 
thereby  the  apparent  westward  motion  of  tho  heave  lly  bodies  (sec  Cole- 
brooke's  Hindu  Algebra,  p.  xxxviii ; Essays,  ii.  467^,  and  so,  of  course, 
that  the  planets  really  moved  eastward  at  an  equal  rate  among  the  stars ; 
and  although  the  later  astronomers  are  nearly  unanimous  against  him, 
we  cannot  nelp  surmising  that  tho  theory  of  the  planetary  orbits  ema- 
nated from  him  or  his  school,  or  from  some  other  of  like  opinion.  It  is 
not  ugon  record,  so  far  as  we  aware,  that  any  Hindu*  astronomer,  of 
any  fji^iod, held,  as  did  sotxieof  the  Greek  philosophers  (see  WhcrwellVtw 
History  of  the  Inductive  Sciences,  B.  V.  ch.  i),  a heliocentric  theory. 


14  Sforya-  SiddMnta,  [i.  27- 

The  absolute  motion  eastward  of  all  the  planets  beinjj  equal,  their 
apparent  motion  is,  of  course,  in  the  (inverse)  ratio  of  their  distance,  or 
ox  the  divxxensions  of  their  orbits. 

The  word  translated  “ revolution 19  is  bhagana,  literally  “ troop  of  aster- 
isms;”  the  verbal  root  translated  “pass  through”  is  MtijF,  “enjoy,”  from 
which  conics  also  the  common  term  for  the  daily  motion  of  a planet, 
bkukti,  literally  “ enjoyment”  When  a planet  has  “ enjoyed  (he  whole 
troop  of  asterisms,”  it  has  made  a complete  revolution. 

The  initial  point  of  the  fUid  Hindu  sphere,  from  which  longitudes  are 
reckoned,  and  at  which  the  planetary  motions  are  held  by  all  the  schools 
of  Hindu  astronomy  to  have  commenced  at  the  creation,  is  the  end  of 
the  asterism  llevatl,  or  the  beginning  of  A$vinl  (see  chapter  viii.  for  a 

Sit  .account  of  the  asterisms).  Tls  situation  is  most  nearly  marked  by 
of  the  principal  star  of  Rcvatl,  which,  according  to  die  Sfirya- 
Siddhjfata,  is  10'  to  the  west  of  it,  but  according  to  other  authorities 
examhr  coincides  with  it.  That  star  is  by  all  authorities  identified  with 
£ Pisraum,  of  which  the  longitudo  at.  present,  as  reckoned  by  us,  from  the 
vernal  equinox,  is  17°  54'.  Making  duo  allowance  for  the  precession,  we 
find  that  it  coincided  in  position  with  the  vernal  equinox  not  far  from  the 
middle  of  the  sixth  century,  or  about  A.  D.  570.  As  such  coincidence 
was  the  occasion  of  the  point  being  fixed  upon  as  tho  beginning  of  the 
sphere,  the  time  of  its  occurrence  marks  approximately  the  era  of  the 
fixation  of  the  sphere,  and  of  the  commencement  of  the  history  of  modern 
Hindu  astronomy.  Wc  say  approximately  only,  because,  in  the  first 
place,  as  will  be  shown  in  connection  with  tho  eighth  chapter,  the  accu- 
racy of  the  Hindu  observations  is  not  to  be  relied  upon  within  a degree ; 
and,  in  the  second  place,  the  limits  of  the  asterisms  being  already  Jong 
before  fixed,  it  was  necessary  to  take  the  beginning  of  some  One  of  them 
as  that  of  tho  sphere,  and  the  Hindus  may  have  regarded  that  of  Agvini 
as  sufficiently  near  to  the  equinox  for  their  purpose,  when  it  was,  in  fact, 
two  or  three  degrees,  or  yet  more,  remote  from  it,  on  either  side ; and 
each  degree  of  removal  would  correspond  to  a difference  in  time  of  about 
seventy  years. 

In  the  most  ancient  recorded  lists  of  the  nindu  asterisms  (in  (he  texts 
of  the  Black  Yajur-Veda  ai^of  the  Atharva-Vcda),  Krttikb,  now  the 
third,  appears  as  the  first,  le  time  when  the  beginning  of  that  astcr- 
isin  coincided  with  the  vernal  equinox  would  be  nearly  two  thousand 
years  earlier  than  that  given  above  for  the  coincidence  with  it  of  the  first 
point  of  A$vinj. 

23.  .Sixty  seconds  (vilcald)  make  a minute  {hill) ; sixty  6t 
these,  a degree  (hhdga) ; of  thirty  of  the  latter  is  composed;  a 
sign  {rfyi) ; twelve  of  these  are  a revolution  {bhagaiiufy  v 

The  Hindu  divisions  of  the  circle  are  thus  seen  to  be  the  same  with 
the  (i^cM’k  and  with  our  own,  and  we  shall  accordingly  make  use,  in 
translating,  of  our  own  familiar  terms.  Of  the.  second  (vikald)  very  little 
practical  use  is  made ; it  is  not  more  than  two  or  three  times1' alluded  to 
in  a\)  the  rest  of  the  treatise.  The  minute  {hold ) is  much  more  often 
called  lipid  (or  liptikd) ; this  is  not  an  o^Wnal^  Sanskrit  word,  bn&was 
borrowed  from  the  Greek  urttov.  The  dtphe  is  called  either  Mjms  or 
an  fa;  both  words,  like  the  equivalent  Greek  word  potpaf  mean  a "part, 


15 


i.  34.]  Translation  and  Notes. 

portion.”  The  proper  signification  of  rdpi,  translated  “ sign,”  is  simply 
•l  heap,  quantity ;”  it  is  doubtless  applied  to  designate  a sign  as  being  a 
certain  number,  or  sum,  of  degrees,  analogous  to  the  use  vof  gana  in 
hhagana  (explained  above,  in.  the  last  note),  and  of  rdgi  iteelf  dinar  dpi, 
“sum  of  days”  (below,  v.  53).  In  the  Hindu  description  of  an  arc,  the 
sign  is  as  essential  an  element  as  the  degree,  and  no  ares  of  greater  length 
than  tltyrty  degrees  are  reckoned  in  degrees  alone,  as  we  are  accustomed 
to  reckon  them.  The  Greek  usage  Was  the.  same.  We  shall  hereafter 
see  that  the  signs  into  which  any  circle  of  resolution  is  divided  are  named 
Aries,  Taurus,  etc.,  beginning  from  the  point  which  is  regarded  as  the 
starting  point ; so  that  these  names  are  applied  simply  to  indicate  the 
order  of  succession  of  the  arcs  of  thirty  degrees.  ? 

29.  In  an  Age  (ytigo),  the  revolutions  of  the  sun,  Meroui^ 
and  Venus,  and  of  the  conjunctions  (fy/hra)  of  Mars,  Saturn, 
and  Jupiter,  moying  eastward,  arc  four  million,  three  hundred 
and  twenty  thousand ; 

30.  Of  the  moon,  fifty-seven  million,  seven  hundred  and  fifty- 
three  thousand,  three  hundred  and  thirty-six;  of  Mars,  two 
million,  two  hundred  and  ninety-six  thousand,  eight  hundred 
and  thirty-two ; 

31.  Of  Mercury’s  conjunction  (5 tyhra\  seventeen  million,  nine 
hundred  and  thirt3T-scvcn  thousand,  ancl  sixty ; of  Jupiter,  three 
hundred  and  sixty-four  thousand,  two  hundred  and  twenty ; 

82.  Of  Venus’s  conjunction  (ctghra),  seven  million,  twenty-two 
thousand,  three  hundred  and  seventy -six : of  Saturn,  one  hun- 
dred and  forty-six  thousand,  five  hundred  and  sixty-eight; 

33.  Of  the  moon's  apsis  ( ucca ),  in  an  Age,  four  hundred  and 
eighty-eight  thousand,  two  hundred  and  three ; of  its  node  (pitta), 
in  the  contrary  direction,  two  hundred  and  thirty -two  tbotisand, 
two  hundred  and  thirty-eight ; 

31.  Of  the  asterisms,  one  billion,  five  hundred  ami  eighty-two 
million,  two  hundred  and  thirty- -seven  thousand,  cigjjt  hundred 
and  twenty-eight. ... 

These;  arc  the  fundamental  and  most  important  elements  upon  which 
is  founded  the  astronomical  system  of  the  Sflrya-Siddlulnta.  AYe  present 
them  below  in  a tabular  form,  but  must  first  explain  the  character  of 
some  of  them,  especially  of  some  of  those  contained  in  verse  29,  which 
we  have  omitted  from  the  tabic.  ^ 

The  revolutions  of  the  sun,  and  of  Mars,  Jupiter,  and  Saturn,  require 
no  remark,  save  the  obvious  one  that  those  of  the  sun  are  in  fact  sidereal 
revolution*  of  the  earth  about  the  sun.  To  the  idereal  revolutions  of 
the  moon  we  add  also  her  synodical  revolutions,  anticipated  from  the  next 
following  passage  (see  v.  35).  By  the  moon's  “apsis”  is  to  be  under- 
stood her  apogee ; ueea  is  literally  “height,”  i.  o.  “ extreme  distance 
the  commentary  explains  it  by  mandorca , “ apex  of  slowest  motion as 
the  same  word  is  used  to  designate  the  aphelia  of  the  planets,  we  were 
obliged  toteko  in  translating  ft  the  indifferent  tenn  apsis,  which  applies 
eqnpfi^|o  both  gfeentric  and  heliocentric  motion.  The  “node”  is  the 
aacenoing  node  (ace  ii.  7);  the  dual  “nodes”  is  never  employed  in  this 


16 


$6ry&Siddhdnj^  [U9t. 

work.  Bil^  the  apparent  motions  of  the  planets  are  greatly  complicated 
by  the  fact^  nnknown  to  the  Greek  and  the  Hindu,  that  they  arc  revolv- 
ing about^  centre  about  which  the  earth  also  is  revel jing.  When  any 
. planet  is  the  opposite  sidti  of  the  sun  from  ns,  and  ii^tccordingly  mov- 
ing in  space  direction,  contrary  to  ours,  the  effect  of  our  change  of 
place  is  to  increase  the  rate  of  its  apparent  change  of  place ; again,  when 
it  is  upon  our  side  of  the  sun,  and  moving  in  the  same  dircction^ith  v*, 
the  effect  of  our  motion  % to  retard  its  apparent  motion,  and  dven 
cause  it  to  seem  to  retrograde;  This  explains  the*  “revolutions  of  ther 
conjunction”  of  the  three  suporior  planets : their  44  conjunctions”  rgrolve 
at'-®|£  same  rate  with  the  earth,  being  always  upon  the  opposite  side  of 
thcroun  from  us;  and  when,  by  the  combination  of  its  pwn  proper 
motion  with  that  of  its  conjunction,  the  planet  gets  into  the  latter,  its 
rate  of  - apparent  motion  is  greatest,  becoming  less  in  proportion  as  it 
removes  from  that  position.  The  meaning  of  the  word  which  we  have 
traumte&  44  con  junction  ” is  “ swift,  rapid : ” a litoral  rendering  of  it 
would  bo  14  swift-point,”  or  “ apex  of  swiftest  motion butj  after 
much.dclibcration,  and  persevering  trial  of  more  than  one  term,  wd  havo 
concluded  that  “ conjunction  ” was  the  least  exceptionable  word  by 
which  we  could  express  it.  In  the  rase  of  the  inferior  planets,'1  the 
revolution  of  the  conjunct iorr takes  the  place  of  the  proper  motion  of 
the  planet  itself.  By  the  definition  given  in  verse  27,  a planet  must,  in 
order  to  complete  a revolution,  pass  through  the  whole  zodiac;  this 
Mercury  and  Venus  are  only  able  to  do  as  they  accompany  the  stm  in 
liis  apparent  annual  revolution  about  the  earth.  To  the  Hindus,  too, 
who,$ad  no  idea  of  their  proper  movement  about  the  sun.,  the  annual 
motten  must  have  seemed  the  principal  one;  and  that  by  vh|ue of  which, 
in  their  progress  through  the  zodiac,  they  moved  now  farter  and  now 
slower,  must  have  appeared  only  of  secondary  importance.  The  term 
41  conjunction,”  as  used  in  reference  to  these  planets,  must  ba^ftlfi€^df 
of  course,  to  the  superior  conjunction.  The  physical  tlieories^by  'which 
the  effect  of  the  conjunction  (fighra)  is  explained,  arc  given  in  the  next 
chapter.  In  the  tabic  that  follows  we  have  placed  opposite  each  planet 
its  own  proper  revolutions  only. 

It  is  farther  to  be  observed  that  all  the  numbers  of  revolution^  ex- 
cepting those  of  the  moon*  apsis  and  node,  are  divisible  by  four,  so 
that,  properly  speaking,  a quarter  of  an  Age,  or  1,080,000  years,  rather 
than  a whole  Age,  is  their  common  period.  This  is  a point  of  so  much 
importance  in  tlio  system  of  the  S&rya  Siddhfcnta,  that  we  have  added, 
in  a second  column,  the  number  of  revolutions  in  the  lesser  period. 

Tn  the  third  column,  we  add  the  period  of  revolution  of  each  planet, 
as  found  by  dividing  by  the  number  of  revolutions  of  each  the  number 
of  civil  days  in  an  Age  (which  is  equal  to  the  number  of  fjjppeal  days, 

fiven  in  v.  34,  diminished  by  the  number  of  revolutions  of 'ttd  sun  ;..see 
clow,  v.  37);  they  are  expressed  in  days,  nkdts,  vinldlaand  respira- 
tions^' the  latter  may  be  converted  into  sexagesimals  of  top.third  order 
by  moving  the  decimal  point  on'fr  place  farther  to  the  rightfp.  . * .. 

In  the  fourth  column  are  given  the  mean  daily  motions.  *** 

We  shall  present  later  some,  comparisoii&f  these  dtfpen 
adopted  in  other  systems  of  astronomy,  ancient  aftd  qgSdeirj 


i:  3*.J  Trffitafatioii  and  Koto.  17 


'Mean  Motions  of  .the  Planets. 


Planet. 

mgateroT 

rmnlioM  in' 
4,330,000^1. 

Neater  ef 
revolution*  ip 
1,080,000  ye  tn. 

Length  of-nTevoldtloa 
In  Acts  telsr  time. 

motion. 

Sun, 

4, 3 30,600 

1,080,000 

'4  V V p 

365  ?5-3i  3.i4 

f II  .11  «i.,‘ 

59  8 10  10.4 

Mercury, 

Venus,351 

17,937,060 

4.484,905 

87  58  10  5.57 

4 5 3a  ao  41-9 

7^*9,376 

1,755,594 

»4^  54  5.o6 

1 36;  7 43  37 J 

Mars, 

2,296,832 

574,208 

6861  5.87 

3i  96  98  11.1 

JupUfT, 

364,220 

9i,o55 

4,33a  19  r4  2.09 

4 59  848.6 

Saturn, 

i46,568 

36,642 

10,765  46  23  0,41 

Moon: 
aider,  rev. 

*7, 753,336 

i4,438,33 4 

27  19  18  0.16 

13  10  34  59';ii 

synod,  rev. 

53,433,336 

48B;2o3 

1 3,358,334 

29  3i  5o  0.70 

12  11  26  4k  53.4" 

rev.  of  apBis, 

i2'j,o5o} 

3,23a  5 37  x.36 

6 40  58  42.5 

" “ node,  | 

232,238 

58,o*J9f 

6,794  23  59  2.35 

3 ip  4443.3 

The  arbitrary  and  artificial  method  in  ’which  the  fundamental  ele- 
ments of  the  solar  system  arc  here  presented  is  not  peculiar  to  the 
Sfirya-Siddli&utn;  it  is  also  adopted  by  all  the  other  textbooks,  and  is 
to  be  regarded  as  a characteristic  feature  of  the  general  astronomical 
system  of  the  Hindus.  Instead  of  deducing  the  rate  of  motion  of  each 

f)lanet  from  at  least  two  recorded  observations  of  its  place,  and  estab- 
ishing  a genuine  epoch,  with  the  ascertained  position  of  each  at  that 
time,1  they  start  with  the  assumption  that,  at  the  beginni«p  of  the 
present  order  of  things,  all  the  planets,  with  tlicir  apsides  and  ttodles, 
commenced  £licir  movement  together  at  that  point  in  the  heavens^ftar 
£ Piscinrn,  ^explained  above,  under  veTsc  27)  fix  od  upon  $3  the  initial 
point  of  the  sidereal  sphere,  and  that  they  return,  at  certi&V  fixed  inter- 
vals, to -Universal  conjunction  at  the  same  point.  As  regards,  however, 
the  thnOv!%hen  the  motion  commenced,  the  frequency  of  recurrence 
of  the  conjunction,  and  the  date  of  that  which  last  took  place,  there  is 
discordance  among  the  different  authorities.  With  the  SftryarSid- 
dhanta,  and  the  other  treatises  which  adopt  the  same  general  method, 
the  determining  point  of  the  whole  system  is  the  commencement  of  the 
current.  Iron  Age  (kali  yttya) ; at  that  enoch  the  planets  are  assumed  10 
have  been  in  mean  conjunction  for  the  last  time  at  the  initial  point  of 
the  sphere,  the  former  conjunctions  having  taken  place  at  intervals  of 
1,080,000  years  previous.  The  instant  at  which  the  Age  is  made  to 
commence  is  midnight  on  the  meridian  of  Ujjayint  (see  below,  under  ▼. 
82),  at  tlie  end  of  the  588,465th  and  beginning  of  the  588,466th  day 
(civil  reckoning)  of  the  Jtiliflm  Period,  or  between  the  17th  and  18th  of 
February  ^£12  J.P.,  or  3102  B.  C.  (see  below,  under  vv,  45-53,  for  the 
comptitatfc^bf  the  number  of  days  since  elapsed  > Now,  although  no 
such  conjunction  as  that  assumed  by  the  Hindu  astronomers  ever  did 
or  ever  will  Jpko  place,  the  planets  were  actually,  at  the  time  gated, 
approximating  somewhat  nearly  to  a general  conjunction  in  the  ncigh- 
hovlfbod  < JUSe  initial  point  of  the  Hindu  sphere;  this  is  shown  by  the 
ne&tatys^in  which  we  give  their  actual  mean  positions  with  reference 
to  (irifltading  also  those  of  the  moon’s  apogee  and  node) ; 

theg&y$im  'been  obligingly  furnished  us  by  Prof.  Winlock,  Superin- 

3 


18  S&rya-Sitldh&nta.  [i.  34. 

tendcnt  of  the  American  Ephcmcris  and  Nautical  Almanac.  The  posi- 
tions of  the  primary  planets  are  obtained  by  LeVcrrior’s  times  of  side- 
real revolution,  given  in  the  Annales  de  FObscrvatoire,  tom.  ii  (also  in 
Biot's  Astronomic,  3mo  edition,  tom.  v,  1857),  that  of  the  moon  by 
Peirce’s  tables,  and  those  of  its  apogee  and  node  by  Hansen’s  Tables  de 
la  Lunc.  The  origin  of  the  Hindu  sphere  is  regarded  as  being  18°  5 9 
8"  cast  of  the  vernal  equinox  of  Jan,  1,  18G0,  and  50°  22'  29'*  west  of 
that  of  Feb.  If,  3102  11.  C.,  the  precession  in  the  interval  being  08°  27' 
37".  We  add,  in  a second  column,  the  mean  longitudes,  as  reckoned 
from,  the  vernal  equinox  of  the  given  date,  for  the  sake  of  comparison 
with"  the  similar  data  given  by  Bentley  (Hind.  Ast.,  p.  125)  and  by 
Bailly(Ast.  Ind.  et  Or.,  pp.  Ill,  182),  which  wc  also  subjoin. 

Positions  of  the  Planets , midnight , at  Ujjayint,  Feb . 17-18,  3102  B.  C. 


Planet. 

i 

.Prom  taglniiinj'  ! 
of  Hindu  ■jriicre.  1 

Longitude. 

Huntley. 

Bnilly.  | 

Sim, 

• 

- 7 

5i 

" i 
•<8 

• 

3or 

45 

a 

43 

• 

3oi 

1 

• 

3m 

1 

5 

f ■ ' 

Mercury, 

- 4i 

3 

20  ' 

268 

34 

5 

267 

35 

yfi 

261 

1 4 

21 

Venus, 

+ a4 

58 

59  ' 

334 

36 

3o 

333 

44 

37 

334 

22 

18 

Mars, 

- J9 

49 

?6  1 

289 

48 

5 

288 

55 

19 

288 

55 

56 

Jupiter, 

+ 8 

38 

36  : 

3i8 

16 

7 

3 1 8 

3 

54 

3io 

22 

10 

Saturn, 

- 28 

1 

i3  : 

281 

36 

18 

260 

1 

58 

293 

8 

21 

Moon, 

- I 

33 

4*  1 

3 08 

3 

5o 

3f/i 

53 

42 

3oo 

5i 

ifi 

do.  apsis. 

+ 9*> 

*9 

ai  i 

4 i 

56 

42 

fir 

12 

2fi 

61 

i3 

33 

do.  node. 

+198 

24 

4-; 

i48 

2 

16 

i44 

38 

3a  | 

1 44 

37 

4i 

The  want  of  agreement  between  the  results  of  the  three  different  in- 
vestigations illustrates  the  difficulty  and  uncertainty  even  yet  attending 
inquiries  into  the  positions  of  the  heavenly  bodies  at  so  remote  an 
epoch.  It  is  very  possible  that  the  calculations  of  the  astronomers  who 
were  Die  framers  of  the  Hindu  system  may  have  led  them  to  suppose 
the  approach  to  a conjunction  nearer  than  it  actually  was;  but,  however 
that  may  be,  it  seems  hardly  to  admit  of  a doubt*  that  the  epoch  was 
arrived  at  by  astronomical  calculation  carried  backward,  and  that  it  was 
fixed  upon  as  the  date  of  the  last  general  conjunction,  .and  mode  to 
determine  the  commencement  of  the  present  Age  of  the  world,  because 
the  errors  of  the  assumed  positions  of  the  planets  at  that  time  would 
be  so  small,  and  the  number  of  years  since  elapsed  so  great,  as, to  make 
the  errors  in  the  mean  motions  into  which  those  positions  entered  as 
an  element  only  trifling  in  amount. 

The  moon's  apsis  and  node,  however,  were  treated  in  a different 
manner.  Their  distance  from  the  initial  point  of  the  sphere,  as  shown 
by  the  table,  was  too  great  to  be  disregarded.  They  were  accordingly 
exempted  from  the  general  law  of  a conjunction  once  in  1,080,000 
ycar^  and  such  a number  of  revolutions  was  assigned  to  tb^m  as  should 
make  their  positions  at  the  epoch  come  out,  the  one  a quadrant,  the 
other  a lialf-revolution,  in  advance  of  the  initial  point,  of  the%>hcre. 

)Ve  can  now  see  why  the  deduction  spoken  of  above  (v.  24),  for  tune 
spent  in  creation,  needed  to  be  made.  In  order  to  bring  all  the  planets 
to  a position  of  mow  conjunction  at  the  epoch,  the  time  prtefously 


Translation  and  Notes.  . 


19 


i.  34.]. 

elapsed  must  bo  an  exact  multiple  of  the  lesser  period  of  1,080,000  years, 
or  the  quarter- Age;  in  order  to  give  its  proper  position  to  the  moon’s 
apsis,  that  time  must  contain  a certain  number  of  whole  Ages,  which 
arc  the  periods  of  conjunction  of  the  latter  with  the  planets,  together 
with  a remainder  of  three  quarter-Ages ; for. the  moon’s  node,  in  like 
manner,  it  must  contain  a certain  number  of  half-Ages,  with  a remainder 
of  one  quarter- Age.  Now  the  whole  number  of  years  elapsed  between  the 
beginning  of  the  A£on  and  that  of  the  current  Iron  Age  is  equal  to  1826 
quarter-Agcs,  with  an  odd  surplus  of  864,000  years:  from  it  subtract 
an  amonnt  of  time  which  shall  contain  this  surplus,  together  with  three, 
seven,  eleven,  fifteen,  or  the  like  (any  number  exceeding  by  threejj^pul- 
tiple  of  four),  quarter-Agcs,  and  the  remainder  will  fulfil  the  coitdnions 
of  the  problem.  The  deduction  actually  made  is  of  fifteen-  periods  + 
the  surplus. 

This  deduction  is  a clear  indication  that,  as  remarked  above  (under 
v.  17),  the  astronomical  system  was  compelled  to  -adapt  itself  to  an 
already  established  Puranic  chronology.  It  could,  indeed,  fix  the  pre- 
viously undetermined  epoch  of  the  commencement  of  the  Iron  Age,  but 
it  could  not.  alter  the  arrangement  of  the  preceding  periods. 

Tt  is  evident  that,  with  whatever  accuracy  the  mean  positions  of  the 
planets  may,  at  a given  time,  be  ascertained  by  observation  by  the 
Hindu  astronomers,  their  false  assumption  of  a conjunction  at  the  epoch 
of  3102  B.  C.  must  introduce  an  element  of  error  into  their  determina- 
tion of  the  planetary  motions.  The  annual  amount  of  that  error  may 
indeed  be  small,  owing  to  the  remoteness  of  the  epoch,  and  the  great 
number  of  years  among  which  the  errors  of  assumed  position  Are  divi- 
ded, yet  it  must,  in  time  grow  to  an  amount  not  to  be  ignored  or  neglect- 
ed even  by  observers  so  inaccurate,  and  theorists  so  unscrupulous,  as  the 
Hindus.  This  is  actually  the  case  with  the  elements  of  the  Surya-Sid- 
dh&nta;  the  positions  of  the  planets,  as  calculated  by  them  for  the 

1>resent  time,  arc  in  some  cases  nearly  9°  from  the  true  places.  The 
atcr  astronomers  of  India,  however,  have  known  how  to  deal  with  such 
difficulties  without  abrogating  their  ancient  text-books.  As  the  Surva- 
Siddk&nta  is  at  present  employed  in  astronomical  calculations,  there  are 
introduced  into  its  planetary  elements  certain  corrections,  called  b>ja 
(more  properly  vtja  ; the  word  means  literally  “ seed”  ;■  we  do  not  know 
how  it  arrived  at  its  present  significations  in  the  mathematical  language). 
That  this  was  so,  was  known  to  Davis  (xVs.  Res.,  ii.  236),  but  he  was 
unable  to  state  the  amount  of  the  corrections,  oxcepting  in  the  case  of 
the  lriSou's  apsis  and  node  (ibid.,  p.  275).  Bentley  (Hind.  Ast.,  p.  179) 
gives  them  in  full,  and  upon  his  authority  we  present  them  in  the 
annexed  tabic.  They  are  in  the  form,,  it  will  bo.  noticed,  of  additions  to, 
or  subtractions  from,  the  number  of  revolutions  given  for  an  Age,-  and 
the  numbers  arc  all  divisible  by  four,  in  order  n *t  to  interfere  with  the 
calculation  by  the  lesser  period  of  1,080,000  years.  AVe  have  added 
*tbo  corrected  number  of  revolutions,  for  both  the  mater  amir  lesser 
period,  the  corrected  time  of  revolution,  expressed  in  Hindu  divisions  of 
the  day,  and  the  corrected  amount,  of  mean  daily  motion. 

These  corrections  were  first  applied,  according  to  Mr.  Bentley* (A*. 
Refe^  yiii.  220),  about  the  beginning  of  th £ sixteenth  century ; they  sire 


nted  by  several  treatises  of  that  as  well  as  of  later  date,  not  having 
yet  superseded  by  others  intended  to  secure  yet  greater  correctness. 

Mean  Motions  of  the  Planets  as  corrected  by  the  klja. 


Pltiiat. 

: 

Corrup- 

tion. 

Corrected  oun 

tin 

in  4,320,000 
jrnri. 

iter  of  revolts- 

“in  1,080,000 

yeere. 

. Corrected 
ttifei  if  revolution. 

Corrected 
dally  motion. 

Sun, 

0 

4,310,000 

1,080,000 

d n v p 

365  i5  3i  3.i4 

• , ff  IX  MX 

59  8 10  10.4 

Morally, 

- l6 

17937,044 

4, 484.361 

87  58  11  1.26 

4 5 3a  19  54-5 

- ia 

7toa  a,  364 

1,755,591 

224  4i  56  i.35 

1 36  7 43  z.8 

0 

2,296,83a 

574,308 

686  59  5o  5.87 

3i  26  28  11. 1 

Jupiter, 

- 8 

364,aia 

91,053 

4,33a  a4  56  5.56 

4 59  8 24-9 

Saturn, 

+■  ia 

i46,58o 

36,645 

10,764  53  3o  1. 11 

2 0 a3  28.9 

Moon, 

0 

57,753,336 

1 4,438,334 

27  19  18  0.16 

i3  10  34  52  3.8 

- apsis, 

- 4 

488,199 

122,049! 

3,a3a  7 13  3.37 

6 4o  58  30.7 

11  nods. 

+ 4 

1 232,242 

58,060} 

6,794  16  58  0.66 

3 10  44  55.o 

We  need  not,  however,  Tely  on  external  testimony  alone  for  informa- 
tion as  to  the  period  when  this  correction  was  made.  If  the  attempt  to 
modify  the  elements  in  bucIi  a manner  as  to  make  them  give  the  true 
positions  of  the  planets  at  the  time  wlieu  they  were  so  modified  was  in 
any  tolerable  degree  successful,  we  ought  to  be  able  to  discover  by  cal- 
culation the  date  of  the  alteration.  If  we  ascertain  for  any  given  time 
the  positions  of  the  planets  as  given  by  the  system,  and  compare  them 
with  the  true  positions  as  found  by  our  best  modern  methods,  and  if  wc 
then  divide  the  differences  of  position  by  the  differences  in  the  mean 
motions,  wc  shall  discover,  in  each  separate,  case,  when  the  error  was  or 
will  be  reduced  to  nothing.  The  results  of  such  a calculation,  made  for 
Jan.  1,  I860,  are  given  below,  under  v.  67.  We  see  there  that,  if  regard 
is  had  only  to  the  absolute  errors  in  the  positions  of  the  plaucts,  no  con- 
clusion of  value  can  be  arrived  at ; the  discrepancies  between  the  dates 
of  no  error  are  altogether  too  great  to  allow  of  their  being  regarded  as 
indicating  any  definite  epoch  of  correction.  If,  on  the  other  hand,  wc 
assume  the  place  of  the  sun  to  have  been  the  standard  by  which  the 
positions  of  the  other  planets  were  tested,  the  dateF  of  no  error  are  seen 
to  point  quite  distinctly  to  the  first  half  of  the  sixteenth  century  as  the 
Lime  of  the  correction,  their  mean  being  A.  i>.  1541,  Upon  this  as- 
sumption, also,  we  see  why  no  correction  of  bija  was  applied  to  Mars  or 
to  the  moon:  the  former  had,  at  the  given  time,  only  just  passed  his 
time  of  complete  accordance  with  the  sun,  and  the  motion  of  the  moon 
was  also  already  so  closely  adjusted  to  that  of  the  sun,  that  the  differ- 
ence between  their  errors  of  position  is  even  now  less  than  161..  Nori 
is  there  any  other  supposition  which  will  explain  why  the  scrioits  error 
in  the  position  of  the  sun  himself  was  overlooked  at  the  time  of  the 
general  correction,  and  why,  by  that  correction,  the  absolute  emirs  of 
position  of  more  than  ono  of  the  planets  are  made  greaterthan  they, 
would.* otherwise  have  been,  as  is  the  ease.  It  is,  in  shor^dHHy  evident 
that  the  alteration  of  the  elements  of  the  Sffry a-Siddh&nupwh ich  was 
effected  early  in  the  sixteenth  centuir,  was  an  adaptation  of.  the  errors 
of  position  of  *ti»c  other  {Janets  to  that  of  tb|&sun,  assumed  to  ^.cor- 
rect and  regarded  as  the  standard.  zyfv 


L*4.] 


Translation  and  Notes.,, 


21 


Now  if  it  is  possible  by  this  method  to  arrive  approximately  at  the; J 
date  of  a correction^applied  to  the  elements  of  a Siddh&nta,  it  should’ 
be  possible  in  like  manner  to  arrive  at  the  date  of  those  elements  them- 
selves. For,  owing  to  the  false  assumption  of  position  at  the  epoch, 
there  is  but  one  point  of  time  at  which  any  of  the  periods  of  revolution 
will  give  the  true  place  of  its  planet : if,  then,  as  is  to  b£  presumed,  the 
true  places  were  nearly  determined  when  any  treatise  was  composed* , 
and  were  made  to  enter  as  an  clement  into  the  construction  of  its  1 
system,  the  comparison  of  the  dates  of  no  error  will  point  to  the  epoch  of 
its  composition.  The  tnethod,  indeed,  as  is  well  known  to  all  thoga^bo 
have  made  any  studies  in  the  history  of  Hindu  astronomy,  has  ompt 
been  applied  to  this  purpose,  by  Mr.  Bentley.  It  was  first  origillt^d 
and  put  forth  by  him  (in  vol.  vi.  of  the  Asiatic  Researches)  at  a time 
when  the  false  estimate  of  the  age  and  value  of  the  Hindu  astronomy 
presented  by  Bailly  was  still  the  prevailing  one  in  Europe ; he  strenu- 
ously defended  it  against  more  than  one  attack  (As.  Res.,  viii,  and  Hind. 
Ast.),  and  finally  employed  it  very  extensively  in  his  volume  on  the 
History  of  Hindu  Astronomy,  as  a incans  of  determining  the  age  of  the 
different  Siddh&ntas.  We  present  below  the  table  from  which,  in  the 
latter  work  (p.  126),  he  deduces  the  age  of  the  Surya-Siddh&nta ; the 
column  of  approximate  dates  of  no  error  wc  have  ourselves  added. 

Bentley's  Table  of  Errors  in  the  Positions  of  the  Planets , as  calculated , 
for  successive  periods , according  to  the  Surya-Siddh&nta . 


From  an  average  of  the  results  thus  obtained,  Bentley  draws  the  con- 
clusion that  the  Sfcrya-Slddhlmta  dates  from  the  latter  part  of  the  elev- 
enth century;  or,  more  exactly,  A.  D.  1091, 

The  general  soundness  of  Bentley’s  method  will,  we  apprehend,  be 
denied  at  the  present  time  by  few,  and  he  is  certainly  entitled  to  not.  a 
little  .credit  for  his  ingenuity  in  devising  it,  for  the  persevering  industry 
sho#n  in  its  application,  and  for  the  zeal  and  boldness  with  which  he 
propounded  and  defended  it.  He  succeeded  in  throwing  not  a little 
light  upon  an  obscure  aud  misapprehended  subj  ct,  and  his  investiga- 
tions have  ^contributed  very  essentially  to  our  present  understanding  of 
the  Hinduraysteras  of  astronomy.  But  the  details  of  his  work  are  not 
; to  bar  accepted  without  careful  testing,  and  his  general  conclusions  arc 
often  unsound,  and  require  essential  modification,  or  are^to  be  rejected 
altegyjtlta.  This  we  will!; attempt  to  Bhow  in  connecritt^with  his  treat- 
ment Of  the  Siirva-Siddhknta.  . t* 


22  S&rya-SiddJidnta.  p.  84. 

j.v^Jn  the  first  place,  Bentley  has  made  a very  serious  error  in  that  put  r 
|p?.;his  calculations  which  concerns  the  planet  Mcrqnry.  As  that  planet  . 
ifasj  sit  tiie  epoch,  many  degrees  behind  its  assumed  place,  it  was  neces- 
sary, of  course,  to  assign  to  it  a slower  than  its  true  rate  of  motion. 
But  the  rate  actually  given  it  by  the  text  is  not  quite  enough  slower, 
and,  instead  of  exhausting  the  original  error  of  position  in  the  tenth 
: ceutury  of  our  era,  as  stated  hv  Bentley,  would  not  so  dispose  of  it  for 
many  hundred  years  yet  tc  come.  lienee  the  correction  of  the  btja,  m 
.reported  by  Bentley  himself,  instead  of  giving  to  Mercury,  as  to  all  the 
rat^  a more  correct  rate  of  motion,  is  made  to  have  tlio  contrary  effect, 
in'  .oider  the  sooner  to  run  out  the  original  error  of  assumed  position, 
and  produce  a coincidence  between  the  calculated  and  the  true  places  of 
the  planet. 

In  the  case  of  tho  other  planets,  the  times  of  no  error  found  by 
Bentley  agree  pretty  nearly  with  those  which  we  have  ourselves  ob- 
tained, both  by  calculating  backward  from  tlic  errors  of  A.  D.  1860, 
and  by  calculating  downward  from  those  of  1>.  C.  3102,  and  which  arc 
presented  in  the  table  given  under  verse  07.  § ITpon  comparing  tho  two 
tables,  however,  it  will  bo  seen  at  once  that  Bentley’s  conclusions  are 
drawn,  not  from  the  sidereal  errors  of  position  of  the  planets,  but  from 
the  errors  of  their  positions  as  compared  with  that  of  the  sun,  and  that 
of  the  sun’s  own  error  lie  makes  no  account  at  all.  This  is  a method  of 
procedure  which  certainly  requires  a much  fuller  explanation  and  justifi- 
cation than  he  has  seen  fit  anywhere  to  give  of  it.  The  Hindu  sphere 
is  a sidereal  one,  and  in  no  wise  bound  to  the  movement  of  the  sun. 
The  sun,  like  the  other  planets,  was  not  in  the  position  assumed  for  him 
at  the  epoch  of  3102  B.  C.,  and  consequently  the  rate  of  motion 
assigned  to  him  by  tbe  system  is  palpably  different  from  the  real  one : 
the  sidereal  year  is  about  three  minutes  and  a half  too  long.  Why  then 
should  the  sun’s  error  be  ignored,  and  the  sidereal  motions  of  the  other- 
planets  considered  only  with  reference  to  the  incorrect  rate  of  motion 
established  for  hirn?  It  is  evident  that  Bentley  ought  to  have  taken 
fully  into  consideration  the  sun's  position  also,  and  to  have  shown  either 
that  it  gave  a like  result  with  those  obtained  from  the  other  planets,  or, 
if  not,  what  was  the  reason  of  the  discrepancy.  By  failing  to  do  so,  he 
has*  in  our  opinion,  omitted  the  most  fundamental  datum  of  the  whole 
calculation,  and  the  one  which  leads  to  the  most  important  conclusions. 
We  have  seen,  in  treating  of  the  bfja%  that  it  has  been  the  aim  of  the 
modern  Llindu  astronomers,  leaving  the  sun’s  error  untouched,  to  amend 
those  of  the  other  planets  to  at>  accordance  with  it.  Now^.a*  things 
are  wont  to  be  managed  in  the  Hindu  literature,  it  would  be  tio  matter 
for  surprise  if  such  corrections  were  incorporated  into  the  text'  ifejeljf: 
had  not  the  Sfirya-Siddh&nta  been,  at  the  beginning  of  the  sirtc&uth. 
century,  so  widely  distributed,  and  its  data  so  universally  known,  and 
had  not  the  Hindu  science  outlived  already  that  growing  and  productive 
period,  «>f  its  history  when  a school  of  astronomy  might  put  forth  a cor-£ 
rected  text  of  an  ancient  authority,  and  expect  to  sec  it  make  its  wpjr^ 
to  general  acceptance,  crowding  out,  aud  finally  causing  to  disappear, ' 
thc«older  version — such  a process  of  altcration^might,  in  our  view,  have 
passed  upon  it,  -gnd  such  a text  might  have  Seen  handed  down  to  our 


Translation  and  Notes . 


i.  34.] 

time  as  Bentley  worilcl  liavc  pronounced,  upon  internal  evidence,  to  hayci 
been  composed  eart/in  the  sixteenth  century;  while,  nevertheless,  iwk 
original  error  of  the  sun  would  remain,  untouched  and  increasing,  to  in- 
dicate what  was  the  true  state  of  the  case. 

But  what  is  the  actual  position  of  things  with  regard  to  our  Sid- 
db&nta  ? We  find  that  it  presents  us  a set  of  planetary  elements,  which, 
when  tested  by  the  errors  of  position,  in  the  manner  already  explained,  " 
do  not  appear  to  have  been  constructed  so  as  to  give  the  true  sidereal 
positions  at  anj  assignable  epoch,  but  which,  on  the  other  hand,  exhibij^ 
evidences  of  an  attempt  to  bring  the  places  of  the  other  planets  into  an 
accordance  with  that  of  the  sun,  made  sometime  in  the  tenth 
century — the  precise  time  is  very  doubtful,  the  discrepancies'  of  the 
times  of  no  error  being  far  too  great  to  give  a certain  result.  Now  it  ia 
as  certain  as  anything  in  the  history  of  Sanskrit  literature  can  be,  that 
there  was  a Sfirya-Siddh&nta  in  existence  long  before  tliat  date ; there 
is  also  evidence  in  the  references  and  citations  of  other  astronomical 
works  (see  Colebrooko,  Essays,  ii.  484  a,  Hind.  Mg.,  p.  1)  that  there  have 
been  more  versions  than  one  of  a treatise  hearing  the  title ; and  we  have 
seen  above,  in  verse  0,  a not  very  obscure  intimation  that  the  present 
work  docs  not  present  precisely  the  same  elements  which  had  been  ac- 
cepted formerly  as  those  of  the  Siirya-Siddhslnta.  What  can  lie  nearer, 
then,  than  to  suppose  that  in  the  tenth  or  eleventh  century  a correction 
of  btja  was  calculated  for  application  to  the  elements  of  the  Siddh&nta, 
and  was  then  incorporated  into  the  text,  by  the  easy  alteration  of  four 
or  five  of  its  verses;  and  accordingly,  that  while  the  comparative  errors 
of  the  other  planets  betray  the  date  of  the  **orrectiun,  the  absolute  error 
of  the  sun  indicates  approximately  the  true  date  of  the  treatise  ? 

Ill  our  table,  the  time  of  no  error  of  the  sun  is  given  as  A.  D.  250. 
The  correctness  of  this  date,  however,  is  not  to  he  too  strongly  insisted 
upon,  being  dependent  upon  the  correctness  with  which  the  sun's  place 
wsis  first  determined,  and  then,  referred  to  the  point  assumed  as  the 
origin-  of  the  sphere.  It  was,  of  course,  impossible  to  observe  directly 
when  the  sun’s  centre,  hy  liis  mean  motion,  was  10'  east  of  ? Piseium, 
and  there  arc  grave  errors  in  the  determination  by  the  Hindus  of  the 
distances  from  that  point  of  the  other  points  fixed  by  them  in  their 
zodiac.  And  a mistake  of  1°  in  the  determination  of  the  sun’s  pla^e 
would  occasion  a difference  of  425  years  in  the  resulting  date  of  no 
error.  We  shall  have  occasion  to  recur  to  this  subject  in  connection 
with  the  eighth  chapter. 

There  ia  also  an  alternative  supposition  to  that  which  we  have  made 
above,  respecting  the.  conclusion  from  the  date  of  no  error  of  the  sun. 
If  the  error  in  the  BnnS  motion  were  a fundamental  feature  of  the  whole 
Hindu  system,  appearing  alike  in  all  the  different  text- books  of  the 
scieucc,  that  date  would  point  to  the  origin  rathe*  of  the  whole  system 
than  offcfty  treatise  which  might  exhibit  it.  But  although  the  different 
Siddh&ntas  nearly  agree  with  one  another  respecting  the  length  «f  the 
' sidereal  year,  they  do  not  entirely  accord,  as  is  made  evident  hy  the 
following'  statement,  in  which  arc  included  all  the  authorities  to  which 
we  have  access,  either  in  the  original,  or  as  reported  by  Colcbrofcte, 
Bentley,  and  Warren : 


:tvJ8Arya-Siddhftatal  ■ . 
PduU$i-8iddhAnta, 
P&rfl^ito-SiddhfiDta, 
Arya^SiddhSota, 
Lagfcii-Arye-SiddhSnta, 
SiddhAnta-fSrowavi, 


+ » *7 
+3  90.99  ■ 
%:+3  19.9^ 
+ 4;-  58..S  .. 


1 of  sMotm]  jpmt.  9 Errtr. 

xam3$a.56  \ + 3m 

365  36 

365  6'  n 3i.5o; 

365  5‘  la  3o.84 
36Svfl  3o 
365  6 1a  9 

/JTlifc  first  fire  tit  these  might  be  regarded  as  unimportant  vlf 
■pf  tjhe  same  error,  but  it  would  seem  that  the  Inst,  is  an  ^idcpendeht'4 
■tentijiiA^on,  and  one  of  later  date  than  the  others ; while,"  if^jall  Are 
hid&pemfent,  that  of  the  Sfiry^Siddli&nta  has  the  appearancS  of  being* 
die  most  ancient.  Such  questions  as  these,  however,  are  not  tb  bo  too\ 
hastily  decided,  nor  from  single  indications  merely ; they  demand  the  ' 
most  thorough  investigation  of  each  different  treatise,  and  the  carefhl 
collection  of  all  the  evidence  which  can  be  brought  to  bear  upon  them. 

Here  lies  Bentley’s  chief  error,  lie  relied  solely  upon  his  method  of 
^examining  the  elements,  applying  even  that,  as  we  have  seen,  only  par- 
tially and  uncritically,  and  never  Allowing  his  results  to  be  controlled 
or  corrected  by  evidence  of  any  other  character.  He  had,  in  fact,  no 
philology,  and  he  was  deficient  in  sound  critical  judgment.  He  thor- 
oughly misapprehended  the  character  of  the  Hindu  astronomical  litera- 
ture, thinking  it  to  be,  in  the  main,  a mass  of  forgeries  framed  for  the 
purpose  of  deceiving  the  world  respecting  the.  antiquity  of  the  Hindu 
people.  Many  of  his  most  confident  conclusions  have  already  been 
Overthrown  by  evidence  of  which  not  even  he  would  venture  to  question 
the  verity,  and  wc  are  persuaded  that  but  little  of  his  work  would  stand  , 
the  test  of  a thorough  examination. 

The  annexed  table  presents  a comparison  of  the  times  of  mean  sidq» 
real  revolution  of  the  planets  assumed  by  the  Hindu  astronomy,  as  rep- 
resented by  two  of  its  principal  text-books,  with  those  adopted  by  the 
great  Greek  astronomer,  and  those  which  modern  science  has  established. 
The  latter  are,  for  the  primary  planets,  from  Le  Vcrrier;  for  tita  rapon, 
from  Nichol  (Cyclopedia  of  the  Physical  Sciences, 

Those  of  Ptolexny  are  deduced  from  the  mean  daily  rates  of  fffttiwltt 
longitude  given  by  him  in  the  Syntaxis,  allowing  for  the  movement  of 
the  equinox  according  to  the  false  rate  adopted  by  him,  of  36"  yearly. 

■ v 1 V 

Comparative  Table  of  the  Sidereal  Revolution*  of  the  Planet*. 


Planet. 

SArya-Slddli&niii.  Slddli&nta-^rbmaul 

Ptolemy. 

■ 

<1  h m ■ 1 d b 1 * 

d jA  m i. 

9t  r*  h. 

Sun, 

365  6 12  36.6J  365  6 12  9.0 

365)|  9 48.6 

Mercury, 

87  23  16  22. 3j  87  23  16  4«-5 

87  »3  if6i9.9 

mtSSm 

Venus, 

224  iG  45  56.a  ■ 224  1646  1.9 

224  i65i  56.8 

224 16  4^^Tb! 

Mu*. 

686  .3  56  93.5,  686  93  57  1.5 

686  23  3i  56.1 

.«®*3  3o.4M 

4,m  u ■ 

Jupiter, 

4,332  7 4 i 44.4!  4,332  5 45  43-7 

4,339  18  9 iM. 5 

Saturn,  n 
Moon : 

10,765  18  33  i3.6j  10,765  19  33  56.5 

10,758  17  48 

10,759  5 16  3tf|| 

sid.  rev. 

\ *7  7 43  124H  27  7 43  1 2.x 

* 59  1244  2.8|#  39  i9  44  2.3 

97  7 43  19.1 

37  7 43  11.4 

synod,  rev. 

49  19  44  3.3 
3,9'39  9 59  >3.6 

*9  W*  a-9 

rev.  of  apsis, 

3,232  2 >4  53.4;1  0,232  17  37  6.0 
6*794  9 35  45.4j  6,792  6.  5 4i-9 

3,a3»  W/fl  99.6 
6,798  #(145  6 

i 6,799  *3  *8  39.4 

.40.] 


Tranah.tuni.and  Noter? 


la  the  additional  notes  at  the  end  of  tfa^work,  we  shaft  imit\ 

' subject  of  these  dat/  and  of  the  light  wolhi  Upon.ti 

and  age  of  the  system.  ^ 

84. ! . . The  iramber  of  risings  of  the  asterisms,  diminished  by 
the  number  of.the  revolutions  of  each  planet  respectively,  gives 
the  number  of  risings  of  the  planets  in  an  Am. 

■\  8Q>  The  number  of  lunar  months  is  the  difference  botweqb  the 
hupiber  of  revolutions  of  the  sun  and  of  the  moon.  Jf  from  ^t- 
. the  number  of  solar  months  be  subtracted,  the  remainder  iigipi 
dumber  of  intercahiry  months. 

86.  Take  tlio  civil  days  from  the  lunar,  the  remainder  is  ine 
number  of  omitted  lunar  days  (tithikshaya).  From  rising  to 
rfeing  of  the  sun  are  reckoned  terrestrial  civil  days; 

87.  Of  these  there  are,  in  an  Age,  one  billion,  five  hundred 
and  seventy-seven  million,  nine  hundred  and  seventeen  thousantL. 
eight  hundred  and  twenty-eight ; of  lunar  days,  one  billion,  sir 
hundred  and  three  million,  and  eighty ; 

38.  Of  intercalary  months,  one  million,  five  hundred  and 
ninety-three  thousand,  three  hundred  and  thirty-six;  of  omitted 
lunar  days,  twenty-five  million,  cighty-two  thousand,  two  hun- 
dred and  fifty-two ; 

' 89.  Of  solar  months,  fifty-one  million,  eight  hundred  and  forty 
thousand.  The  number  of  risings  of  the  asterisms,  diminishetfe-- 
by  that  of  the  revolutions  of  the  sun,  gives  the  number  of  ter- ' 
rcstrial  days. 

40.  The  intercalary  months,  the  omitted  lunar  days,  the  side- 
real, lunar,  and  civil  days — these,  multiplied  by  a thousand,  are 
the  number  of  revolutions,  etc.,  in  an  JEon. 


The  data  here  given  arc  combinations  of,  and  deductions  from,  those 
contained,  in  the  preceding  passage  (vv.  20-34).  For  convenience  of 
reflHhice,  we  present  them  below  in  a tabular  form^ 

In  4,390,000  yean.  In  1,080,000  yam*. 


Sidereal  days, 
deduct  color  revolutions. 

1,582,237,828 

4,320,000 

395,559,457 

1 ,080,000 

Natural,  or  civil  days, 

*,577,917,828 

3^4^4-^457 

SMsraS&lfihaj;  yean, 

lijfegfciply  fey  jm.(of  sslar  months  in  a year, 
Svpr  months 

4,320,000 

K 2 

1,080,000 

12 

5i,84<  ,000 

12^60,000 

Jttoon'sdderetV  revolutions, 
deduct  solar  revolutions, 

57.753.336 

4,33i\qoo 

14436,334 
i ,080,090 

Synodical  revolutions,  lunar  months, 
deduct  solar  months, 

53^433,336 

$t'84o.ooo 

13,358,334 
• 12,960,000 

Intercalary  months, 

'V 593,336 

398,334 

4 


M 


SArya-Siddhdnta , 


[i.  40- 


^jjjjnar  months,  53,433,336 

yfpxnultiplj  by  no.  of  lunar  days  in  a month,  v 3o 

Lunar  days,  i ,603,000,080 

4*duct  civil  days,  1 ,577.91 7£a8 

Omitted  lunar  days,  a5,o8a,a5a 


13,358,334 

3o 


We  add  a few  explanatory  remarks  respecting  some  of  the  tcrnia  em- 

j ^1*  1! il j ■ '■'» 


\ v*  w un  mo  ■ n m 1 tram*  > r >41} 


The  natural  day,  nycthemeron,  is,  for  astronomical  purposes,  reckoned 
in  the  Silrya-Siddli&nta  from  midnight  to  midnight,  and  is  of  invariable 
length ; for  the  practical  uses  of  life,  the  Hindus  count  it  from  'sunrise 
to  sunrise ; which  would  cause  its  duration  to  vary,  in  a latitude  as  high 
aa  our  own,  sometimes  ns  much  as  two  or  three  minutes.  As  above 
noticed,  the  system  of  Brahmagupta  and  some  others  reckon  the  astro-- 
nonncal  day  also  from  sunrise. 

Fottthe  lunar  day,  the  lunar  and  solar  month,  and  the  general  con- 
wbution  of  the  year,  see  above,  under  verse  Hi.  The  lunar 'month, 
which  is  the  one  practically  reckoned  by,  is  named  from  the  solar  month 
in  which  it  commences.  An  intercalation  takes  place  when  two  lunar 
months  begin  in  the  same  solar  mouth  : the  former  of  the  two  is  called 
ail  intercalary  mouth  ( adkimasa , or  culhini&saka,  “extra  month"),  of  the 
same  name  as  that  which  succeeds  it. 

The  term  14  omitted  lunar  day ,J  (i tithikshaya , 44  loss  of  a lunar  day”) 
is  explained  by  the  method  adopted  in  the  calendar,  and  in  practice,  of 
gaming  tlic  days  of  the  month.  The  civil  day  receives  the  name  of  the 
lunar  day  which  cuds  in  it;  but  if  two  lunar  days  end  in  the  same  solar 
day,  the  former  of  them  is  reckoned  as  loss  (kshayu),  and  is  omitted,  the 
day  being  named  from  the  other.  ' 


,,  41.  The  revolutions  of  the  sun  s apsis  (manda),  moving  east- 
ward, in  an  ./Eon,  arc  three  hundred  and  eiglity-seveu;  of  that 
of  Mars,  two  hundred  and  four ; of  that  of  Mercury,  three  hun- 
dred and  sixty-eight ; - jfc 

42.  Of  that  of  Jfcpiter,  nine  hundred ; of  that  of  Venus,  nVe 
hundred  and  thirty-five;  of  the  apsis  of  Saturn,  thirty-nine. 
Farther,  the  revolutions  of  the  nodes,  retrograde,  aTe : 

43.  Of  that  of  Mars,  two  hundred  and  fourteen ; of  that  of 
Meicurv,  Jour  hundred  and  eighty-eight;  of  that  of  Jupiter,  one 
hundred  and  seventy-four ; of  that  of  Venus,  nine  hundred  and 
three ; 

44.  Of  the  node  of  Saturn,  the  revolutions  in  an  j®on  are^ax- 
hundred  and  sixty-two : the  revolutions  of  the  moon’s  apsis  and 
node  have  been  given  here  already. 

In  illustration  of  the  curious  feature  of  the  Hindu  system  of  astronomy 
presented  in  this  passage,  wc  first  give  the  annexed  table ; which  shows 
the  number  of.  revolutions  in  the  /lion,  or  period  of  4,820,000,000  years, 
assigned  by  the  text  to  the  apsis  and  nude  of^hch  planet,  the  resulting 
time  of  revolution,  the  number  of  years  which  cacti  would  reqqjro  to 


Translation  and  Notes. 


i.  44.] 


2* 


pass  through  an  arc  of  ono  minute,  and  the  position  of  each,  accortigte 
to  the  system,  .in  UroO ; the  latter  bei«|fre&Koqed  in  our  method,  Iw 
the  vernal  equinox.  Farther  are  added  the  actual  positions  fcr  Jan.?, 
1850,  as  {riven  by  Biot  (Trait6  d’ Astronomie,  tdm.  ▼.  529) ; and  dully, 
the  errorsof  the  positions  aB  determined  by  this  Siddh&nta.  - 

Table  of  Revolutions  and  Present  Position  of  ike  Apsides  and  Nodes  of 

the  Planets. 


S&rya-Siddhdnta, 


[t  44- 


the  Arya  and  P&r&Garm  Siddli&ntas,  from  which  the  pod- ' 
JjBpfc  given  in  the  table  are  calefdatodi  are  derived  Sfrom  Bentley  (Hind*  * 
mk  pp.  189,  144).  To  each  position  is*  prefixed  the  nuxubcr  of  oom- 
pletqd  revolutions ; or,  in  the  case  of  the  nodes,  of  which  the  motion  is 
retrograde,  the  number  of  whole  revolutions  of  which  each /falls  short 
by  the  amount  expressed  by  its  position. 

JHfe  almost  universal  disagreement  of  these  four  authorities  with1 


"imeM  to  the  number  of  whole  revolutions  accomplished,  and  tbsif  . 
gdteral  agreement  as  to  the  remainder,  which  determines  the  positron,*; 
prove  that  the  Hindus  had  no  idea  of  any  motion  of  the, apsides  and' 
sUfes  of  the  planets  as  an  actual  and  observable  phenomenon ; biit,  *' 


nodes  of  the  planets  os  an  actual  and  observable  phenomenon ; biit,  * 
knowing  that  the  moon’s  apsis  and  node  moved,  they  fancied  that  the 
symmetry  of  the  universe  required  that  those  of  the  other  planets  should 
j’move  and  they  constructed  their  systems  accordingly-  They  held, 
too, r^wil  be  seen  at  the  beginning  of  the  second  chapter,  that  the 
no<fc$g*  and ; apsides,  as  well  us  the  conjunctions  ( ftghrd ),  were  beings, 
stationed  in  the  heavens,  and  exercising  a physical  influence  over  their 
respective  planets,  and,  as  the  conjunctions  revolved,  so  must  these  also. 
In  fiflming  their  systems,  then,  they  assigned  to  these  points  such  a 
number  of  revolutions  in  an  ./Eon  as  should,  without  attributing  to  them 
any  motion  which  admitted  of  detection,  make  their  positions  what  they 
supposed  them  actually  to  be.  The  differences  in  respect  to  tlic  number 
of  revolutions  were  in  part  rendered  necessary  by  the  differences  of  other 
features  of  the  systems;  thus,  while  that  of  the  iSiddh&nta-£iromani 
makes  the  planetary  motions  commence  at  the  beginning  of  the  ./Eon, 
by  that  of  the  Stirya-Siddhanta  they  commence  17,064,000  years  later 
(see  above#?.  24).  and  bv  that  of  the  Arya-Siddhftnta,  3,024,000  years 
later  (Bentley,  Iliud.  Ast.  p.  1 39)  : in  part,  however,  they  are  mdMr 
arbitrary  ; for,  although  the  V&rk^ara-Siddli&nta  agTccs  with  thoflia- 
dhknta-iyiromani  as  to  the  time  of  the  beginning  of  things,  its  numbers 
of'  revolutions  correspond  only  in  two  instances  with  those  of  the  latter. 

It  may  be  farther  remarked,  that  the  close  accordance  of  the  different 
astronomical  systems  in  fixing  tlic  position  uf  points  which  arc  so  difficult 
of  observation  and  deduction  as  the  nodes  and  apsides,  etrongly  indicatcs, 
either  that  the  Hindus  were  remarkably  accurate  observers,  find  all 
arrived  independently  at  a near  approximation  to  the  truth,  or  that  some 
one  of  them  was  followed  as  an  authority  by  the  others,  or  tliaft  all  alike 
derived  their  data  from  a common  source,  whether  native  or  foreign. 
Wc  reserve  to  the  end  of  this  work  the  discussion  of  these  different 
possibilities,  and  the  presentation  of  data  which  may  tend  to  settle^o 
question  between  them. , ^ v 

vSiZo 

. 45.  Nov  add  together  the  time  of  the  six  Patriarchs  (jnftnjjp, 

’ with  their  respective  twilights,  and  with  the  dawn  at  the  com- 
mencement of  the  iEon  (jealpa) ; farther,  of  the  Patriarch  Manu, 
son  o£ Yivasvant, 


i.50.] 

46.  The  twenty-seven  Ages 


tyanslation  and  Sates'. 


29 

.*? 


the  present  Golde/  Age  (krta  yu^jyfmax  their  sum  suh^nct^ 
time  of  creation,  already  stated  in  terms  of  divine  yea**?' 

47.  In  solar  yean:  tneresult  is  the  time  elapsed  at  the  end  of 
the  Golden  Age;  namely,  one  billion,  nine  hundred  and, fifty - 
threS'  million,  seven  hundred  and  twenty  thousand  sola|.y 

v'^We  hare  already  presented  this  computation,  in  filll,  in  the 
vents  S3  and  24. 

.48. 
past. , 


To  this,  add  the  number  of  years  of  the  time 


As  the  S&rya-Siddh&nta  professes  to  hare  been  revealed  by  the  Sun 
aboi£  the  end  of  the  Golden  Age,  it  is  of  course  precluded  frg^tthing  j 
any  notice  of  the  divisions  of  time  posterior  to  that  period  J tiKirb  is 
nowhere  in  the  treatise  an  allusion  to  any  of  the  eras  which  are  Mully 
made  use  of  by  the  inhabitants  of  India  in  reckoning  time,  wjRjh'jWP'eX* 
ception  of  the  cycle  of  sixty  years,  which,  by  its  nature,  ia  bound  to  no 
date  or  period  (sec  below,  r.  55).  The  astronomical  era  is  thflHtom- 
mencement  of  the  Iron  Age,  the  epoch,  according  to  this  Siddhhiita,  of 
the  liist  general  conjunction  of  the  planets;  thin  coincides,  as  stated 
above  (under  vv.  29-341  with  Feb.  ] 8,  1612  J.  J\,  or  3102  B.  C;  From 
that  time  will  hare  elapsed,  npon  the  eleventh  of  April,  1859,  the 
number  of  4960  complete  sidereal  years  of  the  Iron  Age.  The  com- 
putation of  the  whole  period,  from  the  beginning  of  the  present  order 
of  things,  is  then  as  CoIJowr ; 


Kratn  end  of  crcatioii  to  end  of  last  Golden  Age, 

' Silver  Age,  1,396,000 

Brawn  Age,  864,000 

■ Of  boa  Age,  4,960 

Total  from  end  of  creation  to  April,  1859, 


0,000 


9,164,960 

1,955,884,960 


Since  the  Sfirya-Siildh&nta,  as  will  appear  from  the  following  verses, 
reckons  by  luni-solar  years,  it  regards  as  the  end  of  I.  A.  4960  not 
the  end  of  the  solar  sidereal  year  of  that  number,  but  that  cif  the  luui- 
solar  year,  which,  by  Hindu  reckoning,  is  completed  npon  the  third  of 
the  same  month  (sec  Wal'd,  K&la  Sankalita,  Table,  p.  xxxii). 


,48. . ..  Reduce  tbc  sum  to  months,  and  add  the  months 
expired  of  the  current  year,  beginning  with  the  light  half  of 
•paftro.  * 

49.  Set  the  result  down  in  two  places;  multiply  it  by^thaa 
number  of  intercalary  months,  ana  divide  by  that  of  solar  f 
months,  and  add  to  the  last  result  the  number  of  intercalary 
months  thus  found;  reduce  the  sum  to  days,  and  add  tli£  days 
expired  of  the  current  month ; $£»; 

CO.  Set  the  ragilt  down  in  two  places;  multiply  it T5y  the 
number  lu|jp  days,  and  divide  by  that  of  lunar  days; 

subtract  from  the  last  result  the  number  of  omitted  lunar  days 


80 


Mxya-Siddh&nta^  fl.50- 


tkofl  obtained:  the  remainder  is,  at  midnight,  on  the  meridian  of 
I»nktiL_  • \ 

51.  The  sum  of  days,  in  ciyil  reckoning.  • . . 


' In  these  verses  is  taught  the  method  of  one  of  the  most  important 
and  frequently  recurring  processes  in  Hindu  Astronoftiy,  the  finding, 
namely,  of  the  number  of  civil  or  natural  days  which  have  elapsed  at 
trip  given  date,  reckoning  either  from  the  beginning  of  the  present 
creation,  or  (see  below,  v.  56)  from  any  required  epoch  since  that  time. 
In  the  modern  technical  language,  the  result  is  uniformly  styled  the 
ahtrganaL,  “ sum  of  days ; ” that  precise  term,  however,  docs  not  once 
occur  in  the  text  of  the  Si\rya-Siddli&nta : in  the  present  passage  we 
have  dyugana,  which  means  the  same  thing,  and  in  verse  53  dinar&fi , 
“ heap  or  quantity  of  days.” 

The  process  will  be  best  illustrated  and  explained  by  an  cxstthple. 
Let  it  be  required  to  find  the  sum  of  days  to  the  beginning  of  Jan.  I, 
1860. 

It  is  first  necessary  to  know  what  date  corresponds  to  this  in  Hindu 
reckoning.  We  have  remarked  above  that  the  49(H)th  year  of  the  Iron 
Age  is  completed  in  April,  1859  ; in  order  to  exhibit  tlic  place  in  the 
next  following  year  of  the  date  required,  and,  at.  the  same  time,  to  pre- 
sent the  names  and  succession  of  the  months,  which  in  this  treatise  are 
assumed  as  known,  and  arc  nowhere  stated,  we  have  constructed  the 
following  skeleton  of  a Hindu  calendar  for  the  year  4961  of  the  Iron 
Age. 

Solar  Year. 


(I.  A.  49ft 

tint  day. 

IS.  CAitra, 

Mar. 

i3, 

1R59. 

(I.  A.  4961.) 

1.  VAifAkha, 

Apr. 

12. 

do. 

2.  Jyiiahtha, 

May 

i3, 

do. 

3.  AshAdha, 

June 

*4, 

do. 

4.  QrAvana, 

July 

iS, 

do. 

6.  BhAdrapada, 

Aug. 

*6, 

do. 

6.  Alvina, 

Sept. 

i<5. 

do. 

7.  KArttika, 

Oct. 

*c, 

do. 

6.  MArgaglnha, 

Nov. 

1 5, 

Ho 

9 FAuaha, 

Doc. 

if), 

do. 

10.  MAgha, 

Jan. 

iJ, 

i860. 

11.  Fhftlguxu, 

Feb. 

do. 

ia.  CAitra, 

Mar. 

do. 

I4ml -solar  Year, 
month. 

(I.  A.  495i.) 
i.  Ciitra, 
a.  VAifAkba, 

3.  Jyftifihtha, 

4.  Ashfiaha, 

5.  fYttTapa, 
BhAdrapada, 

7.  Agvina, 

8.  Ittrttika, 

9.  MArgafiraha, 
rex  PAusha, 

11.  MAgha,  \ 

12.  Fhalguna,' 

(I.  A.  496a.) 

v.  CAltra, 


lint  day." 


Apt*.  }4i 

May::* 

June  a, 
July  u 
July  )t, 
Aug.  39. 
SaptSS, 
OH.  vj, 
Hot,  aA, 
Dot.  35. 
Jon.  a4. 
Fob.  aa, 


1 85* 

do. 

dfc,? 

■-tf* 

do. 
da 
da 
da 
da  ^ 
do. 
i86d 
do.  - 


Mar.  a3,  do. 


The* names  of  the  solar  months  are  derived  from  the  names  of  the 
asteriflM  (sec  below,  chap,  viii.)  in  which,  at  the  time  of  their  being  first 
so  designated,  Jibe  moon  was  full  during  their  coptijpuanod.  4 The  same 
nanfes  are  transferred  to  the  lunar  months.  Ea$h  lthSar  mijtmi  is  divided 
into  two  parts;  the  first,  called  the  light  half  (pukla  pakiha,  “tjTglt 


ion  and  Notes. 


;lb2.] 


SI 


aide”),  lasts  from  new^moon  to  fall  moon*  or  while  the  moon  is  Waxing; 
the  other,  called  the#9ark  half  (krthna  pataka,  “black  side”),  lasts  Iran 
full  moon  to  new  mooji,  or  while  the  moon  is  waning. 

The  table  shows  that  Jan.  1,  1800,  is  the  eighth  day  of  the  tenth 
month  of  the  Mpst  year  of  the  Iron  Age.  The  time,  then,  for  which 
we  have  to  findHro  sum  of  days,  is  1,955,884,060  y.,  Oni,  7 d. 

Humber  of  complete  yean  elapsed,  1,955,88496°  ' 

multiply  by  number  of  solar  months  in  a year,  is 


Humber  of  months, 
add  months  elapsed  of  current  year, 


-j3,470|6i&5ao 

9 


Whole  number  of  months  elapsed,  23,470,619^629 

Now  a proportion  is  made : as  the  whole  number  of  solar -months 
in  an  Age  is  to  the  number  of  intercalary  months  in  the  same  peifctf,  so 
is  the  number  of  months  ubovc  found  to  that  of  the  corresponding 
intercalary  months : or, 

51,840,000  : 1,593,336  : : 23,470,619,529:  721,384,703  + 

Whole  number  of  months,  as  above,  23^70,619,529 

add  intercalary  months,  721,384,703 

Whole  number  of  lunar  months,  24192,004,232 

multiply  by  number  of  lunar  days  in  a month,  3o 


Humber  of  lunar  days, 

add  lunar  days  elapsed  of  current  mouth, 


725,760^1 26,960 
7 


Whole  number  of  lunar  days  elapsed,  726,760*1 26*9^7 

To  reduce,  again,  tho  number  of  lunar  days  thus  found  to  the  corres- 
ponding number  of  solar  days,  a proportion  is  made,  as  before ; as  the 
whole  number  of  lunar  days  in  an  Age  is  to  the  number  of  omitted  lunar 
days  in  the  same  period,  so  is  the  number  of  lunar  days  in  the  period 
for  which  the  sum  of  days  is  required  to  that  of  the  corresponding 
omitted  lunar  days : or, 


i£o3,ooo,o8o  : 25,082,262  : : 726,760,126,967  : 1 1, 356, 01 8,395  + 

Whole  number  of  lunar  days  as  above,  725,760,126,967 

deduct  omitted  lunar  days,  1 1,356,018,395 

Total  number  of  civil  days  from  end  of  creation  ) g A. 

to  beginning  of  Jan.  i,  i860,  [ 7*4404,108,572 

bis,  then,'  is  tlicr  required  sum  of  days,  for  the  beginning  of  the  year 
A.D.  1860,  at  midityght^  upon  the  Hindu  prime  meridian. 

Hie  first  use  which  we  arc  instructed  to  make  of  the  remit  thus  ob- 
tained is  an  astrological  one. 

61 ... . From  this  may  be  found  the  lords  of  the  day,  the 
iponth,  and  the  year,  counting  from  the  sun.  If  the  number  be 
divided  by  seven,  the  remainder  marks  the  lord  of  the  day,  be- 
ginning with  the  sun.  # 

52.  Divide  the  same  number  by  the  number  of  days  in  a 
moith  and  in  a year,  multiply  the  one  quotient  by  two  and  the 


Mya-SmdtUa,  [U2. 

o^-  ^tkre^  ftdd  one  to  ewb  .product,  and  divide  by  seven ; 
th^ranaindSnf  indicate  the  lords  of  tbe  roonth  and  of  the 
year. 

These  verses  explain  the  method  of  ascertaining,  frosffiAe  sum  of  days 
already  found,  the  planet  which  is  accounted  to  preflln  over  the  day, 
and  mo  those  under  whose  charge  are  placed  the  month  and  year  m 
which  tliat  day  occurs. 

To  find  the  lord  of  the  day  is  to  find  the  day  of  the  week,  since  the 
latter  derives  its  name  from  the  former.  The  week,  with  the  names  and 
succession  of  its  days,  is  the  same  in  India  as  with  us,  having  been 
derived  to  both  from  a common  source.  The  principle  upon  which  the 
assignment  of  the  days  to  their  respective  guardians  was  made  has  been 
handed  down  by  ancient  authors  (see  Ideler,  llandbucli  d.  math.  u.  tech. 
Chronologic,  i.  If  8,  etc.),  and  is  well  known.  It  depends  upon  the 
division  of  the  day  into  twenty-four  hours,  and  the  assignment  of  each 
of  these  in  succession  to  the  planets,  in  their  natural  order;  the  day 
being  regarded  as  under  the  dominion  of  that  planet  to  which  its  first 
hour  belongs.  Thus,  the  planets  being  set  down  in  the  order  of  their 
proximity  to  the  earth,  as  determined  by  the  ancient  systems  of  as- 
tronomy (for  the  Hindu,  sec  below',  xii.  84-88),  beginning  with  tbe 
remotest,  as  follows : Saturn,  Jupiter,  Mars,  sun,  VcnuB,  Mercury,  moon,- 
and  the  first  hour  of  the  twenty-four  being  assigned  to  the  Sun,  as  chief 
of  the  planets,  the  second  to  Venus,  etc.,  it  will  be  found  that  tbe  twenty- 
fifth  hour,  or  the  first  of  the  second  day,  belongs  to  the  moon ; the  forty- 
ninth,  or  the  first  of  the  third  day,  to  Mars,  and  so  on.  Thus  is  obtained 
a new  arrangement  of  the  planets,  and  this  is  the  one  in  which  this 
Siddh&nta,  when  referring  to  them,  always  assumes  them  to  ston^;  (see, 
for  instance,  below,  v.  *70 ; ii.  35-37) : it  has  the  convenient  property 
that  by  it  the  snn  and  moon  are  separated  from  the  other  planets,  from 
which  they  are  by  so  many  peculiarities  distinguished.  Upon  this  order 
depend  the  rules  here  given  for  ascertaining  also  the  lords  of  the  month 
and  of  the  year.  The  latter,  as  appears  both  from  the  explanation  of 
the  commentator,  and  from  the  rales  themselves,  are  no  actual  mouths 
and  years,  but  periods  of  thirty  and  three  hundred  and  sixty  days,  fol- 
lowing one  another  in  uniform  succession,  and  supposed  to  be  nlaccd, 
like  the  day,  under  the  guardianship  of  the  planets  to  whom  belong 
their  first  subdivisions : thus  the  lonl  of  the  day  is  the  lord  of  its  first 
hour ; the  lord  of  the  month  is  the  lord  of  its  first  day  (and  so  of  Up 
first  hour) ; the  lord  of  the  year  is  the  lord  of  its  first  month  (and  tL’ 
of  its  first  day  and  hour).  We  give  below  this  artificial  arrangement 
of  the  planets  with  the  order  in- which  they  are  found  to  succeed  ou$ 
another  as  lords  of  the  periods  If  one,  thirty,  and  three  hundred  arid 
sixty  days ; we  add  their  natural  order  of  succession,  as  lords  of  the 
hours ; and  we  farther  prefix  the  ordinary  names  of  the  days,  with  their 
English  equivalents.  6ther  of  the  numerous  names  of  the  planets,  it 
it  to  be  remarked,  may  be  put  before  the  word  vdra  to  form  the  name 
of  the  day:  vdra  itself  means  literally  “successive  time,9’  or  “turn,” 
ancMgNrot  us£d,  so  far  as  we  are  aware,  in  any  other  connection,  to 
denoted  day.  . 


• kupeor^r; 

RaviTAra, 

SomavAra, 
HaugalaYfira, 
BudhavAra, 

Qnnifin, 

QukravAra, 

QanivAra, 


Monday, 

Tuesday, 

Wednesday, 

Thursday, 

Friday, 

Saturday, 


Moon, 

Man, 

Mercury, 

Jupiter, 

Venus, 

Saturn, 


i 

a 

3 

4 
3 
6 
7 


i 

5 
a 

6 
3 
7 

I 


i i 
6 4 

V ■ 

7 
5 

3 5 


An  the  first  day  of  the  subsistence  of  the  present  order  of  things  is 
supposed  to  have  been  a Sunday,  it  is  only  necessary  to  divide  tbtaus 
of  aays  by  seven,  and  the  remainder  will  be  found,  in  the  first  detain, 
opposite  the  name  of  the  planet  to  which  the  required  day  belongs. 
Tnus,  taking  the  sum  of  days  found  above,  adding  to  it  one,  forjlhe  first 
of  January  itself,  and  dividing  by  Bevcn,  we  have : 


7)714,404,108,573  ^ 

102,057,72^796— 1 


The  first  of  January,  18G0,  accordingly,  falls  on  a Sunday  by  Hindu 
reckoning,  as  by  our  own. 

On  referring  to  the  tabic,  it  will  be  seen  that  the  lords  of  tip  months 
follow  one  another  at  intervals  of  two  places.  To  find,  therefore,  by  a 
summary  process,  the  lord  of  the  month  in  which  occurs  any  given  day, 
first  divide  the  sum  of  days  by  thirty ; die  quotient,  rejecting  the  re* 
mainder,  is  the  number  of  months  elapsed ; multiply  this  by  two,  that 
each  month  may  push  the  succession  forward  two  steps,  add  one  for  the 
current  month,  divide  by  seven  in  order  to  get  rid  of  whole  aeries,  and 
the  remainder  is,  in  the  column  of  lords  of  die  day,  the' munber  of  tho 
regent  of  the  month  required.  Thus  : 


30)714,404,108,572 

23,813,470,2654. 


47.626,949,570 


7)47^26,940^71 

4fio3£A65a-7 

The  regent  of  the  month  in  question  is  therefore  Saturn. 

, By  a like  process  is  found  the  lord  of  the  year,  saving  that,  as  the 

trds  of  tho  year  succeed  one  another  at  intervals  of  three  places,  the 
ultiplication  is  by  three  instead  of  by  two.  Upon  working  out  the 
'process,  it  will  be  found  that  the  final  remainder  is  five,  whisk,  designates 
Jupiter  as  the  lord  of  the  year  at  the  given  time. 

Excepting  here  and  in  the  parallel  passage  xii.  *7, 78,  no  reference  is 
made  in  the  Sftrya-Siddh&nta  to  the  week,  or  to  the  names  of  Ha  days. 
Indeed,  it  is  not  correct  to  speak  of  the  week  at  all  in  cotHection  with 
India,  for  the  Hindus  do  not  seem  ever  to  have  regarded  it  aa  a division 
of  time,  or  a period  to  be  reckoned  by;  they  knew  only  of  p cerUmbrder 
of  succession,  in  which  the  days  were  placed  under  the  regenti^wlhe 
seven  planets.  And  since,  moreover,  as  remarked  above  (under  tv.  11, 


irtade that'  divi6ion;  of  the  day  into  twenty-four  hours 
4pP#ii@l  ^e  older  of  regency  depends,  it  follows  that  the  whole  sys- 
tnh  wda'etfforeign  origin,  and  introduced  into  India  along  with  other 
tMfatits  Of  the  modern  sciences  of  astronomy  and  astrology,  to  which 
‘ if  belonged.  Its  proper  foundation,  the  lordship  of  the  successive  houn, 
is  shown  by  the  other  passage  fxii.  78)  to  have  been  also  known  to  die 
Mfgjfra;  and  the  name  by  which  the  hours  are  .there  called  (hor&m*&Qa) 
frjjjljcates  beyon^a  question  the  source  whence  they  derived  it. 


^5S.  Multiply  the  sum  of  days  (dinardfi)  by  the  number  of 
tfevclutionB  of  any  planet,  and  divide  by  the  number  of  civil 
days;  the  result  is  the  position  of  that  planet,  in  virtue  of  its 
mean  motion,  in  revolutions  and  parts  of  a revolution. 


By  the  number  of  revolutions  and  of  <^ril  days  is  meant,  of  course, 
their  number,  as  stated  above,  in  an  Age.  For  “ position  of  the  planet,” 
etc.,  the  text  has,  according  to  its  usual  succinct  mode  of  expression, 
simply  “ is  the  planet,  in  revolutions,  etc.”  There  is  no  word  for  “po- 
sition” or  “place”  in  the  vocabulary  of  this  Siddh&nta. 

This  verse  gives  the  method  of  finding  the  mean  place  of  the  planets 
at  any  given  time  for  which  the  sum  of  days  has  been  ascertained,  by 
a simple  proportion : as  the  number  of  civil  days  in  a period  is  to  the 
number  of  revolutions  during  the  same  period,  so  is  the  sum  of  days  to 
the  number  of  revolutions  and  parts  of  a revolution  accomplished  down 
to  the  given  time.  Thus,  for  the  sun : 

19577,9*7&B  : 4,3 ao,eoo  : : 714^04,108,573  : 1,955,884,9601**  8*  17°  48'  7" 

The  mean  longitude  of  the  sun,  therefore,  Jan.  1st,  1860,  at  midnight 
On  the  meridian  of  Ujjayini,  is  257°  48'  7".  We  have  calculated  in  qjps 
manner  the . positions  of  all  the  planets,  and  of  the  moon's  apsis  and 
node — availing  cftrselves,  however,  of  the  permission  given  ^idow,  m 
verse  56,  and  reckoning  only  from  the  last  epoch  of  conjunction,  the  be- 
ginning of  the  Iron  Age  (from  which  time  the  sum  of  lays  * is  1,811,945), 
and  abo  employing  the  numbers  afforded  by  the  lesser  period  of 
1,080,000  years — and  present  the  results  in  the  following  table. 


Mean  Placet  of  the  Planets,  Jan . 1 at,  1860,  midnight,  at  Uj/ayM. 


According  to  lire 
^uryo-SiddiiAnia. 

The  tame 

corrected  by  iheM/e. 

Arvlf"  ■ 

• 

* 

.. 

* 

■ 

* 

M 

w 

Sun.  i. 

(4.960)  8 

*7 

48 

7 

8 

*7 

46 

7 

Mercury, 

(30,597)  4 

i5 

i3 

8 

4 

8 

36 

»6 

▼rank, 

(8*o63)  <0 

31 

8 

59 

to 

16 

IK 

111 

Man, 

(».637)  5 

s4 

17 

36 

5 

a4 

17 

38 

Jupiter, 

(4<8)  a 

36 

0 

7 

3 

33 

4i 

4i 

BatufS, 

(166)  3 

30 

IV 

13 

3 

35 

8 

5o 

Moon, 

(66,3 18)  ii 

i5 

a3 

a4 

11 

i5 

33 

*4 

* 

(56©)  IS 

9 

4a 

36 

10 

8 

3 

i3 

■ nods, 

r — 

(u6t-)  9 

>4 

36 

4 

9 

33 

46 

5r 

. _ « are,  given  as  deduced  both  from  the  uumbexe^f 

revolutions  stated  an  the  text,  and  from  -thr  same  as  corrected  by  the 


Thinilatioa^andJ(lkta. 


ml-  an  the  nnmbfft~of.-  complete  iwoh^nt*e$o«t 

' m if.  . . ■ - ■ ' ■ ' « » . % 


HIHW  l«uv  , *ut  via  1,111  VI  wv  WIWV  w.  bjw"  4fywq;w  u ■ imj 

it  vat  necessary  to  employ  the  numbers  of  revolution*,  givenfor  'pe 
vrhole  Age,  these  not  being  divisible  by  four,  and  also  to.  add  to  tjjtdf* 
ascertained  amount  of  movement  their  longitude  at  the  epoch  (see  beje^f* 
under  vv.  57, 58).  ryir , < 

54.  Thus,  also  are  ascertained  the  places  of  the  conjufti^M 
(gtghra)  and  apsis  (mandocca)  of  each  planet,  wlgph  haV^  op|d 
mentioned  as  moving  eastward ; and  in  like  manner  of  thJfati 
which  have  a retrograde  motion,  subtracting  the  result  frpm.:9 
whole  circle. 


The  places  of  the  apsides  and  nodes  have  already  been  given  ifort 
(under  vv.  41-44),  botli  for  the  commencement  of  the  Iron  Age,  and 
for  A.D.  1850.  The  place  of  the  conjunctions  of  the  three  superior 
planets  is,  of  course,  the  mean  longitude  of  the  sun.  In  the  case  of  the  - 
inferior  planets,  the  place  of  the  conjunction  is,  in  fact,  the  mean  place  of 
the  planet  itself  in  its  proper  orbit  and  it  is  this  which  we  have  given  for 
Mercury  and  Venus  in  the  preceding  table  : while  to  the  Hindu  appre- 
hension, the  mean  place  of  those  planets  is  the  same  with  that  of  the  sun. 

55.  Multiply  by  twelve  the  past  revolutions  of  Jupiter,  add 
the  signs  or  the  current  revolution,  and  divide  by  sixty ; the 
remainder  marks  the  year  of  Jupiter’s  cycle,  counting  from 
Vijayfc 

This  is  the  rule  for  finding  the  current  year  of  the  cycle  of  sixty 
yeans  which  is  in  use  throughout  all  India,  and  which  is  called  the  cycle 
of  Jupiter,  because  the  length  of  its  years  is  measured  by  the  passage 
of  that  planet,  by  its  mean  motion,  through  one  sign  of  the  zodiac. 
According  to  the  data  given  in  the  text  of  this  Siddhftnta,  the  length  of 
Jupiter’s  year  is  361J  0“  38m ; the  correction  of  the  btja  makes  it  about 
ljfm  longer.  It  was  doubtless  on  account  of  the  near  coincidenceof 
tliis  period  with  the  true  solar  year  that  it  was  adopted  as  a measure*^ 
time ; but  it  has  not  been  satisfactorily  ascertained,  so  far  as  we  are 
aware,  where  the  cycle  originated,  or  what  is  its  age,  or  why  it  was 
made  to  consist  of  sixty  years,  including  five  whole  revolutions  of  the 
planet.  There  was,  indeed,  also  in  use  a cycle  of  twelve  of  Jupiter's 
years,  or  the  time  of  one  sidereal  revolution  : see  below,  xiv.  I7r  Davis 
(As.  lies,  iii.  209,  etc.}  and  Warren  (K&la  Sanfcalita,  p.  107,  etc.)  have 
cheated  at  some  length  of  the  greater  cycle,  and  of  the  different  modea 
!.irf  reckoning  and  naming  its  years  usual  in  the  different,  provinces  of 
India.  . 

In  illustration  of  the  rule,  let  us  ascertain  the  y >ar  of  the  cycle  cor- 
responding to  the  present  year,  A.  D.  1859.  It  is  net  necessary  to  make 
the  calculation  from  the  creation,  as  the  rule  contemplates;  for,  since 
the  number  of  Jupiter’s  revolutions  in  the  period  of  1,080,000  yiars  is 
divisible  by  five,  a certain  number  of  whole  cycles,  without  a remainder, 
wQ)  have  elapsed  at  the  beginning  of  the  Iron  Age.  Theuwvolutjaos  of 
the  planet  sinqe^that  time,  as  stated  m the  table  test  givet^ar*  itepend 
it  is  in  the  Svff  sign  of  the  419th  revolution  ;the  reduction  bf-tfcewrhote 


HT  S&rya-Siddhdnta,  [i.06- 


MOUti  of  movement  to  signs  allow*  ns  that  the  current  year  u the 
5019th  since  the  epoch : divide  this  by  60,  to  cast -out  whole  cycles,  and 
the  remainder,  80,  is  the  number  of  the  year  in  the  current  cycle.  This 
Iteatne  nowhere  gives  the  nuncs  of  the  years  of  Jupiter,  but,  as  in  tho 
“case  of  the  months,  the  signs  of  the  zodiac,  and  other  similar  matters, 
assumes  them  to  be  already  familiarly  known  in  their  succession : wc 
accordingly  present  them  below.  We  take  them  from  Mr.  Davis’s  paper, 
alluded  to  aoore,  not  having  access  at  present  to  any  original  authority 
which  ^pntain,  them. 


i.  Vys/a. 

а.  Jays. 

з.  Manmatha. 
4 Dunnukha. 

5.  HemaUunba. 

б.  Vilamba. 

7.  VikArin. 

8.  CHTftrt. 

9 Plava. 

ia  Cabhakrt 

и.  Qubbana. 
vi.  Krodhin. 
i3.  VijrAvsau. 
i4  Mbhan. 

1 5.  Plavanga. 
i6l  Kilaka. 

17.  SAumyt. 

18.  SAdhArana. 

19.  Virodhakrt. 
aa  ParidhArin. 


*1.  PrnraAdin. 

?2.  Anando. 

23.  KAkshaaa. 

24  Auala. 

25.  ringala. 

26.  KAlayukta. 

27.  Siddharthin. 

28.  RAudro. 

29.  Durmati. 

30.  Dundubhi. 

31.  RudhirodgArin. 

32.  RaktAksha. 

33.  Krodhaoa. 

34  Kshaya. 

35.  Prabhava. 

36.  Vibhava. 

37.  Vukln. 

38.  Pramoda. 

39.  PrajApatL 

40.  Angiraa. 


41.  Crimukho. 

42.  BliAva. 

43.  Yu  van. 

44.  DhAfcar. 

45.  t^vara. 

46.  Bnhudhanya. 
47-  PrnniAthin. 

48.  Vikrama. 

49.  Bhryyo. 

5«l  CitrabhflniL 

51.  SubhAnu. 

52.  TAra^a. 

53.  PArthiva. 

54.  Vvaya. 

55.  Sarvejit. 

56.  SurvadhArin. 

57.  Virodhin. 

58.  Vikrtu. 

5i/  Khara. 

60.  Nandana. 


It  appears,  then,  that  the  current  year  of  Jupiter’s  cycle  is  named 
Ptaj&pati:  upon  di\iding  by  the  planet's  mean  daily  motion  the  j>art  of 
the  current  sign  already  passed  over,  it  will  be  found  that,  according  to 
the  text,  that  year  commenced  on  the  twenty -third  of  February,  18&0 ; 
or,  if  the  correction  of  the  hija  be  admitted,  on  the  third  of  April. 

Although  it  is  thus  evident  that  the  Shrya-Siddh&nta  regards  both 
the  existing  order  of  things  and  the  Iron  Age  as  having  begun  with 
Vyaya,  that  year  is  not  generally  accounted  as  the  first,  but  as  the 
twenty-seventh,  of  the  cycle,  which  is  thus  made  to  commence  with 
Prabhava.  An  explanation  of  this  discrepancy  might  perhaps  throw 
important  light  upon  the  origin  or  history  of  the  cycle. 

This  faethod  of  reckoning  time  is  called  (sec  below,  xiv.  I,  2)  the 
bdrfuupatya  mdna, 11  measure  of  Jupiter.” 


56.  The  processes  which  have  thus  been  stated  in  foil  detail, 
are  practically  applied  in  an  abridged  form.  The  calculation  of 
the  mean  place  of  the  planets  may  be  made  from  any  epocjj 
(yuga)  that  may  be  fixed  upon. 

57*  Now,  at  the  end  of  the  Golden  Age  Qcrta  yuga\  all  the 
planets,  by  their  mean  motion— excepting,  however,  their  nodes 
gnd  apsides  [rn^ndocca) — are  in  conjunction  in  tho  first  of  AricsA 
68<  The  moon's  apsis  (ucea)  is  in  the  first  of  Capricorn,  alid^ 
its  node  is  in  the  first  of  Libra ; and  the  rest,  which  have  been 


Translation  and  Notes. 


i.48.] 


ft* 


stated  above  to  bare  a alow  motion — tkeir  position  eantaofc  be 
expressed  in  whole  signs. 

It  is  curious  to  observe  how  the  SArya-Siddli&nta,  lest  it  should  seem 
to  admit  a later  origin  than  that  which  it  claims  in  the  second  verse  of 
this  chapter,  is  compelled  to  ignore  the  real  astronomical  epoch,  the 
beginning  of  the  Iron  Age;  and  also  how  it  avoids  any  open  .recog- 
nition of  the  lesser  cycle  of  1,080,000  years,  by  which  its  calculations 
ard  so  evidently  intended  to  bo  made. 

The  words  at  the  end  of  verse  56  the  commentator  interprets  to  mean : 
“from  the  beginning  of  the  current,  i.  c.,  the  Silver,  Age.”  In  this  he 
is  only  helping  to  keep  up  the  pretence  of  the  work  to  immemorial  an- 
tiquity, even  going  therein  beyond  the  text  itself,  which  expressly  says: 

11  from  any  desired  (ishtatas)  yuga .”  Possibly,  however,  we  have  taken 
too  great  a liberty  in  rendering  yuga  by  44  epoch,"  and  it  should  rather 
be  14  Age,”  i.  c.,  14  beginning  of  an  Age  ” The  word  yuga  comes  from 
the  root  yuj,  “to  join  ” (Latin,  jungo ; Greek,  £eCy wui  \ the  word  itself 
is  the  same  with  jugum , twyo*),  and  seems  to  have  been  originally  ap- 
plied to  indicate  a cycle,  or  period,  by  means  of  which  the  conjunction 
or  correspondence  of  discordant  modes  of  reckoning  time  was  kept  up ; 
thus  it  still  signifies  also  the  l us tr inn,  or  cycle  of  five  years,  which,  with 
an  intercalated  month,  anciently  maintained  the  correspondence  of  the 
year  of  3G0  days  with  the  true  solar  year.  From  such  uses  it  was  trans- 
ferred to  designate  the  vaster  periods  of  the  Hindu  chronology. 

As  half  an  Age,  or  two  of  the  lesser  periods,  are  accounted  to  have 
elapsed  between  the  end  of  the  (SoMcii  and  the  beginning  of  the  Iron 
Age,  the  planets,  at  the  latter  epoch,  have  again  returned  to  a position 
of  mean  conjunction  : the  moon’s  node,  also,  is  still  iu  the  first  of  Libra, 
hut  her  apsis  has  changed  its  place  half  a resolution,  to  the  first  of 
Cancer  (sec  almve,  under  vv.  2!»- 34).  The  positions  of  the  apsides  and 
nodes  of  the  other  planets  at  the  same  time  have  been  given  already, 
under  verses  41—14. 

The  Hindu  names  of  the  signs  correspond  in  signification  with  our  own, 
having  been  brought  into  India  from  the  West.  There  is  nowherg  ia 
this  work  any  allusion  to  them  as  constellations,  or  as  having  any  fixed 
position  of  their  own  in  the  heavens : they  are  simply  the  names  of  the 
successive  signs  (rdyi,  bha ) into  which  any  circle  is  divided,  and  it  is  left 
to  be  determined  by  the  connection,  in  any  ease,  from  what  point  they 
shall  be  counted.  Here,  of  course,  it  is  the  initial  point  of  the  fixed 
Hindu  sphere  (sec  above,  under  v.  27).  As  the  signs  are,  in  the  sequel, 
frequently  cited  by  name,  we  present  annexed,  for  the  convenience  of 
reference  of  those  to  whose  memory  they  are  not  familiar  in  the  order 
of  their  succession,  their  names,  Latin  and  Sanskrit  their  numbers,  and 
the  figures  generally  used  to  represent  them.  Those  enclosed  in 
brackets  do  not  chance  to  occur  in  our  text. 


i.  Ax tee,  HP  uunha^aja. 
a.  Taurus,  y vrthan. 

1.  Gemini.  Q mithun a. 

4.  dancer,  G karka,  karkatu. 

5.  Leo,  4}  [eifiAa]. 
ft  Vfago.  up  kanyd. 


7.  Libra,  tuld. 

8.  Scorpio,  III  [rrprifaj  dti. 

9.  Sagittarius,  / dArinus. 

10.  GapricornuB,  Vf  fnakara,  mjyx 

11.  Aquarius,  « kmMrn.  * 

ix  Pines.  H [mfna]. 


8&  S&rya-SiddJi&nta,  [L  58-" 

In  the  translation  given  above  of  the  second  half  of  verse  58,  not  h 
little  violence  is  done  to  the  natural  construction.  This  would 'seem 
require  that  it  be  rendered : “ and  the  rest  arc  in  whole  signs  (have  come 
to  a position  which  is  without  a remainder  of  degrees) ; they,  being  of 
slow  motion,  arc  not  stated  here.’1  Blit  the  actual  condition  of  things 
at  the  epoch  renders  necessary  the  former  translation,  which  is  that  of 
the  commentator  also.  Wc  cannot  avoid  conjecturing  that  the  natural 
rendering  was  perhaps  the  original  one,  and  that  a subsequent  alteration 
of  the  elements  of  the  treatise  compelled  the  other  and  forced  interpre- 
tation to  be  put  upon  the  passage. 

The  commentary  gives  the  positions  of  the  apsides  and  nodes  (those 
of  the  nodes,  however,  in  reverse)  for  the  epoch  of  the  end  of  the  Golden 
Age,  but.  strangely  enough,  both  in  the  printed  edition  and  in  our  manu- 
script, commits  the  blunder  of  giving  the  position  of  Saturn's  node  a 
second  time,  for  that  of  his  apsis,  and  also  of  making  the  seconds  of  the 

Eosition  of  the  node  of  Mars  12,  instead  of  24.  Wc  therefore  add  them 
clow,  in  their  correct  form. 

Motion  of  the  Apsides  and  Xodes  of  the  Planets , to  the  End  of  the  last 

Golden  Aw\ 

Plant*!.  Ajwi*.  Node. 

■ i 

; (rev.)  h ....  tr»'V.)  a .... 

i Sun.  ( 1 75  j •»  7 ah  i? 

Mercury,  (166)  5 i 4 48  (aao)  8 n 16  48 

Venus,  Mb)  n f’i  ai  c«  (4*18)  4 17  a5  48* 

Man*,  (9?)  J 1 14  a.*  b/i)  9 11  30  a4 

Jupiter,  Mo?)  o 9 o o (78)  8 8 56  24 

Saturn,  (i~)  7 19  '35  34  M99)  4 '■»<>  i3  13 

The  method  of  finding  the  liuan  places  of  the  planets  for  midnight 
011  the  prime  meridian  having  been  now  fully  explained,  the  treatise 
proceeds  to  show  how  they  may  be  found  for  other  places,  and  for  other 
times  of  the  duv.  To  this  the  first  requisite  is  to  know  the  dimensions 
of  the  earth. 

59.  Twice  eight  hundred  yojanas  are  the  diameter  of  the  earth : 
the  square  root  of  ten  times  the  square  of  that  is  the  earth’s  cir- 
cumference. 

60.  This,  multiplied  by  the  sine  of  the  co-latitude  (lambujyd\ 
of  any  place,  and  divided  by  radius  (iryfwJ),  is  the  corrected 
(sphvta)  circumference  of  the  earth  at  that  place 

There  is  the  same  difficulty  in  the  way  of  ascertaining  the  exactness 
of  the  Hindu  measurement  of  the  earth  as  of  the  Greok ; the  uncer- 
tain value,  namely,  of  the  unit  of  measure  employed.  The  eycjana  is 
ordinarily  dnidud  into  krofa,  “ cries”  (i.  c.,  distances  to  which  a certain 
cry  may  be  heard);  the  krorji  into  dhanus , 14 bow-lengths,”  or  danda, 
u poles;"  ami  these  again  into  Aosta , 41  cubits.”  By  its  origin,  the  latter 

* The  printed  edition,  by  an  error  of  the  pms,  gives  4. 


Translation  and  Notes. 


4.00.] 


I v 

jought  not  to  vary  far  from  eighteen  inches ; but  the  higher  measures 
^differ  greatly  in  their  relation  to  it.  The  usual  reckoning  makes  the 
.ytijana  equal  32,000  cubits,  but  it  is  also  sometimes  regarded  as  com- 
posed of  16,000  cubits;  and  it  is  accordingly  estimated  by  different  au- 
thorities at  from  four  and  a half  to  rather  more  than  ten  miles  English. 
This  uncertainty  is  no  merely  modem  condition  of  things : lliuen-Tlisang, 
the  Chinese  monk  who  visited  India  in  the  middle  of  the  seventh  cen- 
tury, reports  (see  Stanislas  Julien’s  Momoires  do  llioucn-Thsaug,  i.  59, 
etc.)  that  in  India  “according  to  ancient  tradition  a yojana  equals  forty 
It;  according  to  the  customary  use  qf  the  Indian  kingdoms,  it  is  thirty 
li;  but  the  yojana  mentioned  in  the  sacred  books  contains  only  sixteen 
K:w  this  smallest  yojana,  according  to  the  value  of  the  li  given  by  Wil- 
liams (Middle  Kingdom,  ii.  154),  being  equal  to  from  live  to  six  English 
miles.  At  the  same  time,  Iliiicn-Thsuiig  states  tin*  subdivisions  of  the 

H'ana  in  a maimer  to  make  it  consist  of  only  16,000  cubits.  Such 
ng  the  condition  of  things,  it  is  clearly  impossible  to  appreciate  the 
value  of  the  Hindu  estimate  of  the  earth's  dimensions,  or  to  determine 
how  far  the  disagreement  of  the  different  astronomers  on  this  point  may 
be  owing  to  the  difference  uf  their  standards  of  measurement.  Arva- 
bhatta  (see  Culcbruokcs  ilind.  Alg.  p.  xxxviii : Ks*ays,  ii.  468)  states  the 
earth’s  diameter  be  1050  ynjanas:  IJhuskar.i  (Siddh.-£ir.  viL  1)  gives 
it  as  1581  : the  latter  author,  in  hi*  Lilavati  (i.  K 6),  makes  the  yojana 
consist  of  32, 0(H)  cubits. 

The  ratio  of  the  diameter  t«»  the  circumference  of  a circle  is  here 


made  to  be  1 : v/10,  or  1 : 3.10*23,  which  is  no  very  near  approximation. 
It  is  not  a little  surprising  to  find  tin."  determination  in  the  same  treatise 
with  the  much  more  accurate  one  afforded  by  the  table  of  sines  given  in 
tlie  next  chapter  (vv.  17-21),  of  343*  : lo.iSho,  „r  1 : 3.14136  ; aiid  then 
farther,  to  find  the  former,  and  not  the  latter,  made  u&e  of  in  calculating 
the  dimensions  of  the  planetary  orbits  (see  below,  xii.  83).  Hut  the 
name  inconsistency  is  found  also  in  other  astronomical  and  mathematical 
authorities.  Thus  Arvahhatta  (see  t'olebrooke,  as  above)  calculates  the 
earth’s  circumference  from  its  diameter  by  the  ratio  7 : 22,  «»•*  1 : 3.14286, 
but  makes  the.  ratio  1 : */lu  the  basis  of  his  table  of  sines,  and  Brahma- 
gupta and  ^ridhnra  also  adopt  tin*  latter.  Hhaskarn.  in  stating  the 
earth’s  circumference  at  4907  yojanas.  is  very  near  the  truth,  since 
1581 : 4067  : : 1 : 3.14108  : his  Liiftvati  (v.  201 ) gives  7 : 22,  and  also, 
as  more  exact,  1230  : 3027,  or  1 : 3.1416.  This  subject  will  be  reverted 
to  in  connection  with  the  table  of  sines. 

The  greatest  circumference  of  the  earth,  as  calculated  according  to 
the  data  and  method  of  the  text,  is  5059.556  yojai.as.  The  astronomical 
yojana  must  he  regarded  as  an  independent  standard  of  measurement, 
by  which  to  estimate  the  value  of  tin*  other  dimensions  of  the  solar 
system  stated  in  this  treatise.  To  make  the  earth’s  ncan  diameter  cor- 
rect as  determined  by  the  Surya-Siddhanta,  the  yoiaua  should  equal 
4.94  English  miles ; to  make  the  circumference  correct,  it  should  tequal 
4.01  miles. 

The  rule,  for  finding  the  circumference  of  the  earth  upon  a parallel  of 
latitude  is  founded  upon  a simple  proportion,  viz.,  rad. : cos.  latitude : : 
circ.  of  earth  at  equator  : do.  at  the  given  parallel ; the  cosine  of  the 


IdHjjple  Ikmgf^n  effect,  tlie  radios  of  the  circle  of  latitude.  Radius  and  «■ 
.'come  of  latitude  are  tabular  numbers,  derived  from  the  table  to  be  ., 
given  afterward  (see  below,  ii.  17-21).  This  treatise  is  not  accustomed  - 
to  employ  cosines  directly  in  its  calculations,  but  has  special  names  for 
'the  complements  of  the  different  arcs  which  it  has  occasion  to  use. ' 
Terrestrial  latitude  is  styled  aksha , “axle,”  which  term,  as  appears  from 
xii.  42,  is  employed  elliptically  for  aluhonnati,  44  elevation  of  the  axle,” 
i.e.,  “of  the  pole:"  lamba,  coJatitude,  which  properly  signifies  “lag- 
ging, dependence,  falling  off,”  is  accordingly  tlie  depression  of  the  pole, 
or  its  distance  from  the  zenith,  pircctions  for  finding  the  co-latitude 
are  given  below  (iii.  13, 14). 

The  latitude  of  'Washington  being  38°  54',  the  sine  of  its  co-latitude 
is  2075';  tlie  proportion  3438  : 2075  : : 5050.04  : 3936.75  gives  us,  then, 
the  earth's  circumference  at  Washington  as  3030.75  yojanas. 

60. . . . Multiply  the  daily  motion  of  a planet  by  the  distance 
in  longitude  (de$&ntara)  of  any  place,  and  divide  by  its  corrected 
circumference ; 

61.  The  quotient,  in  minutes,  subtract  from  the  mean  position 
of  the  planet  as  found,  if  the  place  be  cast  of  the  prime  meridian 
(: reJchd ) ; add,  if  it  be  west ; the  result  is  the  planet’s  mean  po- 
sition at  the  given  place. 

The  rules  previously  stated  have  ascertained  the  mean  places  of  the 

Elancts  at  a given  midnight  upon  the  prime  meridian ; this  teaches  us 
ow  to  find  them  for  the  same  midnight  upon  any  other  meridian,  or, 
how  to  correct  for  difference  of  longitude  the  mean  places  Already  found. 
The  proportion  is : as  the  circumference  of  the  earth  at  the  latitude  of 
the  point  of  observation  is  to  the  part  of  it  intercepted  between  that 
point  and  the  prime  meridian,  so  is  the  whole  daily  motion  of  each 
planet  to  the  amount  of  its  motion  during  the  time  between  midnight 
on  the  one  meridian  and  on  the  other.  The  distance  in  longitude 
(def&ntara,  literally  “difference  of  region")  is  estimated,  it  witt^fcob- 
aerved,  neither  in  time  nor  in  arc,  but  in  yojanas.  How  it  is  ascertained 
is  taught  below,  in  verses  83-G5. 

The  geographical  position  of  the  prime  meridian  (rvAAd,  literally 
44  line  ")  is  next  stated. 

62.  Situated  upon  the  line  which  passes  through  the  haunt  of 
the  demons  ( rdkshasa ) and  the  mountain  which  is  the  seat  of  the 
gods,  are  Rohitaka  and  Avanu,  as  also  the  adjacent  lake. 

The  “ haunt  of  tlie  demons  " is  Lank&,  tlie  fabled  seat  of  ll&vana,  the 
chief  of  the  R&kshasas,  the  abduction  by  whom  of  It&ma’s  wife,  with 
the  expedition  to  LankA,  of  her  heroic  husbaud  for  her  rescue,  its  ac- 
complishment, and  the  destruction  of  Ii&vana  and  his  people,  form  the 
subject  of  the  epic  poem  called  the  R&m&yana.  In  that  poem,  and  to 
the  general  apprehension  of  the  Hindus,  LankA  is  tlie  island  Ceylon ; in 
t^e  astronomical  geography,  however  (see  below,  xii.  90),  it  is  a city, 
situated  upon  the  equator.  How  far  those  who  established  the  meridian 
.may  have  regarded  the  actual  position  of  Ceylon  as  identical  with  that 


i.  62.]  * Trmwlatiion  and  Ifates. 

assigned  tJKbnkk  might  not  be  easy  to  determine.  The '“  mat  of , the 
jpds”  te  Mcftnt  Mere,  situated  at  the  north  pole  (see  below,  xii.  34,v&fc.). 
The  meridian  is  usually  styled  that  of  LankA,  and  “at  LankA”  is  the 
ordinaiy  phrase  made  use  of  in  this  treatise  (as.  for  instance,  above,  v. 
60 ; below,  iii.  43)  to  designate  a situation  either  of  no  longitude  or  of 
no  latitude. 

But  the  circumstance  which  actually  fixes  the  position  of  the  prime 
meridian  is  the  situation  of  the  city  of  Ujjayini,  the  OJi/vi/  of  the  Greeks, 
the  modern  Ojein.  It  is  called  in  the  text  by  one  of  its  ancient  names, 
Avantl.  It  is  the  capital  of  the  rich  and  populous  province  of  MAlava, 
occupying  the  plateau  of  the  Viudhya  mountains  just  north  of  the 
principal  ridge  and  of  the  river  KarmadA  (Ncrbudda),  and  from  old 
time  a chief  scat  of  Hindu  literature,  science,  and  arts.  Of  all  the  cen- 
tres of  Hindu  culture,  it  lay  nearest  to  the  great  ocean-route  by  which, 
during  the  first  three  centuries  of  our  era,  so  important  a commerce  waa 
carried  on  between  Alexandria,  as  the  mart  of  Rome,  and  India  and  the 
countries  lying  still  farther  cast.  That  the  prime  meridian  was  made 
to  pass  through  this  city  proves  it  to  have  been  the  cradle  of  the  Hindu 
science  of  astronomy,  or  its  principal  seat  during  its  early  history.  Its 
actual  situation  is  stated  by  Warren  (Kala  Santa!  it  a,  p/9)  as  lat.  23° 
11 f 30"  N.,  long.  7f»°  f.3'  E.  from  Greenwich  : a later  authority,  Thorn- 
ton’s Gazetteer  of  India  (Loudon : 1357),  makes  it  to  he  in  lat.  23°  10'  N, 
long.  75°  47'  E. ; in  our  farther  calculations,  we  shall  assun\e  the  latter 
position  to  be  the  correct  one. 

The  situation  of  Uoliitaka  is  not  so  clear ; we  have  not  succeeded  iu 
finding  such  a place  mentioned  in  any  work  on  the  ancient  geography 
of  India  to  which  wr  have  access,  nor  is  it  to  he  traced  upon  Lassen’s 
map  of  ancient  India.  A city  called  Kohtuk,  however,  is  mentioned  by 
Thornton  (Gazetteer,  p.  83G)j  as  the  chief  place  of  a modern  British 
district  of  the  same  name,  and  its  situation,  a little  to  the  north-west  of 
Delhi,  in  the  midst  of  the  Ancient  Kurukshetra,  leads  us  to  regard  it  as 
identical  with  the  Roliltaka  of  the  text.  That  the  meridian  of  LankA 
was  expressly  recognized  as  passing  over  the  Kurukshetra,  the  memora- 
ble site  of  the  great  battle  described  by  the  Mah&bharata,  seems  clear. 
Bh  Askar  a (Siddh.-f irn  Gan.,  xii.  2)  describes  it  as  follows:  “the  line 
which,  passing  above  Lanka  and  Ujjayini,  and  touching  the  region  of 
the  Kurukshetra,  etc.,  goc*  through  Mem— that  line  is  by  the  wise 
regarded  as  the  central  meridian  (uiadkyarvkhd)  of  the  earth.'1  Our 
own  commentary  also  explains  sannihitam  saruh , w hich  wc  have  transla- 
ted “adjacent  lake,”  as  signifying  Kurukshetra.  Warren  (as  above) 
takes  the  same  expression  to  be  the  name  of  a city,  which  seems  to  us 
highly  improbable ; nor  do  we  see  that  the  w..rd  rarer*  can  properly  be 
applied  to  a tract  of  country : we  have  therefore  thought  it  safest  to 
translate  literally  the  words  of  the  text,  confessing  that  we  do  not  know 
to  what  they  refer. 

If  Rohltuka  and  Rolituk  signify  the  same  place,  wc  have  here  a 
measure  of  the  accuracy  of  the  ilindu  determinations  of  longitude; 
Thornton  gives  its  longitudo  as  76°  38',  or  61'  to  the  east, of  Ujjayini. 

The  method  by  which  an  observer  is  to  determine  his  distance  from  - 
the  prime  meridian  is  next  explained. 

6 


42 


[i-  as- 


, tyL  When,  in  a total  eclipse  of  the  moon,  tb^pnergence 
{urmlhna)  takes  place  after  the  calculated  time  for  its  occur- 
rence, then  the  place  of  the  observer  is  to  the  cast  of  the  central  . 
meridian ; 

64.  When  it  takes  place  before  the  calculated  time,  his  place 
is  to  the  west:  the  same  thing  may  be  ascertained  likewise  from 
(he  immersion  (nimilana).  Multiply  by  the  difference  of  the  4 wo 
times  in  nfidis  the  corrected  circumference  of  the  earth  at  the 
place  of  observation, 

65.  And  divide  by  sixty : the  result,  in  yojanas,  indicates  the 
distance  of  the  observer  from  tbs  meridian,  to  the  eftst  or  to  the 
west,  upon  his  own  parallel ; and  by  means  of  that  is  made  the 
correction  for  difference  of  longitude. 

Choice  is  made,  of  course,  of  a lunar  eclipse,  and  not  of  a solar,  for 
the  purpose  of  the  determination  of  longitude,  because  its  phenomena, 
being  unaffected  by  parallax,  are  seen  everywhere  at  the  same  instant  of 
absolute  time;  and  the  moments  of  total  disappearance  and  first  reap- 
pearance of  the  moon  in  a total  eclipse  are  farther  selected,  because  the 
precise  instant  of  their  occurrence  i<  observable  with  more  accuracy  than 
that  of  the  first  and  last  contact  of  the  moon  witli  tlic  shadow!  For 
the  explanation  of  the  term-  here  used  see  tin'  chapters  upon  eclipses 
(below,  iv-vi). 

The  interval  between  the  computed  and  observed  time  being  ascer- 
tained, the  distance  in  longitude  (drfantam)  is  found  by  the  simple 
proportion : as  the  whole  number  of  uadis  in  a day  (sixty)  is  to  the  inter- 
val of  time  in  nhdis,  so  is  the  circumference  of  the  earth  at  the  latitude 
of  the  point  of  observation  to  the  distance  of  that  point  from  the  prime 
meridian,  measured  on  the  parallel.  Thus,  for  instance,  the  distance  of 
Ujjjayini  from  Greenwich,  in  time,  being  5**  8m  fc*,  and  that  of  Washing- 
ton from  Greenwich  5h  8ni  ll8  (Am.  Xaut.  Almanac),  that  of  Ujjayinl 
from  Washington  is  1011  11 111  IIIs,  or,  in  Hindu  time,  ?5n  2fcv  1P.8,  or 
26M718:  and  by  the  proportion  <50  : 25.471k  : : 393G.75  : 1671.28,  we 
obtain  1671.28  yojanas  as  the  distance  in  longitude  (derdntara)  of 
Washington  from  the  Hindu  meridian,  the  constant  quantity  to  be  em- 
ployed in  finding  the  imam  places  *»f  the  planets  at  Washington. 

We  might  have  expected  that  calculators  so  expert  as  the  Hindus 
would  employ  the  interval  of  time  directly  in  making  Ylu;  correction  for 
difference  of  longitude,  instead  of  reducing  it  first  to  its  value  in  yojanas. 
That  they  did  not  measure  longitude  in  our  manner,  in  degrees,  etc.,  is 
•owing  to  tins  fact  that  they  seem  never  to  have  thought  of  applying  to 
die  globe  of  the  earth  the*  system  of  measurement  by  circles  and  divi- 
sions of  circles  which  they  used  for  the  sphere  of  the  heavens,  but,  even 
when  dividing  the  earth  into  zones  (see  below,  xii.  59-06)  reduced  all 
Jfclieir.  distances  laboriously  to  yojanas. 

66/  The  succession  of  the  week-day  (vdra)  takes  place,  to  the 
east  of  the  meridian,  at  a time  after  midnight  equal  to  the  differ-' 
j&m  of  longitude  in  nfidts;  to  the  west  of  the  meridian,  at  a 
corresponding  time  before  midnight. 


i.  67.]  Translation  and  Notes.  48 

This  verse  appears  to  os.  to  be  an  astrological  precept,  asserting  the  * 
regency  of  the  ann  and  the  other  planets,  in  their  order,  over  the- suc- 
cessive -portions  of  time  assigned  to  each,  to  begin  everywhere  at  the 
same  instant  of  absolute  time,  that  of  their  true  commencement  upon 
the  prime  meridian ; so  that,  for  instance,  at  Washington,  Sunday,  as 
the  day  placed  under  the  guardianthip  of  the  sun,  would  really  Virgin  at 
eleven  minutes  before  two  on  Saturday  afternoon,  by  local  time.'  The 
commentator,  however,  secs  in  it  merely  an  intimation  of  what  moment 
of  local  time,  in  places  cast  and  west  of  the  meridian,  corresponds  to 
the  true  beginning  of  the  day  upon  the  prime  meridian,  and  he  is  at 
much  pains  to  defend  the  verse  from  the  charge  of  being  superfluous 
and  unnecessary,  to  which  it  is  indeed  liable,  if  that  be  its  only  meaning. 

The  rules  thus  far  given  have  directed  us  only  how  to  find  the  mean 
places  of  the  planets  at  a given  midnight.  The  following  verse  teaches 
the  method  of  ascertaining  their  position  at  any  required  hour  of  the 
day.  . 4_ 

67.  Multiply  the  mean  daily  motion  of  a planet  by  the  number 
of  nail  is  of  the  time  fixed  upon,  and  divide  by  sixty : subtract 
the  quotient  from  the  place  of  the  planet,  if  the  time  be  before 
midnight;  add,  if  it  be  after:  the  result  is  its  place  at  the  given 
time. 

The  pro|Mirti»u  is  as  fallows : as  the  number  of  n&dis  in  a day  (sixty) 
is  to  those  in  the  interval  between  midnight  and  the*  time  for  which  the 
mean  place  of  the  planet  i*  sought,  so  is  the  whole  daily  motion  of  the 
planet  to  its  motion  during  the  interval:  and  the  result  is  additive  or 
subtractive,  of  course,  according  a?*  the  time  fixed  upon  is  after  or  before 
midnight. 

In  order  to  furnish  a practical  test  of  the  accuracy  of  this  text-bopk  / 
of  astronomy,  and  of  its  ability  to  yield  correct  results  at  the  present 
time,  we  have  calculated,  b\  die  rule  giien  in  this  verse,  the  mean  longi- 
tudes of  the  piuncts  for  a time  after  midnight  of  the  first  of  Januaiy, 
•I860,  on  the  meridian  of  I'jjayint,  which  is  equal  to  the  distance  m 
time  of  the  meridian  of  Washington,  viz.  lij11  ■jy'''  1^.8.  or  0d.4k2453 ; and- 
wc  present  the  results  in  the  annexed  table.  The  longitudes  arc  given 
as  reckoned  from  the  vernal  equinox  of  that  date,  which  we  make  to  bo 
distant  18°  o*  tS'VJ.i  from  the  point  established  by  the  S& rya-Sidjftftota 
as  the  beginning  of  the  Hindu  sidereal  sphere ; this  is  (see  belowvcbap. 
viii)  10*  east,  of  t L'iscium.  Wo  have  ascertained  the  mean  places  both 
as  determined  by  the  text  of  our  Siddli&nta,  and  by  the  same  with  the 
correction  of  the  bija.  Added  are  the  actual  mean  places  at  the  time 
designated : those  of  the  primary  planets  have  b<  en  found  from  Le  Ver- 
ricr's  elements,  presented  in  Biots  treatise,  as  c.cod  above  ;*  those  of 
the  moon,  and  of  her  ap«is  and  node,  were  kindly  furnished  us  from  tho 
office  of  tile  American  Nautical  Almanac,  at  Cambridge.  . 


* We  would  warn  our  readers,  howover,  of  a serious  error  of  (lie  press  in  the 
table  as  given  by  Biot;  as  the  yearly  motion  of  the  earth,  read  1,295,977.38, instSSf"” 
of . . . 972.88.  * ■ - -•  - - . - - - 


44  Sfoya-SiddhdrUa,  [i.  67- 

$ Jfetii  Longitudes  of  the  Planets,  Jan . Ilf,  I860,  midnight,  at  Washington . 


According  to  Sdrya-SiddliAnla : 

According 

to 

1. 

j PllAlt. 

text. 

with  btja. 

modemi 

| 

98 

1 

18 

I* 

21  < 

96 

i 

18 

if 

21 

■ 

IOO 

1 

5 

M 

6 

j Mercury, 

i55 

1 

3o 

i48 

25 

39 

i5i 

28 

20 

! Venus, 

339 

54 

55 

334 

57 

18 

336 

i3 

36 

Mars, 

192 

36 

5 

192 

36 

5 

*97 

26 

32 

Jupiter, 

104 

7 

22 

IOO 

48 

56 

io3 

35 

17 

j Saturn, 

i?8 

*7 

11 

1 33 

i4 

49 

i37 

10 

10 

j Moon, 

9 

4 

9 

9 

4 

9 

■ 12 

41 

23 

J " apsis, 

327 

5o 

24 

326 

1 1 

11 

326 

47 

35 

" node, 

3ia 

29 

5i 

3io 

5o 

38 

3l2 

48 

10 

In  the  next  following;  table  is  farther  given  a view  of  the  errors  of  the 
Hjpdu  determinations — botli  the  absolute  errors,  as  compared  with  the 
actual  mean  place  of  each  planet,  ami  the  relative,  as  compared  with 
the  place  of  the  sun,  to  which  it  is  the  aim  of  the  Hindu  astronomical 
systems  to  adapt  the  elements  ol'  the  other  planets.  Annexed  to  each 
error  is  the  approximate  date  at  which  it  was  nothing,  or  at  which  it 
will  hereafter  disappear,  ascertained  by  dividing  the  amount  of  present 
error  by  the  present  yearly  loss  nr  gain,  absolute  or  relative,  of  each 
planet;  excepting  in  the  case  of  the  moon,  where  wc  have  made  allow- 
ance, according  to  the  formula  used  by  the  American  Nautical  Almanac, 
for  the  acceleration  of  her  motion. 


Error 8 of  the  Mean  Longitudes  of  the  Planets , as  calculated  according  to 
the  Sun/a-Siddhanta . 


To  complete  the  view  of  the  planetary  motions,  and  the  statement  of 
the  elements  requisite  for  ascertaining  their  position  in  the  sky,  it  only 
remains  to  give  the  movement  in  latitude  of  each,  its  deviation  from  the 
general  planetary  path  of  the  ecliptic.  This  is  done  in  the  concluding 
verses^of  the  chapter. 

68.  The  ngoon  is,  by  its  node,  caused  to  deviate  from  the  limit  of 
declination  (krdnti),  northward  and  southward,  to  a distance, 
wh$n  greatest,  of  an  eightieth  part  of  the  minutes  of  a circle; 


i.  70.]  Translation  and  Nates . 46 

69.  Jupiter,  to  the  ninth  part  of  tbfit  multiplied  by  two; 
Mare,  to  the  name  amount  multiplied  by  three ; Mercury,  Venus, 
%nd  Saturn  are  by  their  nodes  caused  to  deviate  to  the  same 
amount  multiplied  by  four. 

70.  So  also,  twenty -seven,  nine,  twelve,  six,  twelve,  and  twelve, 
multiplied  respectively  by  ten,  give  the  number  of  minutes  of 
mean  latitude  (i vikshepa] ) of  the  moon  and  the  rest,  in  their  order. 

The  deviation  of  tlie  planets  from  the  plane  of  the  ecliptic  is  here 
stated  in  two  different  ways,  which  give,  however,  the  same  results; 
thus: 


Moon, 

aifkx/ 

“ flo  " 

= 

270' 

nr 

27'  X 

TO 

= 370* 

= 4°  3o' 

Mars, 

Tx3 

= 

90' 

or 

9'  X 

IO 

= 90' 

= i®  3</ 

Mercury, 

370' 

V * 4 

= 

1 If/ 

or 

ta'  X 

IO 

120* 

= 3° 

Jupiter, 

270' 

TX1 

= 

fa' 

or 

O'  X 

IO 

= fit/ 

= IB 

Venue, 

■v"x4 

= 

1 an' 

or 

ii'  X 

IO 

= I jo' 

= 2° 

Saturn, 

370' 

9X4 

= 

130* 

or 

13'  X 

10 

— 1 30' 

= 2° 

The  subject  of  the  latitude  of  the  planet*  w completed  in  verses  6-8, 
and  verse.  57,  of  the  following  chapter;  the  former  passage  describes 
the  manner,  and  indicates  the  direction,  in  which  the  node  produces  its 
disturbing  effect ; the  latter  give*  the  rule  for  calculating  the  apparent 
latitude  of  a planet  at  any  point  in  its  rc\ elution. 

There  is  a little  discrepancy  her  ween  the  two  specifications  presented 
in  these  verses,  as  regards  the  description  of  the  quantities  specified: 
the  one  states  them  to  be  the  amounts  of  greatest  [jhirama)  deviation 
from  the  ecliptic;  the  other,  of  mean  (//it/ Jhtfa)  deviation.  Both  de- 
scriptions are  also  somewhat  inaccurate.  The  first  is  correct  only  with 
reference  to  the.  moon,  and  the  two  terms  require  to  be  combined,  in 
order  to  be  made  applicable,  to  the  other  planets.  The  moon  has  its 
greatest  latitude  at  00°  from  its  node,  and  this  latitude  is  obviously 

SVto  the  inclination  of  its  orbit  to  the  ecliptic;  for  although  its 
ute  distance  from  the  ecliptic  at  this  point  of  its  course  varies,  as 
docs  its  distance  from  the  earth,  on  account  of  the  eccentricity  of  its 
orbit,  and  the  varying  relation  of  the  line  of  N apsides  to  that  of  its 
nodes,  its  angular  distance  remains  unchanged.  So,  to  a;  observer  sta- 
tioned at  the  sun,  the  greatest  latitude  of  any  one  >f  tlje  primary  planets 
would  be  the  same  in  its  successive  revolutions  from  node  to  node, 
and  equal  to  the  inclination  of  its  orbit.  But  its  greatest  latitude  as 
seen  from  the  earth  is  very  different,  in  different  revolutions,  both  on 
fcconnt  of  the  difference  of  its  absolute  distance  from  the  ecliptic 
when  at  the  point  of  greatest  removal  from  it  in  the  two  •halves  of  its 
orbit,  and,  much  more,  on  account  of  its  varying  distance  from  the  earuiT" 
The  former  of  these  two  causes  of  variation  was  not  recognised  by  the 


Hindus:  in  this  treatise,  At  least,  tho  distance  of  the  node  from  tho 
apsis  (mandocca)  is  not  introduced  as  an  element  into  the  process  for 
determining  a planet V latitude.  The  other  eanse  of  variation  is  duly 
allowed  for  (see  below,  ii.  57).  Its  effect,  in  the  case  of  the  three  supe- 
rior planets,  is  to  make  their  greatest  latitude  sometimes  greater,  and 
sometimes  less,  than  the  inclination  of  their  orbits,  according  as  the 
planet  is  nearer  to  us  than  to  the  sun,  or  tho  contrary ; hence  the  values 
given  in  the  text  tor  Mars,  Jupiter,  nud  Saturn,  as  they  represent  the 
meau  apparent  values,  as  latitude,  of  the  greatest  distance  of  each  planet 
from  the  elliptic,  should  nearly  equal  the  inclination.  In  the  case  of 
Mercury  and  Venus,  also,  the  quantities  stated  are  the  mean  of  the  differ- 
ent apparent  values  of  the  greatest  heliocentric  latitude?  but  this  mean 
is  of  course  loss,  and  for  Mercury  very  much  less,  than  the  inclination. 
Ptolemy,  in  the  elaborate  discussion  of  the  theory  of  the  latitude  con- 
tained in  the  thirteenth  book  of  his  Syntax  is,  has  deduced  the  actual 
inclination  of  the  orbits  of  the  two  interior  pluucts:  this  the  Hindus  do 
not  seem  to  have  attempted. 

We  present,  below  a comparative  table  of  the  inclinations  of  the 
orbits  of  the  planets  as  determined  by  Ptolemy  and  by  modern  astrono- 
mers, with  those  of  the  Hindus,  so  far  as  given  directly  by  tho  Shrva- 
Siddh&nta. 

Inclination  of  the  Orbits  otm  the  Planets , according  to  Different  Authorities . 


1 PI  a 11  t t. 

.Siirya-SuMhunta  ■ 

Ptolemy. 

j Modem*.  | 

Mercury, 

• 1 

a 

7 

B 

1 ; 

0 

8 i 

Venus, 

3 

3o 

. 3 

al 

31 

‘ Mar*, 

i • 3n  | 

( 

i « 

5i 

5 i 

| Jupiter, 

! . 1 

f 

3o 

! « 

18 

40  j 

l Saturn, 

\ a 1 

a 

3o 

■ 2 

>9 

28 

! Moon. 

4 3o 

5 

‘ 5 

H 

4«  ! 

The  verb  in  verses  OS  and  (»*.».  which  wo  hn\o  translated  “ caused  to 
deviate,"  is  vi  kshij/yate,  litoral }y  hurled  awa\."  disjiritur ; from  it  is 

derived  tho  term  used  iri  this  t.ivaiM*  to  signify  celestial  latitude,  rikshe - 
pa,  a disject  ion."  Tho  Hindus  measure  this  latitude,  however,  as  wo 
shall  have  occasion  to  notice  more  particularly  hereafter,  upon  a circle 
of  declination,  and  not  upon  21  secondary  to  the  ecliptic.  I11  the  words 
chosen  to  designate  it  is  seen  the  influence  of  the  theory  of  the. node's 
action,  as  stated  in  the  first  verses  of  the  next  chapter.  The  forcible 
removal  is  from  the  point  of  declination  (kranti.  “gait,”  or  apukrama, 
“withdrawal,”  i.  c.,  from  the  celestial  equator)  which  the  planet  ought 
at  the  time  to  occupy,  ;i*  ■ 

The  title  given  to  this  first  Chapter  ( adhikh.ru , “subject,  heading”)  is 
madhj/atnAdhikAra,  which  we  have  represented  in  the  title  by  “mean 
motions  of  the  planets,”  although  it  would  be  more  accurately  rcudere^ 
by  11  mean  pigeon  of  the  planet? that  is  to  say,  the  data  and  methods 
Msaquisite  for  ascertaining  their  mean  places.  Sow  follows  the  speuAlA* 
dfrk&ra,  “ chapter  of  the  true,  or  corrected,  places  of  the  planets.” 


ii.  8.]  Translation,  and’ Soles.  47 


CHAPTER  II. 

or  THE  TBUE  PLACES  OP  THE  PLANETS. 

OovmmM-8,  causes  of  the  irregularities  of  the  planetary  motions;  4-5,  disturb- 
ing influence  of  the  apsis  and  conjunction;  0-8,  of  the  node;  9-11,  different 
degree  of  irregularity  of  the  motion  of  the  different  planets;  12-18,  different 
kinds  of  planetary  motion;  14,  purjwso  of  this  chapter;  16-18,  rule  for  con- 
structing the  table  of  sines;  17-22,  table  of  sines;  22-27,  table  of  versed  sines; 

28,  inclination  of  the  ecliptic,  and  rule  for  finding  the  declination  of  any  point  in 
It;  29-30,  to  ffmfthe  sine  and  cosine  of  Ike  anomaly;  81-32,  to  find,  by  interpo- 
lation, the  sine  or  versed  sine  corresponding  to  any  given  arc;  33,  to  find,  in  like 
manner,  the  arc  corres|)on<ling  to  a given  sine  or  versed  sine;  34-37,  dimensions 
of  the  epicycles  of  the  planets;  38,  to  find  the  true  dimensions  of  the  epicycle  at 
any  point  in  the  orbit  ; 39,  to  find  the  equation  of  the  apMs.  or  of  the  centre; 
40-42,  to  find  the  equation  of  the  <*•  injunction,  or  the  annual  equation;  43-46, 
application  of  these  equation*  in  finding  the  true-  places  of  the  different  placets ; 

40,  correction  of  the  pluce  of  n planet  for  difference  between  mean  and  apparent 
solar  time;  47-49,  how  to  correct  the  daily  motion  of  tlif*  planets  for  the  effect  of 
the  npsis;  60-51,  the  sumo  for  that  of  the  conjunction;  51-55.  retrogradalion  of 
the  lesser  planets;  68,  correction  of  the  place  of  the  node ; 57-58,  to  find  the  celes- 
tial latitude  of  a planet,  mid  it*  declination  as  affected  by  latitude;  59,  to  find  the 
length  of  tlic  day  of  any  planet;  *30.  to  find  the  radius  of  the  disjnttl  circle; 
61-03,  to  find  the  duy-binc.  and  the  respective  length  of  the  day  and  night ; 64, 
to  find  the  number  of  fc-tvrbm*  traversed  by  a phmtf,  and  of  days  elapsed,  since 
the  commencement  of  tlit*  current  revolution ; o.V  t».  find  The  u'ffa ; 86,  to  find 
the  current  lunar  day,  and  the  time  in  u m"  u given  instant : 67-69,  of  the  divisions 
of  the  lunar  month  coiled  kurotio. 

1.  Forms  of  Time,  of  invisible  shape,  stationed  in  the  zodiac 
(bhagauu),  culled  the,  eonjunclion  (■■'"jhixcca),  apsis  ( mandocca ), 
and  node  (pdfo),  arc  causes  of  the  motion  of  the  planets. 

2.  The  planets,  attached  to  these  beings  by  cords  of  air,  are 
drawn  away  bv  them,  with  the  right  and  left  hand,  forward  or 
backward,  according  to  nearness,  toward  tlieir  own  place. 

8.  A wind,  moreover,  culled  prormtor  (/ muuha ) impels  them 
toward  their  own  apices  {ticca) ; being  draw  n away  forward  and 
backward,  they  proceed  by  u varying  motion. 

4.  The  so-called  apex  (ucoj),  when  in  the  half-orbit  in  front  of 
the  planet,  draws  the  planet  lbrward:  in  like  manner,  when  in 
the  half-orbit  behind  the  planet,  it  draws  it  1 ackward. 

6.  When  the  planets,  drawn  away  by  their  apices  {ucca),  move 
forward  in  their  orbits,  the  amount  of  the  motiou  so  caused  ia 
called  their  excess  ( dfutna ) ; when  they  move  backward,  -it  is 
called  their  deficiency  (rno). 

In  these  verses  ia  laid  before  us  the  Hindu  theory  of  the  general— ■ 
suture  of  the  forces  which  produce  the  irregularitiesof  the  apparent 


43 


J&ry&Siddhdnta,  [ii.  5. 

motions,  regarded  as  beinjfthe  real  motions,  of  the  planets.  The  world- 
wide difference  between  the  spirit  of  the  Hindu  astronomy  and  that  of 
the  GreejMs  not  less  apparent  here  than  in  the  manner  of  presentation 
of  the  elements  in  the  last  chapter : the  one  is  purely  scientific,  devis- 
ing methods  for  representing  and  calculating  the  observed  motions,  and 
attemj&ng  nothing  farther the  other  is  not  content  without  fabricating 
k a fantastic  and  absurd  theory  respecting  the  superhuman  powers  which 
occasion  the  movements  with  which  it  is  dealing.  The  Ilindu  method 
has  this  comcnient  peculiarity,  that  it  absolves  from  all  necessity  of 
adapting  the  disturbing  forces  to  one  another,  and  making  them  form 
one  consistent  system,  capable  of  geometrical  representation  and  mathe- 
matical demonstration ; it  regard  the  planets  as  actually  moving  in 
circular  orbits,  and  the  whole  apparatus  of  epicycles,  given  later  in 
the  chapter,  as  only  a device  for  estimating  the  amount  of  the  force, 
and  of  its  resulting  motion,  exerted  at  any  given  point  by  the  disturb- 
ing cause. 

The  commentator  gives  two  different  explanations  of  the  provector 
wind,  spoken  of  in  the  third  verse : one,  that  it  is  the  general  current, 
mentioned  below,  in  xii.  73,  as  impelling  the  whole  firmament  of  stars, 
and  which,  though  itself  moving  westward,  drives  the  planets,  in  some 
"unexplained  way,  towards  its  own  apex  of  motion,  in  the  cast;  the 
other,  that  a separate  vortex  for  each  planet.,  railed  provector  on  account 
of  its  analogy  with  that  general  current,  although  not  moving  in  the 
same  dirystion,  carries  them  around  in  their  orbits  from  west  to  cast, 
leaving  only  the  irregularities  of  their  motion  to  be  produced,,  by  the 
disturbing  forces.  This  latter  we  regard  as  the  proper  meaning  of  the 
text:  neither  is  very  consistent  with  the  theory  uf  the  lagging  behind 
of  the 'planets,  given  abo\r,  in  i.  2.i,  20,  as  the  explanation  of  their 
apparent  eastward  motion.  The  commentary  also  states  more  explicitly 
the  method  of  production  of  the  disturbance : a cord  of  air,  equal  in 
length  to  the  orbit  of  each  planet  less  the  disk  of  the  latter  itself;  is 
attached  to  the  extremities  of  its  diameter,  and  passes  through  the  two 
hands  of  the  bring  stationed  at.  the  point  of  disturbance;  and  he  always 
drawB  it  toward  himself  by  the  shorter  of  the  two  parts  of  the  cord. 
The  term  ticca,  which  wc  have  translated  “apex,"  applies  both  to  the 
apsis  (manefa,  rnavdocca , 4‘ apex  of  slow c&l  motion" — the  apogee  in  the 
case  of  the  sun  and  moon,  the  aphelion,  though  not  recognized  as  such, 
in  the  case  of  the  other  planets),  and  to  the  conjunction  [ftghra,  yfpA- 
rocca,  44 apex  of  swiftest  motion").  The  statement  made  of  the  like 
effect  of  the  two  upon  the  motion  of  the  planet  is  liable  to  cause  diffi- 
culty, if  it  bo  not  distinctly  kept  in  mind  that  the  Hindus  understand 
by  the  influence  of  the  disturbing  cause,  not  its  acceleration  and  retarda- 
tion of  the  rate'  of  the  planet's  motion,  but  its  effect  in  giving  to  the 
planet  a position  in  advance  of,  or  behind,  its  mean  place.  It  may  be 
well,  for  the  sake  of  aiding  some  of  our  readers  to  form  a dearer  appre- 
hension of  the  Ilindu  view  of  the  planetary  motions,  to  expand  and 
illustrate  a little  this  statement  of  the  effect  upon  them  of  the  two 
principal  disturbing  forces.  <• 

First,  as  regards  the  apsis.  This  ia  the  remoter  extremity  of  the  major 
eiia  of  the  planet’s  proper  orbit,  and  the  point  of  its  slowest  motion. 


ii.  s.]  Translation  and  Notes.  49 

Upon  passing  this  point,  the  planet  begins  to  fall  behind  its  mean  place, 
but  at  the  same  time  to  gain  velocity,  so  that  at  the  quadrature  il  is 
farthest  behind,  but  is  moving  at  its  mean  rate ; during  the  next  quail- 
rant  it  gains  both  in  rate  of  motion  and  in  place,  until  at  the  perigee,  or 
perihelion,  it  is  moving  most  rapidly,  and  has  made  up  what  it  before 
lost,  so  that  the  mean  and  true  places  coincide.  Upon  passing  t£at  point 
again,  it  gains  upon  its  mean  place  during  the  tir.-t  quadrant,  and  loses 
what  it  thus  gained  during  the  second,  until  mean  and  true  place  again 
coincide  at  the  apsis.  Thus  tint  equation  of  motion  is  greatest  at  the 
apsides,  and  nothing  at  the  quadratures  while  tin'  equation  of  place  is 
greatest  at  the  quadratures,  and  nothing  at  the  apsides ; and  thus  tin ■ 
planet  is  always  behind  its  mean  place,  while  passing  from  the  higher  to 
the  lower  apsis,  ami  always  in  advance  of  it  while  pas>ing  from  the 
lower  to  tlm  higher;  that  is,  it  is  constantly  drawn  away  from  its  mean 
place  toward  the  higher  apsis,  mandorcu. 

In  treating  of  the.  ell'ccl.  of  the  conjunction,  the  r"ihr<jrcu,  we  have  to 
distinguish  two  hinds  of  ea>t  *.  With  Mern in  and  V»niis  (s--e  above, 
i.  20,  31,  32  j,  the  rev*  Jut  ion  of  the  eoiijuieM  ion  tak«-s  the  place,  in  tins 
Hindu  system  as  in  the  tireek.  of  that  of  the  planet  ilsi-lf,  the  conjunc- 
tion being  regarded  as  making  tlm  circuit  of  the  xndiue  in  the  same 
time,  ami  in  the  same  direction,  as  the  planet  really  rcxolxts  about  the 
sun;  while  the  mean  place  of  these  planets  is  always  that  of  the  sun 
itself.  While,  therefore,  the  conjunction  is  making  the  half-tour  of  tlm 
heavens  eastward  from  the.  sun,  the  planet  is  making  its  eastward  elon- 
gation and  returning  to  the  sun  again,  being  all  the  time  in  advance 
of  il*  mean  plan-,  the  sun  ; when  the  emijunctuui  reaches  a point  in  tlm 
heavens  nppo.of.e  to  tin-  sun.  the  planet  i-  in  hs  inferior  conjunction,  ur 
at  its  mean  place;  during  the  other  halt  of  tin-  revolution  of ’the.  con- 
junction, when  it  ir*  nearest  tin:  plane!  up  mi  the  western  side,  tin*  latter 
is  making  and  losing  its  western  elongation,  or  U behind  its  moan  place. 
Accordingly,  as  stated  in  the  text,  tin-  planet  i>  o'hMaiiily  drawn  away 
from  its  mean  place,  tins  sun,  toward  that  side  of  the  heavens  in  which 
the  conjunction  is.  * 

Once,  more,  as  concerns  the  superior  planets.  The  revolutions  as- 
signed to  these  hv  the  Hindus  are  their  true  revolution*;  their  mean 
places  are  their  mean  helioi  entric  h uigit  tides : ami  the  place  of  the.  con- 
junction (fiy/irocca)  of  each  i>  the  mean  place  of  the  sun.  Since  they 
move  but  slowly,  as  compared  with  the  miii,  it  i-*  their  conjunction 
which  approaches,  overtakes,  and  passes  them,  ami  not  they  tlm  eon- 
junction.  Their  time  of  slowest,  motion  is  w hen  in  opposition  with  the 
pud;  of  swiftest,  when  in  conjunction  with  him:  from  opposition  on  to 
conjunction,  therefore,  or  while  the  sun  is  api  coaching  them  from  be- 
hind, they  arc,  with  constantly  increasing  veh  *ity  of  motion,  all  the 
while  behind  their  mean  places,  or  drawn  away  irom  them  in  the  direc- 
tion of  tlie  sun ; but  no  sooner  has  the  sun  overtaken  and  passed  them, 
than  they,  lca\ing  with  their  hu»t.  rapid  motion  the  point  of^coinci 
donee  between  mean  and  true  plaee,  are  at  once,  in  advance,  and  e«*n- 
tinue  *o  be  so  until  opposition  is  reached  again;  that  i}  to  say,  they 
arc  still  dr*  win*  aw  ay  from  their  mean  place  in  the  direction  of  iLfet 
conjunction. 


7 


' The  wfcrds'used  in  vene  S for  “ excess  ” and  **  deficiency,”  or  for  adpi- 
tire  and  subtractive  equation,  mean- literally  "wealth”  (dhana)  and 
“debt*  (raa)i 

6.  In  liko  manner,  also,  the  node,  R&hu,  by  its  proper  force, 
causes  the  deviation  in  latitude  (vikshepa)  of  the  moon  and  tho 
other  planets,  northward  and  southward,  from  their  point  of 
declination  (apakrama). 

7.  When  in  the  half-orbit,  behind  the  planet,  tho  nodo  causes 
it  to  deviate  northward ; when  in  the  half-orbit  in  front,  it  draws 
it  away  southward. 

8.  fn  the  ease  of  Mercury  and  Venus,  however,  when  the 
node  is  thus  situated  with  regard  to  the  conjunction  (tfyhra), 
these  two  planets  arc  caused  to  deviate  in  latitude,  in  the  manner 
stated,  by  the  attraction  exercised  by  the  node  upon  the  con- 
junction. 

The  name  Ralm,  l>y  which  tho  ascending  noilc  is  here  designated,  is 
properly  mythological,  ami  belongs  to  the  monster  iu  the  heavens,  which, 
by  the  ancient  Hindus,  as  by  more  than  one  oilier  people,  was  believed 
to  occasion  the  eclipses  of  the  sun  and  moon  l>y  attempting  to  devour 
them.  The  won!  which  wo  have  translated  “force”  is  rankus,  more 
properly  “ rapidity,  violent  motion:"  in  employing  it  here,  the  text  evi- 
dently intends  to  suggest  an  etvmnlogy  for  nil, in,  as  coming  from  the  root 
rah  or  m»l,  “to  rush  on”:  with  this  smut*  root  Welicr  (Ind.  Stud.  i. 
272)  has  connected  tho  group  of*  words  in  which  r&hu  seems  to  belong. 
For  the  Hindu  table  ropL*cting  Hahn,  stu  Wilmn’s  Vishnu  Puraivi,  p.  7ri. 
The  moon  "s  defending  nude*  was  also  person ilii»d  in  a similar  way,  under 
the  name  of  Ketu,  but  to  this  no  reference  is  made  in  tho  present  treatise. 

The  description  of  the  effect  of  tho  node  upon  the  movement,  of  the 
planet  is  to  be  understood,  in  a manner  analogous  with  that  of  the  effect 
of  the  apices  in  the  nest  preceding  passage,  as  referring  to  the  direction 
in  which  the  planet  is  maae  to  deviate  from  tho  •*<*liptii\  and  not  to  that 
in  which  it  is  moving  with  reference  to  the  ecliptv-.  From  the  ascending 
node  around  to  tho  descending,  of  course,  or  while  tho  node  is  nearest  to 
the  planet  from  behind,  tho  hiiitudu  is  northern ; in  the  oth<*r  half  of  tho 
revolution  it  is  southern. 

For  an  explanation  of  some  of  the  terms  used  here,  see  the  note  to  the 
last  passage  of  the  preceding  chapter. 

As,  in  the  case  of  Mercury  and  Venus,  the  revolution  of  iha  conjunc- 
tion takes  the  place  of  that  of  the  planet  itself  in  its  orbit,  it  iracoe&aiy, 
in  order  to  give^e  node  its  proper  effect,  that  it  be  made  to  exercise 
its  influence  upon  tho  planet  through  tho  conjunction.  The  commen- 
tator gives  hiiuself  here  not  a little  trouble,  in  the  attempt  to  show  why 
Mercury  and  Venus  should  in  this  resect  constitute  an  exception  to  the 
general  rule,  but  without  being  able  to  make  out  a very  plausible  cafe. 

. ;■  i* 

, . 9.  Owing,  to  the  greatness  of  its  orb,  the  san.jp  drawn  Away 
«*ly,  a very  little;  the  moon,  by  reason  of  the  smallness  of  its 
is  drawn  away  much  more ; 


ii.  14.]  Translation  and  Notes.  51 

10.  Mara  and  the  reBt,  on  account  of  their  small  aisSe^are,  by 
the  supernatural  beings  (< daivata ) called  conjunction  fctghroccn) 
and  apsis  {tnandocca),  drawn  away  very  far,  being  caused  to 
vacillate  exceedingly. 

11.  Ilencc  the  excess  (dhana)  and  deficiency  (rna)  of  these 
latter  is  very  great,  according  to  their  rate  of  motion,  'fhus  do 
the  planets,  attracted  by  those  beings,  move  in  the  firmament, 
carried  ou  by  the  wind. 

The  dimensions  of  tlic  miii  and  moon  are  staled  below,  in  iv.  1 ; those 
of  the  other  planets,  in  vii.  13. 

We  have  ventured  t«>  translate  at  the  end  of  the  tenth  verso, 

as  it  is  given  above,  because  that  translation  seemed  so  much  better  to 
suit  the  requirements  of  the  sense  than  Lhe  better-supported  rendering 
“ caused  to  move  u ith  exceeding  velocity.1'  In  so  doing,  we  have  assumed 
that  tins  noun  m/n,  of  which  the  word  in  question  i«  a denominative,  re- 
tains something  of  the  proper  meaning  of  the  root  vij,  u to  tremble” 
from  which  it  comes. 

12.  The  motion  of  the  planets  i*  of  eight  kinds:  retrograde 

( vdkrd j,  somewhat  jvtnigi-sidu  rransxerso  (kutila). 

slow  (inn/idif),  very  plow  liuHnditfara),  iwu  also,  very 

swift  (rh/Itr'dar'i).  and  swill  ('.'Vo"). 

13.  Of  these,  the  very  swill  {uft\'ljhrti)%  llial  called  swift,  the 
slow,  the  very  slow,  tin*  even-all  those  ii\c  are  forms  of  the 
motion  called  direct  (/>■) ; tin;  somewhat  retrograde  is  retrograde. 

This  minute  elasMli.-aiiuii  of  1 1n-  phases  »»i  a planet’s  motion  is  quite 
gratuitiMis,  so  far  a>  rhi>  Siddliiini.'  i-  c-iik  ern-d.  for  tin*  Terms  here  given 
do  not  mice  ne«-ur  afi^rwar-1  in  die  l-\'i,  with  the  single  exception  of 
mkrtti  which,  with  h+  •l«:i,ivati\i>.  is  in  n« muv.pe-iit  u>e  to  designate 
retrogradiitimi.  V*r  dm*  the  >inmi-iit:iry  l.ibn  th»*  trouble  to  explain 
the  precise.  •lillhreiicr-s  of  the  kind'*  of  uimimi  spocifii'd.  According  to 
Mr.  IloiMngton  (oriental  .Wmii-micr  [Tamil  and  KnglidiJ,  Jntfna:  184S, 
p.  133),  aiitirakra  is  applied  to  tlie.  motion  of  a piano,  when,  in  retro- 
grading. it  parses  into  a preceding  sign.  Krom  the  ckt'silication  given  in 
the  seeond  of  1 h«-  two  verges  it  will  be  noticed  that  kutllu  is  omitted:  ac- 
cording to  the  eoiiuiLeututor.  it  is  meant  to  bo  included  among  the  forms 
of  retrograde  motion : wo  have  conjectured,  however,  that  it  might  possi- 
bly be  used  to  designate  the  motion  of  a planet  when,  being  for  the 
moment-' Stnl imuin  in  respect  to  longitude.  and  accordingly  neither  ad- 
vancing nor  retrograding,  ii  is  changing  its  lat'iudc;  and  wc  have  trans- 
lated the.  word  accordingly. 

14.  By  reason  of  this  ami  that  rate  of  motion,  from  day  to 
day,  the  planets  thus  conic  to  an  accordance  with  their  observed 
places  (rf?r) — tli is,  their  correction  (sft/iu/!kamna)7 1 shall  care- 
fully explain. 

'Having  now  disposed  of  matters  of  general  theory  afld  preliminary 
explanation,  the  proper  subject  of  this  chapter,  the  calculation  of  the  true* 
(itphiila)  from  the  moan  places  of  tl&e  different  planets,  is  ready  to  lie 


52  S(irya-Siddhdnta}  [ii.  14- 

taken  up.  And  the  first  thing  in  order  is  the  tabic  of  sines,  by  means' of 
which  all  the  after  calculations  are  performed. 

15.  The  eighth  part  of  the  minutes  of  a sign  is  called  the  first 
sine  (jy&rdha ) ; that,  increased  by  tlic  remainder  left  .after  sub- 
tracting from  it  the  quotient  arising  from  dividing  it  by  itself,  is 
the  second  sine. 

1(>.  Thus,  dividing  the  tabular  sines  in  succession  by  the  first, 
and  adding  to  them,  in  each  case,  what  is  left  after  subtracting 
the  quotients  Irom  the  first,  the  result  is  twenty-four  tabular 
sines  ( in  order,  as  follows: 

17.  ‘Two  huinlred  and  twenty-live;  lour  hundred  and  forty- 
iiiiu1;  six  hundred  and  seventy-oiu*;  eight  hundred  and  ninety  ; 
eleven  hundred  and  live:  thirteen  hundred  and* fifteen ; 

18.  Fifteen  hundred  and  twenty:  seventeen  hundred  and  nine- 
teen : nineteen  hundred  and  ten  ; two  thousand  and  ninety-three ; 

19.  Two  thousand  two  hundred  and  sixty-seven  ; two  thous- 
and four  hundred  and  thirty -one:  two  thousand  Jive  hundred 
and  eighty-live:  two  thousand  seven  hundred  and  twenty-eight; 

20.  Two  thousand  eight  hundred  and  fifty-nine ; two  thousand 
nine  hundred  and  so venty -eight ; three  thousand  and  eighty- 
four;  three  thousand  one  hundred  and  seventy -seven  ; 

21.  Three  thousand  two  hundred  and  ti fly-six : three  thousand 
three,  hundred  and  twenty -one:  three  thousand  three  hundred 
and  seventy-two:  three  thousand  four  hundred  and  nine.; 

22.  Tli ii v thousand  four  hundred  and  thirty-one;  three  thous- 
and four  huinlred  and  thirty -eight.  Subtracting  these,  in  re- 
verSL'd  order,  from  the  hall-diameter,  gives  the  tubular  versed- 
sines  {xitk ra ni a /?/' wJuapin duhi) : 

23.  Seven:  twenty-nine:  sixtv-six;  one  hundred  and  seven- 
teen; one  hundred  and  eighty -iwo;  two  hundred  and  sixty -one ; 
three  hundred  and  fifty-four ; 

24.  Four  hundred  and  sixty ; five,  hundred  and  seventy-nine ; 
seven  hundred  and  ten;  eight  hundred  and  fifty-three:  one 
thousand  and  seven:  eleven  hundred  and  scveniy-onc; 

25.  Thirteen  hundred  and  forty-five ; fifteen  hundred  and 
twenty-eight;  seventeen  hundred  and  nineteen;  nineteen  hund- 
red and  eighteen ; 

26.  Two  thousand  one  hundred  and  twenty-three  ; two  thous- 
and three  hundred  and  thirty-three;  two  thousand  five  hundred 
and  forty-eight ; two  thousand  seven  hundred  and  sixty-seven ; 

27.  Two  thousand  nine  hundred  and  eighty-nine;  three  thous- 
and two  hundred  and  thirteen ; three  thousand  four  Hundred  and 
thirty <aighl:  these  are  the  versed  sines.* 

AVf;  first  present,  in  thq  following  tabic,  in  a form  convenient  for  refer* 
and  usc/thts  Hindu  sines  and  versed  sines,  with  the  arcs  to  which 
they  belong,  the  latter  expressed  both  in  minutea  and  in  degrees  and 
minutes.  To  facilitate  the  practical  use  of  the  table  in  making  calcuLv 


Translation  and  Notes . 


53 


ii.2 1.] 

tions  After  the  Hindu  method,  we  have  added  a column  of  the  difference* 
of  the  sines,  and  have  farther  turned  the  sines  themselves  into  decimal 
parts  of  die  radius.  For  the  purpose  of  illustrating  the  accuracy  of  the 
table,  we  have  also  annexed  the  true  values  of  the  sines,  in  minutes,  as 
found  by  our  modern  tables.  Comparison  may  also  be  made  of  the  deci- 
. mal  column  with  the  corresponding  values  given  in  our  ordinaiy  tables 
of  natural  sines. 

Table  of  Sines  and  Versed  Sines . 


54 


Sdrya-SidiMnta,  [ii.  27. 

and  fiQjftn,  through  tho  wholo  serios,  any  fractiou  larger  than  a' half  being 
coAfited  as  one,  and  a smaller  fraction  being  rejected.  In  the  majority  of 
cases,  as  is  made  evident  by  the  table,  this  process  yields  corroct  results : 
we  have  marked  in  the  column  of  “ true  sines”  with  a plus  or  minus  sign 
such  modern  values  of  the  sines  as  differ  by  more  than  half  a minute 
from  those  assigned  by  the  Hindu  table. 

It  is  not  to  be  supposed,  however,  that  the  Hindu  sines  were  originally 
obtained  by  tin*  process  described  in  the  text.  That  process  was,  in  all 
probability,  suggested  by  observing  the  successive  differences  in  tho  values 
of  the  sines  a*  already  determined  by  oilier  methods.  NY»r  is  it  diflicult 
to  discover  what  wore  those  methods;  they  arc  indicated  by  the  limita- 
tion of  the  table  to  arcs  differing  from  one  another  by  3°  45',  and  by 
what,  we  know  in  general  of  the  trigonometrical  methods  of  the  Hindus. 
The  two  inaiu  principles,  by  the.  aid  of  which  tins  greater  portion  of  all 
the  Hindu  calculations  are  made,  arc.  on  tin*  one  hand,  tho  equality  of  the 
square  of  the  hypoTlionuse  in  a right-angled  triangle  to  ihe  sum  of  the 
squares  of  the  other  two  sides,  and,  «»n  the  other  hand,  the  proportional 
relation  of  the  corresponding  pari*  «»f  similar  triangle*.  The  iirsi  of  these 
principles  gave  the  Hindu*  the  sine  uf  the  complement  nf  any  are  of 
which  rhe  sine  wa*  already  Icn-ovii.  il  bring  equal  In  the  square  root  of 
the  difference  between  the  square*  of  radii1.*  and  of  the  given  sine,  'this 
led  farther  to  Ihe  rule  lor  limling  the  vrr*rd  sine,  which  is  given  above  in 
the  text:  it  was  pjainly  equal  to  tin-  difference  between  the  sine  comple- 
ment and  radius.  Again,  the  comparison  iff  similar  triangles  showed  that 
the  chord  of  an  arc  was  a nn-an  proportional  between  its  \eiscd  sine  and 
the  diameter ; and  this  In]  to  a method  of  finding  the  sine  of  half  any 
arc  of  which  tin-  sine  wa*  known:  it  wa*  rqiinl  in  half  the  square  root 
of  the  product  of  tlir  diaiiu  ter  into  tin*  \ers«-d  .*iur.  That  the  Hindus 
had  deduced  tin*  hid  rule  do. « i.nt  dinvily  appear  from  tin*  text  of  (Ms 
Siddhanta,  nor  from  tin:  cnimm-ntary  of  Jtanganatha.  which  is  the  one 
given  by  our  manuscript  and  by  lln*  pul»ii*li«:«l  ediiimi ; bul  il  is  distinctly 
stated  in  the  commentary  which  I >u\  is  had  in  hi*  hands  ( A*,  lies.  ii.  247) ; 
and  it  might  be  confidently  a*Miined  to  be  kimwp  up.-ii  the  evidence  of 
the  table  itself;  for  the  principles  and  ruh*a  which  we  have  here  stated 
would  give  a table  just  <in,Ii  a*  the  one  hen*  cnn*rrueled.  Tlio  sino 
of  00a  was  obviously  «*qual  in  radius  an*!  t li**  sine  of  :m'J  to  half  radius: 
from- the  first  could  b.-  found  the  si’.es  of  4.V,  :U»\  ami  31° 

from  the  latter,  lho-.e  of  i:i°.  7°  30#,  and  I.V.  The  sines  thus  ob- 
tained would  give  those  of  th-.  is  implement  ary  arcs,  or  iff  Jo',  82° 
30',  78°  45',  75°,  etc.;  and  tins  sino  of  75u,  again,  would  give  those  of 
37°  30'  and  18°  45'.  By  continuing  lln.*  same  processes,  the  table  of  sines 
would  soon  be  made  complete  tor  tho  twenty-four  divisions  of  tho  quad- 
rant; but  these  processes  could  yield  nothing  farther,  unless  by  intro- 
ducing fractions  of  minutes;  which  was  undesirable* because  the  symmetry 
of  the  table  would  thus  be  destroyed,  and  no  corresponding  advantage 
gained;  the  table  wo*  already  sufficiently  ex  tended  to  furnish,  by  inter- 
polation, the  sines  intermediate  between  those  given,  with  all  the  accu- 
racy which  Mins  Hindu  calculations  required. 

If,  now,  an  attempt  were  made  to  ascertain  a law  of  progression  for 
the  series,  and  to  device  an  empirical  rule  by  which  its  members  might 


65 


21.  2$.]  . ‘ Translation  and  Notes. 

be  developed,  the  one  from  the  other,  in  order,  nothing,  could  fee  more 
natural  then  to  take  the  differences  of  the  successive  sines,  and  the 'differ- 
ences of  those  differences,  as  we  have  given  them  under  the  headings  A' 
and  A"  in  the  annexed' table. 


Hindu  Sines , with  their  First  and  Second  Differences . 


No. 

Sine. 

m 

Sine. 

a'  ■ 

A* 

s 

0 

000 

32*5 

■ 

12 

243i 

1 54  ! 

10 

1 

2 

3 

4 

aa5 

449 

«7l 

890 

224 

272 

219 

2L5 

; ’ 
3 

1 : 

i3 

J 4 

ir> 

16 

u58*i 

>728 

*859 

*978 

i43 
i3i  : 
119  j 

10G  ! 

11 

12 

12 

13 

5 

G 

7 

8 

V 

10 

1 10O 
i3i5 

1 5ao 
1719 
19m 
J1.9J 

210 

20r» 

T97 

191 

i83 

; : 
: 

■ ri 

! v 

’7 

iB 

’9 

20 

; 7i 

i va 

3o84 
3177 
3»V» 
33a  1 
Vn 
34»»9 

V3  1 
1 79 

! G5  ; 

; 37 

j2  ! 

1 

13 

14 

14 

14  ! 
r4 

1 r> 

11 

22(17 

■ 1- 1 

• m 

! 

3.ni 

ir» 

1 j 

-i43  1 

i04 

i 10 

1 2.4 

3138 

1 7 

1 

With  these  differences  before  hint,  an  acute  observer  could  hardly  fail 
to  notice  the  remarkable*  fact  that  the  differences  of  the  second  order  in- 
crease as  the  sines:  ami  that,  each,  in  fact,  is  about  the  -jj-^th  part  of  the 
corresponding  sine.  Now  lot  the  successive  sines  be  represented  by  0,  sf 
s',  s"\  s"’\  and  so  on : and  lot  7 c«|iia!  yi-,  or  * : let  the  first  differ- 

ences be  d -- 0,  d'  - s — /,  d'f,z=g  ‘'— s'\  etc.  The  sec- 
ond differences  w ill  be : - stj  = •)' - (/,  - *'•/  =(/"—  d\  - s"q  =cf'M—  d'ry 
etc.  These  last  expressions  give 

d"  =</  — *7  =s  — s'/ 

d " =i/f  — S 'if  = « — sq  — *'7 

d'"=  t/"-  s",y  -=  — *7  - *'7  -#"7,  etc. 

Hence,  also, 

*'  = s j-  c/'  = « + 9 - «7 

«'*  =*'  + //"  -•=*'  -f-  .t  — «f/  - if  y 

a*  f—  i d 1 1 ,==  a — *7  — a '7  — 

and  so  on,  according  to  the  rule  given  in  the  text. 

That  the  second  differences  in  the  \ allies*  of  the  si ues  were  proportional 
to  the  sines  themselves,  was  probably  known  to  the  Uindus  only  by  ob- 
servation. ITad  their  trigonometry  sufficed  to  demonstrate  it,  they  might 
easily  have  constructed  a much  more  complete  and  accurate  table  off 
sines.  Wc  add  the  demonstration  given  by  Dolan  bre  (llistoire  de  l’As- 
trouomie  Ancienne,  Lgk58),  front  whom  the  wews  hero  expressed  hav*, 
been  substantially  taken. 

Let  a be  any  arc  in  the  series,  and  put  3°  45'  ji  n.  Then  sin  (<w—  n), 
ein  a,  sin  (a  a),  will  bo  three  successive  terms  in  the  series ; sin 
a—  sin  (a— «),  and  sin  (a  + n)  — sin  a,  will  be  differences*  of  the  ftret 
order ; and  their  difference,  sin  (a  + n)  + sin  (0  — n)  — 2 sin  a,  will 
be  a difference  of  the  second  order.  But  this  lost  expression,  by  virtue 


of  the  formula  Jt  sin  (a±n)  = sin  a cosn  =b  cos  a sin  ft,  reduces  to 


a cos  n -r-E—  2 sin  a,  or  2 


(cosn  \ . 

s--1  “ 


sin  a.  That  is  to  say,  the 


second  difference  is  equal  to  the  product  of  the  sine  of  the  arc  a into  a 
certain  constant  quantity,  or  it  varies  as  the  sine.  When  n equals  3°  45', 
as  in  the.  Hindu  table,  it  is  easy  to  show,  upon  working  out  the  last  cx- 

Iiressiou  by  means  of  the  la  dies,  that  the  constant  factor  is,  as  stated  by 
)elambre,  instead  of  being  as  empirically  determined  by 

the  Hindus. 


It  deserves  to  bo  noticed,  that  tlio  commentary  of  Rangnn&thu  recog- 
nizes the  dependence  of  the  rule  given  iu  the  text  upon  the  value  of  the 
second  differences.  According  to  him,  however,  it  is  by  describing  a 
circle  upon  the  ground,  laving  off  the  arcs,  drawing  the  sines,  and  deter- 
mining their  relations  by  inspection,  that  the  method  is  obtained.  Tho 
differences  of  the  sim-s,  lie  sax*,  will  he  observed  to  decrease,  while  the 


differences  of  those,  differences  increase:  and  it  will  bo  noticed  that  the 


last  second  difference  is  15'  in''  48"\  A proportion  is  then  made:  if  at 
the  radius  tlie  second  difference  is  of  this  value,  what  will  it  be  at  any 
sine!  or,  taking  the  first  sine  as  an  example,  3-138' : If/  16"  48'"  : : 225 
: 1.  Nothing  can  be  clearer,  however,  than  that  this  pretended  result  of 
inspection  is  one  of  cal  nil  at  ion  merely.  It  would  be  utterly  impossible 
to  estimate  by  the  eye  the  value  of  a difference  with  such  accuracy,  and, 
were  it  possible,  tliat  difference  would  he  found  very  considerably  removed 
from  the  om*  here  given,  being  actually  only  about  14'  45".  The  value 
15' 10' 48"' is  ic*»iimej  only  in  order  1o  make  its  ratio  to  the  radius 
exactly 

The  earliest  substitution  of  the  sines,  in  calculation,  for  the.  choids, 
which  wep1  employed  by  the  Greeks,  is  generally  attributed  (see  WhewelPa 
History  of  the  Inductive  Sciences,  ]».  111.  ch.  iv.  8)  to  the  Arab  astron- 
omer Albategnius  (ul-Tiattam),  who  flourished  in  the  latter  part  of  the 
ninth  century  of  our  era.  It  can  lnirdlv  admit  of  question,  however, 
that  sines  hail  already  at  that  time  ln;en  long  employed  by  the  Hindus. 
And  considering  tlie.  derivation  by  the.  Aral*  from  India  iff  their  system 
of  notation,  and  of  so  many  of  the  clcmi'ius  of  their  mathematical 
science,  it  would  seem  not  unlikely  that  tic*  nr^t  hint  of  this  so  conveni- 
ent and  practical  improvement,  of  the  methods  of  calc.ulalion  may  also 
have  come  to  them  from  that  country.  This*  cannot  be  asserted,  however, 
with  much  confidence,  because  the  substitution  of  the  sines  for  the  chords^ 
seems  no  natural  and  easy,  that  it  may  well  enough  have  been  hit  upon 
independently  by  the  Arabs ; it  is  a matter  for  astonishment,  as  remarked 
by  Delambre  (Histoire  do  P Astronomic  du  Moyen  Age,  p.  12),  that 
Ptolemy  himself,  who  came  so  near  it,  should  have  failed  of  it.  If 
Albategnius  got  the  Miggostion  from  India,  he,  at  any  rale,  got  no  more 
than  that.  His  table  of  sines,  much  more,  compete  than  tliat  of  the 
Hindus,  was  made  from  Ptolemy's  tabic  of  chords,  by  simply  halving  them. 
The*  method,  too,  whydi  in  India  remained  comparatively  barren,  led  to 
valuable  developments  in  the  hands  of  this  Arab  mathematicians,  who 
went  on  by'degrees  to  form  also  tables  of  tangents  and  co-tangents,  secants 
andWsecant* ; while  the  Hindus  do  not  Beem  to  have  distinctly  appreci- 
ated the  significance  even  of  the  cosine. 


it,  SB.]  Ttonffltiok  and  Notes.  \ ?$7 

In  this  passage,  the  sine  h called  jy&rdha,  “ half-chord ; ” hereafter, 
however,  that  term  does  not  once  occur,  but  jy&  “ chord  ” (literally 11  Mr- 
string”)  is  itself  employed,  as  are  also  its  synonyms  jtv&,  m&unrika,  to 
denote  the  sine.  Tlie  usage  of  Albatcgnius  is  the  same.  The  sines  of  the 
table  are  called  pinda , orjydpinda , “the  quantity  corresponding  to  the 
sine.”  The  term  used  for  versed  Bine,  ulkramajyd,  means  “ inverse-order 
sine,”  the  column  of  versed  sines  being  found  by  subtracting  that  of 
sines  in  inverse  order  from  radius. 

The  ratio  of  the  diameter  to  the  circumference  involved  in  tlie  expres- 
sion of  the  value  of  radius  by  3438'  is,  as  remarked  above  (under  i.  59, 
00),  1 : 3.1 4180.  The  commentator  asserts  that  value  to  come  from  the 
ratio  1250  : 3927,  or  1 : 3.1410,  and  it  is,  in  fact,  the  nearest  whole  num- 
ber to  the  result  given  by  that  ratio.  If  tlie  ratio  were  adopted  which 
has  been  stated  above  (in  i.  59),  of  I : «/l0,  the  value  of  radius  would  be 
only  341 5'.  It  is  to  be  observed  with  regard  to  this  latter  ratio,  that  it 
could  not  possibly  be  the  direct  result  of  any  actual  process  adopted  for 
ascertaining  the  value  of  the  diameter  l'mni  that  of  the  circumference,  or 
the  contrary.  It  was  probably  fixed  upon  by  the  Hindus  because jfjt 
looked  and  sounded  well,  and  was  at  the  same  time  a sufficiently  near 
approximation  to  the  truth  to  be  applied  in  cases  where  exactness  was 
neither  attainable  by  their  methods,  nor  of  much  practical  consequence; 
os  in  fixing  the  dimensions  of  the  earth,  and  uf  the  planetary  orbits. 
The  nature  of  the  system  of  notation  of  the  Hindis,  and  their  constantly 
recurring  extraction  of  square  roots  in  their  trigonometrical  processes, 
would  cause  the  suggestion  to  them,  much  more  naturally  than  to  the 
Greeks,  of  this  artificial  ratio,  as  not  far  from  the  truth  ; and  their  science 
was  just  of  that  character  to  choose  fur  some  iim**.  a relation  expressed  iu 
a manner  so  simple,  and  of  an  aspect  so  systematical,  even  though  known 
to  be  inaccurate.  We  do  not  n-gard  the  ratio  in  question,  although  so 
generally  adopted  among  the  Hindu  astronomers,  as  having  any  higher 
value  and  significance  than  this. 

- 28.  The  sine  of  greatest  declination  is  thirteen  hundred  and 
ninety-seven;  by  this  multiply  any  sine,  and  divide  bv  radius; 
the  arc  corresponding  to  the  result  is  said  to  be  the  declination. 

The  greatest  declination,  that  is  to  say,  the  inclination  of  the  plane  of 
the  ecliptic,  is  here  stated  to  be  24°,  13!) 7'  being  the  sine  of  that  angle. 
The  true  inclination  in  the  year  300  of  our  era,  which  we  may  assume 
to  have  been  not  far  from  the  time  when  the  Hindu  astronomy  was 
established,  was  a little  less  than  23°  40',  so  that  the  error  of  the  Hindu 
determination  was  then  more  than  20' : at  present,  it  is  32'  34".  The 
value  assigned  by  l’tolcmy  (Svnlaxis.  i)  lo  the  inclination  was  between 
23°  50'  and  23°  ;i2#  30" ; an  error,  as  compared  v\  ill  its  true  value  in 
tlie  time  of  Uippuivims.  of  only  about  7'. 

The  second  half  of  the  verse  gives,  in  the  usual  vague  and  elliptical 
language  of  the  treatise,  the  rule  for  finding  the  declination  of  any  given  " 
point  ill  the  ecliptic.  We  have  not  in  this  case  supplied  the  elligegs  in 
our  translation,  because  it  could  not  be  done  succinctly?  or  without 
introducing  nu  element,  that  of  the  precession,  which  possibly  wf$  uut 
taken  into  account  when  the  rule  was  made.  See  what  is  said  upon  this 

j 


o 8 


[ii.  28- 


S(krya-SiddMhta, 


• 

pgjjfoct  under  verses  9 and  10  of  the  next  chapter.  The  “sine”  em- 
prafed  in,  of  course,  the  nine  of  the  distance  from  the  vernal  equinox,  or 
of  the  longitude  as  corrected  hy  the  precession. 

The  anntacd  figure  will  explain  the  rule,  and  the  method  of  itn 
demonstration. 


Let  ACE  represent  a quadrant  of  the  plane  of  the  equatorial,  and 
A(?Oa  quadrant  of  that  of  the  ecliptic,  AC  being  the  line  of  their 
intersection  : then  A V in  the  equinoctial  colure,  I’  K the  solstitial,  G E, 
or  the  angle  (ICE,  the  incliuation  of  the  ecliptic,  or  the  greatest  decli- 
nation (puramapakrama,  or paramnkmnti),  and  CD  its  sine  ( parama - 
krdntijyd).  Let  S he  the  position  of  the  sun,  and  dravfthc.  circle  of 


declination  PH:  S II,  or  the  angle 
SCH,  is  the  declination  of  the  sun 
at  that  point,  and  SF  the  sine  of 
declination  [krAntijyA).  From  S and 
F draw  S B and  F ii  at  right  angles 
to  A C ; then  S B is  the  sine  of  the 
ill'  AS,  or  of  the  sun's  longitude. 
Rilt  GCI)  and  SHF  are  similar 

SAt-anglctl  triangles,  having  their 
jglcs  at  C and  Ii  each  equal  to  the 
inclination.  TUi  rrfon-  < ' < S : < » I > : : 

SB:SF:  and  S F = ; 


, ....  sin  iin  l.Xsin  long, 

that  is,  sm  dec].  = - - - • 

Ji 

The  sam**  result  is,  by  our  modern 
methods  obtained  ilirectly  from  the  formula  in  right-angled  spherical 
trigonometry;  sine «=sin«  sin or,  in  the  triangle  ASll,  right-allied 
at  II,  sin  Sil=-sin  S A bin  S AH. 


29;  Subtract  the  longitude  of  a planet  from  that  of  its  apsis 
(nvMidoeca);  so  also,  subtract  it  from  that  of  its  conjunction 
(figlba);  ue  remainder  is  its  anomaly  (kendra) ; from  that  is 
(Ott&d  the  quadrant  (noth) ; from  this,  the  base-sine  (bhujajyA), 
audUkeerise  that  of  tneperpendicuiar  tfcoti). 

m In  an  odd  (vithama)  quadrant,  the  base-sine  is  taken  from 
the  fjprt  past,  the  perpendicular  from  that  to  come ; but  in  an 
eye^  ^j/ltgma)  quadrant,  the  base-sine  ( hdhnjya ) is  taken  from 
the  pari  to  crane,  and  Hie  perpendicular-sine  from  that  past  ■ 

- Hie  distsses  of  a planet  from  either  of  its  two  apices  of  motion,  or 
eentfes  of  disturbance,  is  called  its  kendra ; according  to' the  corament- 
ite  djjjtpnce  from  the  apsis  (aumdocea)  is  called  mandairndra,  and 
^dmt  from  the  conjunction  (pghroeca)  is  called  fighraktndra : the  Sfiryn- 
Siddh&nta,  however,  nowhere  lies  occasion  to  employ  these  terms.  The 
fetJBfer  of  the  two  corresponds  to  what  in  modern  Astronomy  is  called 
the  .anomafy,  the  latter  to  what  is  known  as  the  commutation.  Tho 
word  .kendra  is  not  of  Sanskrit  origin,  but  is  the  Greek  nhrqor ; it  is  a 
' circumstance  no  lew  significant  to  meet  with  a Greek  word  thus  at  the 


ii.  30.]  . ''  Notes.  59 

very  fouudation  of  the  method  of  calculating  the  true  place  of  a planet 
by  means  of  a system  of  epicycles,  than  to  find  one,  as  noticed  ab$ve 
(under  i.  52),  at  the  base  of  the  theory  of  planetary  regency  upon  which 
depend  the  names  and  succession  of  the  days  of  the  jBIgjk.  Both 
anomaly  and  commutation,  it  will  be  noticed,  are,  acccfflmig  to  this 
treatise,  to  be  reckoned  always  forward  from  the  planet  to  its  apsis  and 
conjunction  respectively ; excepting  that,  in  the  case  of  Mercury  and 
Veuus,  owing  to  the  exchange  with  regard  to  those  planets  of  the  place 
of  the  planet  itself  with  that  of  its  conjunction,  the  commutation  is 
really  reckoned  the  other  way.  The  functions  of  any  arc  being  the 
same  with  those  of  its  negative,  it  makes  no  difference,  of  course, 
whether  the  distance  is  measured  from  the  planet  to  the  apex  ( ucca ),  or 
from  the  apex  to  the  planet. 

The  quantities  actually  made  use  of  iu  the  calculations  which  are  to 
follow  are  the  sine  and  cosine  of  the  anomaly,  or  of  the  commutation. 
The  terms  employed  in  the  text  require  a little  explanation.  Bhvja 
means  ^urm;”  it  is  constantly  applied,  as  are  its  synonyms  bdhu  and 
dosf  to  designate  the  base  of  a right-angled  triangle ; koti  is  properly 
“ a recurved  extremity and,  as  used  to  signify  the  perpendicular  in 
such  a triangle,  is  conceived  of  as  being  the  end  of  the  bhujv%  or  base, 
bent  up  to  an  upright  position  : bknjajya  and  kotijyd,  then,  are  literally 
the  values,  as  sines,  of  the  base  and  perpendicular  of  a right-angled 
triangle  of  which  the  hypothenuse  is  made  radius : owing  to  the  relation 
to  one  another  of  the  oblique  aiurlis  of  such  a triangle,  they  are  re- 
spectively a*  sine  and  cosine.  We  haw  nut  been  willing  to  employ 
tfiese  latter  terms  in  translating  them,  ln>*>aiisil.  as  before  remarked,  the 
Hindus  do  not  seem  to  have  conceived  of  tin;  uusiuc,  the  sine  of  the 
complemriit,  of  an  are,  a*  being  a function  of  the  arc  itself. 

To  find  the  sine  and  cunim;  of  the  planet’s  distance  from  either  of  its 
apices  (ucca)  is  accordingly  the 
object  of  the  direction*  given  in 
verse  30  and  the  latter  part  of 
the  preceding  vei>c.  The.  rule 
itself  is  only  the  uukuard  Hindu 
method  of  stating  the  familiar 
truth  that  the  sine  and  cosine  of 
an  arc  and  of  its  supplement  arc 
equal.  The  accompanying  figure 
will,  it  is  believed,  illustrate  the 
Hindu  manner  of  looking  at  the. 
subject,  Irtt  V he  the  place  of  a 
planet,  and  divide  its  orbit  into 
flic  four  quadrants  V <i,  Q R,  R S, 
and  SI*;  the  first  a ml  third  of 
these  arc  called  the  odd  (ruvAama) 

quadrants;  the  second  and  fourth,  _ 

i lie  even  (yuyma)  quadrants,  F.ct  A,  B,  C,  and  D,  be  four  positions  of 
the  apsis  (or  of  the  conjunction);  then  the  aTCsPA^PQH,  PQltC, 
PQKSD  will  l»c  the  values  of  the  anomaly  in  each' case.  AM/ the 
base-sine,  or  sine  of  anomaly,  when  the  apsis  is  in  the  first  qnadlMt,  is 


60 


. -.4 
- ■ 

■ w ..  . 


[iu30- 


deteriuined  by  the  arc  A P,  the  arc  passed  c$rerri£  jjWBmng  the  aflom- 
alyt while  A 6 or  EM,  the  perpendicular-sine,  or  cosine^  is  taken  from 
the  arc  AQ,  the  remaining  part  of  the  quadrant.  The  same  is  true  in' 
the  other  jlfai  quadrant,  US;  the  sine  C II,  or  EL,  coincs  from  RC, 
the  part  or%e  quadrant  between  the  planet  and  the  apsis;  the  cosine 
CL  is  from  its  complement,  Butin  the  even  quadrants,  QK  and  81\ 
the  case  is  reversed ; the  sines,  IS  II,  or  EF,  and  DM,  are.determined  by 
the  arcs  Bit  and  DP,  tho  parts  of  the  quadrant  not  included  in  the 
anomaly,  and  the  cosines,  B F and  K I),  or  E M,  correspond  to  the  other 
portions  of  each  quadrant  respectively. 

This  process,  of  finding  what  ]R>rtion  of  any  arc  greator  than  a quad- 
rant is  to  be  employed  in  determining  its  .sine,  is  ordinarily  called  in 
Hindu  calculations  ‘Making  the  bhvja  of  an  arc.” 


31.  Divide  the  minutes  contained  in  any  arc  by  two  hundred 
and  twenty -five ; the  quotient  is  the  number  of  the  preceding 
tabular  sine  (jydpindaka).  Multiply  the  remainder  by  the  differ- 
ence of  the  preceding  and  following  tabular  sines,  and  divide 
bjp  two  hundred  and  twenty-five ; 

^82.  The  quotient  thus  obtained  add  to  the  tabular  sine  called 
we  preceding;  the  result  is  tho  required  sine.  The  same  method 
is  prescribed  also  with  respect  to  the  versed  sines. 

33.  Subtract  from  any  given  sine  the  next  loss  tabular  sine; 
multiply  the  remainder  by  two  hundred  and  twenty-five,  and 
divide  by  the  difference  between  the  next  less  and  uext  greater 
tabular  sine5* ; add  the  quotient  to  the  product  of  the  serial  num- 
- ber  of  the  next  less  sine  into  two  hundred  and  twenty -five:  the 
"'result  is  the  required  arc. 


The  table  of  sines  and  versed  sines  gives  only  those  belonging  to  arcs 
which  arc  multiples  of  3°  45';  the  first  two  verses  of  this  passage1  state. .. 
the  method  of  finding,  by  simple  interpolation,  llie  sine  or  versed  sine 
of  any  intermediate  arc;  while  the  third  verse  gives  the  rule  for  the 

contrary  process,  for  converting  any  given  sine  or  \ersed  sine  in  the 

same  manner  into  the  corresponding  arc. 

In  illustration  of  the  first  rule,  let  ns  asi 'rtain  the  sine  corresponding 
to  an  arc  of  24°,  or  1440'.  Upon  dividing  the  latter  number  by *225, 
we  obtain  the  quotient  6,  and  the  remainder  90'.  Tins  preliminary  step 
■ is  necessary,  because  the  Hindu  table  is  not  regarded  as  contaimfcg'^ay  v. 
designation  of  the  arcs  to  which  the  sines  belong,  but  as  competed 
simply  of  the  sines  themselves  in  their  order.  The  sine  cumspoadfhg 
to  the  quotient  obtained,  or  the  sixth,  is  1316':  the  difference  between 
and  the  next  following  sine  is  205'.  Now  a proportion  is  made:  if, 
;at  this  point  in  the  quadrant,  an  addition  of  225' Jo  the  an:  causes  an 
'increase  in  the  sine  of  205'v  what  increase  will  be  caused  by  an  addition 
to  the  arc  of  90M  that  is  to  say,  225  : 205  : : 90  : 62.  Upon  adding  the 

tesult,  82',  to  the  sixth  sine,  the  amount,  1397',  is  the  sine  of  the  given 

s^arev  as  stated  jp,  verse  28.  The  actual  value,  it  may  be  remarked,  of 
' tbeme  of  24°,  is  1398'.20. 

THfeother  rule  is  the  reverse  of  this,  and  does  not  requiro  illustration. 


ii.  88.]  . Translation  and  Notes. 


61 


The  extreme^ concbenem  aimed  at  in  the  phraseology  of  the  text,  and 
not  nnfreqnently carried  by  it  beyond  the  limit  of  distinctness,  or  even 
of  intelligibility,  is  well  illustrated  by  verse  83,  which,  literally  trans- 
lated, reads  thus : “ having  subtracted  the  sine,  the  remainder,  multi- 
plied by  225,  divided  by  its  difference,  having  added  to  the  product  of 
the  number  and  225,  it  is  called  the  arc.  In  Verse  31,  also,  the 
important  word  “ remainder"  is  not  found  in  the  text. 

The  proper  place  for  this  passage  would  seem  to  be  immediately  after 
the  table  of  sines  and  versed  sines : it  is  not  easy  to  see  why  verses 
28-30  should  have  been  inserted  between,  or  indeed,  why  the  subject  of 
the  inclination  of  the  ecliptic  is  introduced  at  all  in  this  part  of  the 
chapter,  as  no  nse  is  made  of  it  for  a long  time  to  come. 


84.  The  degrees  of  the  sun's  epicycle  of  the  apsis  (manda- 
paridhi)  are  fourteen,  of  that  of  the  moon,  thirty-two,  at  the  end 
of  the  even  quadrants;  and  at  the  end  of  the  odd  quadrants, 
they  are  twenty  minutes  le.«.s  for  both. 

35.  At  the  cud  of  the  even  quadrants,  they  arc  s«venty-$ve, 
thirty,  thirty-three,  twelve,  forty-nine ; at  the  odd  (oja)  they 
seventy-two,  twenty-eight,  thirty-two,  eleven,  forty-eight,  * 

86.  For  Mars  and  the  rest:  further,  the  degrees  of  the  Epi- 
cycle of  the  conjunction  (rh/lmt)  are,  at  the  end  of  the  even 
quadrants,  two  hundred  and  thirty-live,  one  hundred  and  thirty- 
three,  seventy,  two  hundred  and  sixty-two,  thirty-nine; 

37.  At  the  end  of  the  odd  quadrants,  they  are  stated  to  be 
two  hundred  atul  thirty-two,  one  hundred  and  thirty-two, 
seventy-two,  two  huudreii  and  sixty,  and  iortv,  as  made  use  of 
in  the  calculation  for  the  conjunction  ( rlyhrobinnan ). 

38.  Multiply  the  base-sine  {bhujuji/d)  by  the  difference  of  the 
epicycles  at  the  odd  and  even  quadrants,  and  divide  by  radius 
( trif'yd );  the  result,  applied  to  the  even  epicycle  (yrlta\  and 
adt  litive  (dhana)  or  subtractive  (r/*a),  according  as  tins  is  less  or 
greater  than  the  odd,  gives  the  corrected  ( '*phu(ii ) epicycle. 


The  corrections  of  the  moan  longitudes  of  the  planets  for  the  dis- 
turbing effect  of  the  apsis  (mnmlocca)  and  conjunction  (ftghrocca)  of 
eatih— -that  is  to  say,  for  the  effect  of  the  ellipticitv  of  their  orbits,  and: 
forithat  of  the  annual  parallax,  or  of  the  motion  of  the  earth  in  its 
* orbit— arc  made  in  Hindu  astronomy  by  the  I’lolemaic  method  ofepi- 
; cycles,  or  secondary  circles,  upon  the  cireu  infer*' nee  of  which  the  planet 
is  regarded  as  moving,  while  the  centre  of  the  cmcycle  revolves  about 
the  general  centre  of  motion.  The  details  of  the  method,  as  npplied?%y 
the  Hindus,  will  be  made  dear  by  the  figures  and  processes  to  be  pre- 
sented a little,  later;  in  this  passage  we  have  only  the  dimensions  of  the 
epicycles  assumed  for  each  planet.  For  eonvcnicnce  of  calculation,  they 
are  measured  in  degrees  of  the  orbits  of  the  planets  to  which  tliey 
pally  belong;  hence  only  their  relative  dimensions,  •»»  compared 


the  orbits,  are  givcii  us.  The  data  of  die  teat  belong  to  the^a; 

ich  these  succeed  one  another  as  regents  of  :ffie  c 


in  the  order  in  which 


in  eta 
davs 


62 


S&rya-Siddh&niai 


[ii.  38- 


of  the  week,  viz.,  Mars,  Mercury,  Jupiter,  Venus,  and  Saturn  (see 
above/ under  i.  51,  52).  The  annexed  table  gives  the v dimensions  of 
the  epicycles,  both  their  circumferences,  which  are  presented  directly 
by  the  text,  and  their  radii,  which  we  have  calculated  after  the  method 
of  this  Siddliiinta,  assuming  the  radius  of  the  orbit  to  be  3438'. 

Dimensions  of  the  Epicycles  of  the  Planets . 


Epicycle  of  the  apaia : 


Epicycle  of  the  conjunction  s 


PlMMt. 

■l  eves  quadrant, | 

at  add  quadrant, 

at  even  quadrant, 

at  odd  quadrant, 

riw. 

rad.  I 

circ. 

rad. 

circ.  ; 

rad. 

circ. 

rad- 

Sun, 

i4u 

1 33#.*?o 

i3w  4o' 

i3o\5a 

....  < 

( . , , * 

Moon, 

3i° 

3uV.6o 

3i“  4<S 

3o2'.4a 

j 

.... 

Mercury. 

3ow 

a86’.5o 

a67,.«iu 

i33u  i 

i?7o'.i5 

132° 

i a6o,.6o 

Venus, 

i»* 

i i4'.6o 

1 1M 

10V.0O 

atiJ®  j 

?502'.IO 

a(jo° 

a483'.oo 

Man, 

75“ 

■?i6\a5 

7* 

! 335“  i 

j 244'.  a 5 

a3a° 

22|5'.6o 

Jupiter,  . 

33“ 

3i5'.i5 

3 1* 

JnV.Co 

i 7U“  : 

G6S'  5o 

?ae  j 

! 687\6o 

Saturn,  j 

49° 

46?'-90 

48° 

: 45B'..jo 

i 39“ 

37^.45 

4o° 

38a'.oo 

4rAyjfigniarkablo  peculiarity  of  the  Hindu  system  is  that  the  epicycles 
aife  supposed  to  contract  their  dimensions  as  they  leave  the  apsis  or  the 
r^cpiijlinction  respectively  (excepting  in  the  case  of  the  epicycles  of  the 
*■''  e iyunctioTi  of  Jupiter  and  Saturn,  which  expand  instead  of  contracting), 
becoming  smallest  at  the  quadrature.  llicn  again  expanding  till  the  lower 
apsis,  or  opposition,  is  reached,  and  decreasing  and  increasing  in  like 
manner  in  the  other  half  «»f  the  orbit ; tin;  rate  of  increav..*  and  diminu- 
tion being  as  the  sine  of  tin;  distance  from  the  ap-is  or  eniijunction. 
Hence  the  rule  in  verse  38,  for  finding  the  true  dimeiisious  of  the  cpi- 
;ti  cycle  at  any  point  in  the  orbit.  It  i*  founded  upon  the  simple  propnr- 
as  radius,  the  sine  of  tin*  distance  at  which  the  diminution  (or 
•'  increase)  is  greatest,  is  to  the  amount  of  diminution  (or  of  increase)  at 
that  point,  so  is  the  sine  of  the  given  distance  to  the  corresponding 
diminution  (or  increase) ; the  application  of  tli  ■ correction  thus  blamed 
to  the  dimensions  of  the  epicycle  at  the  Apsis,  or  conjunction,  jives  the 
true  epicycle. 

Wc  shall  revert  farther  nn  to  the  subj  ct  of  iliis  change  in  the  dimen- 
sions of  the  epicycle. 

The  term  employed  to  denote  the.  epicycle,  jnridhi,  means  simply 
44 circumference/'  or  “circle;”  it  is  Hk  same  which  is  used  elsewhere  in 
this  treatise  for  the  circumference  of  tl  ; earth,  etc.  In  a single  instance, 
in  verse  38,  we  have,  vrtta  inst.-nd  of  jnridhi ; its  signification  is  the 
same,  and  its  other  uses  arc  closely  analogous  to  those  of  the  mere 
usual  term. 


. 69.  By  the  corrected  epicycle  multiply  the  base-sine  (bhujujyd) 
and  perpcndicular-sine  (kotjjya)  respectively,  and  divide  by  "the 
number  of  degrees  in  a circle : then,  the  arc  corresponding  to 
the  result  from  the  base-sine  (bhujajydphala)  is  the  equation  of 
the  apsis  (mdnda  phala),  in  minutes,  etc. 

All  the  preliminary  operations  having  been  already  performed,  tlh  is 
the  .Ufa  process  by  which  is  ascertained  the  equation  of  the  spot,  or 
thelmount  by  which  a planet  is,  at  any  print  in  its  revolution,  drawn 


Translation  and  Notes. 


ii.  39.] 


68 


away  from  its  me an  place  by  the  disturbing  influence  of  the  apsis.  In 
modern  phraseology,  it  is  called  the  first  inequality,  due  to  the  eiliptieity 
of  the  orbit;  or,  tnfc  equation  of  the  centre. 

Figure  9,  upon  the  next  page,  will  serve  to  illustrate  the  method  of 
t lie-  process. 

Lot  A MM' P represent  apart  of  the  orbit  of  any  planet,  which  is 
supposed  to  be  a true  circle,  having  E,  the  enrth,  for  its  centre.  Along 
this  orbit  the  planet  would  move,  in  the  direction  indicated  by  the 
arrow,  from  A through  M and  M'  to  IJ,  and  so  on,  with  an  equable 
motion,  were  it  not  for  the  attraction  of  the  beings  situated  at  the  apsis 
(tnanducea)  and  conjunction  (piyhrocca)  respectively.  The  general  mode 
of  action  of  these  beings  has  been  explained  above,  under  verses  1-5 
of  this  chapter : wc  have  now  to  ascertain  the  amount  of  the  disturb- 
ance produced  by  them  at  any  given  point  in  the  planet’s  revolution. 
The  method  devised  is  that  of  nu  epicycle,  upon  the  circumference  of 
which  the  planet  revolves  with  an  equable  motion,  while  the  centre  of  the 
epicycle  traverses  the  orbit  will*  a velocity  equal  to  that  of  the  planet's 
mean  motion,  having  always  a position  coincident  with  the  mean  place 
of  the  planet.  At  present,  we  have  to  do  only  with  the  cpicvclK  which 
represents  the  disturbing  effect  of  the  apsis  (mamtocca).  The  period  of 
the  planet's  revolution  about  tin*  centre  of  the  epievele  is  the  time 
which  it  takes  the  latter  to  make  the  circuit  of  the  orbit  from  the  apsia 
around  to  llic  apsis  again,  or  the  period  of  its  anomalistic  revolution. 
This  is  filnmst  precisely  equal  to  the  period  of  sidereal  revolution  in  the 
ease  of  all  the  planets  excepting  the  Jiiomi,  since  their  apsides  are  re- 
garded by  the  Jlimln*  as  stationary  (see  above,  under  i.  41-44) : the 
moon’s  apsis,  linwetcr,  lias  a forward  motion  ot  more  than  40°  in  a 

iresir;  hence  the  moon's  sinouudii-lic  revolution  is  very  perceptibly, 
ongcr  than  its  sidereal,  beinif  ‘27*1  I:**1  1 Sm.  The  are  of  the  cpicydff 
traversed  by  the  planet  at  any  im-an  point  in  its  revolution  is  accord*  :- 
ingly  always  equal  to  the  aiv  of  the  orbit  intercepted  between  that 
point  and  the  apsis,  or  to  the  ncan  anomaly,  when  the  latter  is  reckoned, 
in  the  usual  manner,  from  the  apsis  forward  to  the  planet.  Thus, in  the 
figure,  suppose  A to  be  the  place  of  the  apsis  (i mandocra , the  apogee  of 
the  sun  and  moon,  the  aphelion  of  the  other  planets),  and  P that  of  the 
opposite  point  (perigee,  or  perihelion ; it  lias  in  this  treatise  no  distinct- 
ive name) ; and  let  M and  M*  be  two  mean  positions  of  the  planet,  or 
actual  positions  of  the  centre  of  the  epicycle;  the  lesser  circles  drawn 
about  tnesc  four  points  represent  the  epicycle : this  is  made,  in  the  figure, 
of  twice  the  size  of  ih&t  assumed  for  the  moon,  or  a little  smaller  than 
that  of  Mars.  Then,  when  the  centre  of  thn  epicycle  is  at  A,  the 
planet’s  place  in  the  epicycle  is  at  a ; as  the  centre  advances  to  M,  M', 
and  P,  tne  planet  moves  in  the-  opposite  direetio  »,  to  m,  m\  and 
are,  aftn  being  equal  to  A M,  a " m1  to  A M',  and  a"  p to  A P.  It  b as'if, 
while  the  axis  E a revolves  about  E,  the  part  of  it  A a remained  con- 
stant, in  direction,  parallel  to  EA,  assuming  the  positions  Mm, Apin', 
and  1*  p successively.  The  effect  of  this  combination  of  motions  is  to 
rnfjkp  the  planet  virtually  traverse  the  orbit  indicated  in  the  figure  by 
th*1)rokcn  line,  whirl)  is  a circle  of  equal  radius  with  the  true  orbit, 
but  having  its  centre  removed  from  E . toward  A,  by  a distance  equal  to 


A a,  the  radius  of  the  epicycle.  This  identity  of  the  virtual  orbit  with 
an  eccentric  circle,  of  which  the  eccentricity  is  equal  to  the  radius  of 
was  doubtless  known  to  the  Hindus,  as  to  Ptolciny : the 
Jlpm^ra  the  third  hook  of  his  Svntnxis,  demonstrates  the  equivalence  of 
tftfe  Suppositions  of  an  epicycle  and  an  eccentric,  and  chooses  the  latter 
torepresent  the  first  inequality:  the  Hindus  have  preferred  the  other 
supposition,  as  belter  suited  to  their  methods  of  calculation,  and  as  ad- 
mitting a general  similarity  in  the  processes  for  the  apsis  and  the  con- 
junction. The  Hindu  theory,  however,  ns  remarked  above  (under  vv. 
1-5  of  this  chapter),  rejects  'he  idea  «>f  the  actual  motion  of  the  planet 
in  the  epicycle,  or  on  the  ereentrie  circle:  the  method  is  but  a device 
for  ascertaining  the  cIF«  « t of  the  attractive  force  of  the  being  at  the 
«SML  Thus  liie  planet  really  moves  in  the  circle  A M M#  P,  and  if  the 
Em'  be  drawn,  meeting  the  orbit  in  o and  o',  its  actual  place 
% and  o',  when  its  mean  place  is  at  M and  M#  respectively.  To 
ascertain  the  value  of  the  arcs  o M and  o' M',  which  are  the  amount  of 
removal  from  the  mean  place,  or  the  equation,  is  the  object  of  the  pro- 
Sttft  prescribed  by  the  text. 

jf  Suppose  the  planet’s  mean  place  to  be  M,  its  mean  distance  from  the 
apsis  feiM  AM:  it  has  traversed,  a«  above  explained,  an  equal  arc,  a'm, 
in  the  .OTfcycb*.  Prom  M draw  M II  and  M F,  and  from  m draw  at  n, 
ft  right  angles  to  the  lim*s  upon  which  they  i^pcctively  fall : then  MB 
is  the  base-sine  ( hknjajya ),  or  the  sine  of  mean  ansn^dy,  and  M F,  or  its 
equal  EB,  is  the  perpendicular-tine  (hot 'j yd),  Or-Cftitae,  and  m n and 
n M are  corresponding  sine  and.  co>ine  in  the  epioycle.  But  as  the  rela- 
tion of  the  circum fere  nee.  of  the  orbit  to  that  of  the  epicycle  is  known, 
and  as  all  corresponding  parts  of  two  circles  are  to  one  another  ae  their 
ftSpective  circumferences,  the  values  of  wn  and  nil  are  found  .by  a 
proportion,  as  follows : us  300°  is  to  the.  number  of  degrees  in  thweir- 
cunifcnmfte  of  the  epicycle  at  M,  so  is  MB  to  Jttn,  andEB  to  sM. 
I It*  net*  run  is  culled  the  •* result  from  the  base-sine”  ( [bhujajydphala , or, 
more  briefly,  bhujuphula , or  bdhvj)hala)%  and  nM  the  11  result  from  the 
perpeudicuMr-sine"  {kotijydphala,  or  kot.iphala) : the  latter  of  the^ tjjjpy 
however,  is  not  employed  in  the  process  for  calculating  the  equati$|;ibf 
thejtjftis.  Now,  as  the  dimensions  of  thMUoycle  W the  apsis  aft  in 


ft  30.]  " 


TMnslatiori  and  Notes. 


all  cases  smi 
be 


ftKS 

its  cc^mepo; 


wjnay  without  afifr  considerable  error  be  assumed  to 
'WT'Wb  & th&  Arc ; wMf  the  equatHft : this 
the  conversion  of  m a,  as  sine,  int6; 
- gives  the  equation  required. 

Kcw.fi  explanation  applies  to  the  position  of  the  plantet  at  Uy : a'1 
\ the  equivalent  of  A M M',  is  here  the  arc  of  the  epicycle  traversed ; 
m1  d,  its  sine,  is  calculated  from  M'  IV,  as  before,  and  is  assigned  to 
equal  dq^  the  sine  of  the  equation  d M#.;  * 

To  give  a farther  and  practical  illustration  of  the  process,  we  wiil 
proceed  to  calculate  the  equation  of  the'  apsis  for  the  moon,  at  the  time 
for  which  her  mean  plane  has  been  found  in  the  notes  to  the  last  chap- 
ter, viz.,  the  1st  of  January,  I860,  midnight,  at  Washington. 

Moon’s  mean  longitude,  midnight,  at  ITjjayini  (i.  S3),  1 1**15*  a3f  a4/; 

add  the  equation  for  difference  of  meridian  (tWoniamphal^  ) 
or  for  lier  molioti  between  midnight  ar  I jj.  ami  Wsihli.  ( i.  CU,  01 1,  ) J ” 

Moon’s  mean  longitude  at  required  tum-, 

Longitude  of  moon’t^kpsis,  midnight.  at  rjjnyiid  \i.  53j, 
add  for  difference  of  meridian.  us  above, 

Longitude  of  moun'si  :ip«is  at  required  lime, 
deduct  moon's  mean  longitude  i ii.  l*‘j i, 

Moon’s  mean  anomaly 


1 1 

ao 

59  > 

10 

9 

id 

9 

45  »t> 

1 1 

ao 

59  r 

lO 

18 

46  i5 

4 


The  anomaly  bring  reckoned  l'« »r\\ :ii • l «»n  tin-  orbit  from  the  planet, 
the  position  thus  fnimd  fur  tin-  »m  r.-!:iiivc-  t«»  the  ap«d>  is,  nearly 
enough  for  pnrpo*i>  «•!’  ilhi-tiati-Mi,  r.-» t«— « -i! ! t ii  h\  M in  the  rignre.  By 
the  rule  given  siIhiii*.  in  w-rsc  :»» *.  t *i--  ha-e-Mi.i*  i f»hnjnj  pi) — since  thet 
anomaly  is  in  the  fmirili.  an  even,  •jii.uiiv.ut  — is  t«»  be  taken  from 
part  of  the  quadrant  m*t  included  in  tin-  anomaly,  or  A M ; the 
pondicular-sine  (kotij>/«)  is  that  •'orrtsiioiiJing  to  it*  complement,  or" 
Ml).  That  is  tu  wu': 


From  tlie  anomaly, 

deduct  three  quadrants 
remains  the  arc  M I), 
take  this  from  a quadranr, 
remains  the  are  A M, , 


in»  1 6°  t%" 

2 ' 

i 16  46  i5 
3 

i ir  1 3 45 


And  by  the  method  already  illustrated  under  verse*  r<  J.  32,  the  sine 
corresponding  to  the  latter  are,  which  i*  the  b •'•e-sine  ( hh njojt/tt)m  or  the 
sine  of  mean  niuunnly,  M B.  is  tnuinl  to  be  22H*'':  that  from  M D,  which 
is  MK,  or  K l\  the  perpcudicular-Mnc  {kotij*n'\  or  o mho  of  mpau 
anomaly,  is  25N.V.  : f: 

The  next-  point  is  to  livitl  the  true  size  of  tie’  epic;, ole  at  M.  By 
verse  34,  the  run  tract  ion  of  it*  rireuniferonee  amounts  at,  *D  to  20'; 
hence,  according  to  the  rule  in  vers*1  3S,  we  make  the  proportwii,  siu 
A l)  : 20' : : sin  A M : diminution  at  M : or, 

3 i 38 : ?o : : jjiiiii  : iJ  * 

Deducting  from ^2°,  ljie  circumference  of  ihe  epicycle  at  A,  the  amount 
of  diminution  thiis  ascertained,  wo  have  31°  -17'  As  its  dimensions  at  M. 

VfD 


96  Sfaya-Siddh&TUfy  [ii.39- 

Onec  more, -by  verso  30,  we  make  tlio  proportion,  circ,  of  orbit : circ. 
y.  of  Epicycle  : : M B : m n ; or, 

^ 3(10° : 3i°  4t'  : : aa66 : *joo 

The  value,  then,  of  mu,  the  result  from  the  base-sine  (i bhujajydphala ), 
200';  which,  as  win  is  assumed  to  equal  oq,  is  the  sine  of  the  equa- 
tion. Being  less  than  225',  its  arc  (see  the  table  of  sines,  above)  is  of 
*uie  same  value : 3°  20',  accordingly,  is  the  moonV  equation  of  the  apsis 
(nulmla  phala)  at  the  given  time  :"the  figure  >h«»ws  it  to  be  subtractive 
(ran),  as  the  rule  in  verse  15  also  dcclmvs  it.  Hence,  from  the 

Moons  mean  longiluiic,  1 1"  ?o°  5gr 

deduct  the  equation.  3 ?n 

Mono's  true  longitude,  n 17  39 

Ve  present  below.  in  a briefer  form,  the  results  of  a similar  calcula- 
tion made  for  the  sun,  at  the  same  time. 


Sun's  mean  iomhiudSfilbidi.L'hi.  at  I'jjnviui  c i.  53), 
add  for  difference  cf  meridian  (i.  f>0F  fil), 

Sun's  mean  kmcriiudo  at  required  tinu*, 

^Longitude  of  sun*  np-i-  \i.  1 1 >. 

Sun's  mean  anouin'.y  1 ii.  29  \ 
subtract  from  two  quadranss  ( ii.  i-0», 


8-  170  .18'  7,f 

$ _ a5  6 
8 18  i3  t3 
a 1^  17  74 

39  4 11 


Arc  detcrm'ioirur  Lu-e-ine.  55'  49" 

Base-sine  (/•/«  1.  5h' 

Dimensions  of  rpicyi-h*  (ii.  !>i.  i.Ju 

„ Result  from  !»*•■ -^in.*  i,i/i*o-*/i/d phala),  or  sine  of  equation  (ii.  39).  a' 

^Equation  ;#/W.q  u.  1 0 1,  -|-a; 

%unvfl  (me  lorigiiudc.  ifi°  i5' 


In  making  these  calculations,  we  have  neglected  the  pccothIn,  rejecting 
the  fraction  of  a minute,  or  enuming  it  as  a minute.  according  as  it  was 
teas  or  greater  than  a half.  Fur,  c juddering  that  this  method  is  followed 
in  the  table  of  sine*,  w!ii«-h  lii-s  at  tins  foiii'daliou  of  the  whole  process, 
and  considering  that  tin*  '•im*  of  i In-  use  in  i!r*.  epicycle  is  assumed  to  be 
equal  to  that  of  tins  **qu:iii.iii.  it  would  evidently  be  a waste  of  labor,  and 
an  affectation  of  an  exactness  greater  than  the.  process  eontem plates,  or 
than  its  general  method  render*  pr.-rtn-iMt:,  to  carry  into  secunds  the  data 
employed. 

As  staled  below,  in  verse  43,  the  equation  thus  found  is  the  only  one 
required  in  determining  the  true  longitude  of  the  sun  and  of  the  moon : 
in, the  case  of  tint  other  planets  however,  of  which  the  apparent  place  is 
affected  by  the  motion  of  the  earth,  a much  longer  and  more  complicated 
process  it  necessary,  of  which  the  explanation  commences  with  tno  next 
following  passage. 

The  YbAi unair  method  nf  making  the  calculation  of  ilio  equation  of 
the  centre  for  the  sun  and  moon  is  illustrated  by  the  annexed  figure 
(Fig.  4).  The  points  E,  A,  M,  a,  m,  and  0,  correspond  with  those  smii- 
Uiiy  marked  iiHthe  last  figure  (Fig.  9),  SE^«oatca.fof  the  eccentric 


Translation  and  Notes . 


ii.42.] 


circle  is  at  e,  abd  Eef  which  equals  Ac,  is  the  eccentricity,  which  is  given." 
Join  em;  thiraqgl  emea  equals  ME  A,  the  mean  anomaly,  and  Em  e 
equals  M E o,  the  equation . Extend 
me  to  rf,  where  it  meets  Erf,  a per- 
pendicular let  fall  upon  it  from  E. 

Then,  in  the  right-angled  triangle 
Kerf,  the  side  Ee  and  the  angles 
— since  Kerf  equals  mca — are 
given,  to  find  the  other  sides,  erf 
and  rf  E.  Add  e d to  e m,  the  ra- 
dius; add  the  square  of  the  sum 
to  that  of  Erf;  the  square  root 
of  their  sum  is  Em : then,  in  the 
right-angled  triangle  mErf,  all 
the  sides  and  the  right  angle  are 
given,  to  find  the  angle  E w r.  the 
equation. 

This  process  is  equivalent  to  a transfer  of  the  epitftrlu  from  M to  E; 
Erf  becomes  the  result,  from  the  base-sine  (hh'ijnjyhphahi).  and  rfetbat 
from  the  perpendicular  sine  (tmnhjyt)}>halo),  and  the.  angle  of  the  equation 
is  found  in  the.  same  manner  an  its  sine.  cc.  is  found  in  the  Hindu  process, 
next  to  be  explained : while,  in  that  which  we  hav.-  boeu  considering,  Erf 
is  assumed  to  be  equal  to  cr . 

Ptolemy  also  mhU  tn  tlm  miners  «>rbit  an  epiryrle,  lo  account  for  her 
second  inequality,  the  lo-rtion,  tin.*  discovery  «*r'  whii-h  does  him  so  much 
honor.  Of  this  inequality  the  Hindu?  l ike  t.*i  in'li'-i-. 

40.  Tho  result  from  t ho  ■oiiiiii,:i *:o"- -it:*'  i kofiph^h)  of  the 

distance  from  the  conjunction  i?  !■ » l.*-  :i- !■  L«:« l l«»  radius,  when  the 
distance  (fcemhv)  i.>  in  the  hall-vi l.-'o  Uv-inning  wiili  (.'apricom^j 
but  when  in  that  boginniiiL'  with  i i\.r  result  from  the" 

pcrpendirular-siiui  i.s  Lo  hr  suolrurivd 

41.  To  the  square  of  this  sum  or  diHrivnee  add  tlie  square  of 

the  result  from  the  Inw.-sinr  tin-  squuiv  root  of 

their  sum  is  the  liypoLhenuso  iirtinpi)  eulh'i^  variable  (cata). 
Multiply  the  result  from  the  hasr  -ine  by  radius.  aud  divide  by 
the  variable  hypothonuse : 

42.  The  arc  corresponding  to  the  quotient  »s.  in  minutes,  etc., 
the  equation  of  the  conjunction  (y./fy hnja  / /.• ilu ) ; it  i*  employed 
*u  the  first,  and  in  the  fourth  process  of  urrection  {kannan)  lor 
Mars  and  the  other  planets. 

The  process  prescribed  by  this  passage  is  essent  illy  the  same  with  (hat 
explained  and  illustrated  under  the  preceding  verse,  the  only  difference! 
being  that  here  tho  sine  uf  die  required  iquadim,  instead  of  being 
assumed  equal  lo  that  of  the  arc  traversed  by  riio  pinuet  in  tho  epicycle, 
is  obtained  by  calculation  from  it.  The  aum-MMl  figure  (Fig.  5)  win  ex- 
hibit the  method  pursued.  • 

xfio  larger  circle,  C M M'  0,  represents,  as  before,  the  orbit  in  which 
any  ono  of  tho  plancU,4Ui  also  the  being  at  its  conjunction  (fighroceif)  are 


JS&rya-SiddJi&nta, 


[M2. 


Fig.  6,. 


miking  the  circuit  of  the  heavens  about  E,  the  earth,  as  a centre,  in  the 
, direction  indicated  by  the  arrow,  from  C through  M And  M'  to  O,  and  no 
on.  But  since,  in  every  case,  the  conjunction  moves  more  rapidly  east- 
ward than  the  planet.,  overtaking  and  passing  it,  if  we  suppose  the  con*1 
junction  stationary  at  C,  the  virtual  motion  of  the  planet  relative  to  that 
point  is  backward,  nr  from  0 through  M'  and  M to  C,  its  mean  rate  of 
approach  toward  C being  the  difference  between  the  mean  motion  of  the 
planet  and  that  of  the  sun.  As  before,  the  amount  to  which  the  planet, 
is  drawn  away  from  it*  mean  place  toward  the  conjunction  is  calculated 
by  means  of  an  epicycle.  Tho  circles  drawn  in  the,  figure  to  represent 
ji [the  epicycle  aie  of  the  relative  diinciiMons  of  that  assigned  to  Mercury, 
or  a little  more  than  half  that  ol‘  Mar*.  The  direction  of  the  planet's 
motion  in  the  epicycle  is  the  revere*  of  that  in  the  cpiejele  of  the  apsis, 
as  regards  the  actual  motion  of  tin*  planet  in  its  oiI.it,  bi*ing  eastward  at 
the  conjunction ; as  regards  the*  motion  of  the  planet  relative  to  the  con- 
junction, it  is  the  J*ginc  .n  in  tin:  fmin'-r  case,  being  in  the  contrary  direc- 
tion at  the  con  j unci  ion  : its  effect.  t*f  course  is  to  iiicieuse  the  rate  of  the 
eastward  movement  at  that  point.  The  time  of  the  planet's  revolution 
about  the  centre  of  tlm  cpiru'le  is  the  interval  between  two  successive 
pat  through  the  point  C,  llm  conjunction  : that  is  to  say,  it  is  equal 
to  the  period  c»f  synodical  revolution  of  each  planet.  These  periods  are, 
according  to  the  elements  presented  in  the  text  of  this  Siudlninta,  as 
follows:  % 

Mercury,  u5d  ail»  4*“ 

\ emu,  563  ai  37 

„ Mars,  779  ^sa  xi*' 

\ , Jupiter,  398  ai  * ao( 

Saturn,  3?8  3 4 


The  arc  of 'ilm  epicycle  traversed  by  the  planet,  at  any  point  in  itt*$Bvo- 
rfiou.  is  equal  to  its  distance  from  the  copjuuo^n,  when  reckoned" 'for- 
'4  from  the  planet^ccurding  to  the  jgi|^^^fescribed  in  verse  20. 


M2.] 


Translation  and  Notes. 


69 


Suppose,  now,  the  mean  place  of  the  planet,  relative  to  it*  conjunction 
'{ftgkroeoay  at  0,.fo  be  at  M : its  place  in  the  epicycle  ia  at  mi  as  far  from  • 
c"\  in  either  direction,  as  M from  C.  The  arc  of  the  epicycle  already  y 
traversed  ia  indicated  in  this  figure,  as  in  Fig.  8V  by  the  heavier  Hue. 
Draw  Em,  cutting  the  orbit  in  o;  then  o ia  the  planet’s. truepbepe,  and 
o M ia  the  equation,  oc  the  amount  of  removal  from  the  tnean  jdeee  :by 
the  attraction  of  the  being  at  0.  - ■ - ' 

The  aine  and  cosine  of  the  distance  from  the  conjunction,  the  dimen- 
sions of  the  epicycle,  and  the  value  of  the  correspondents  in  the  epicycle 
to  the  sine  and  cosine,  arc  found  as  in  the  preceding  process.  AddnM, 
the  result  from  the  cosine  ( kotijy&phala ),  to  ME,  the  radius:  the  result 
is  the  perpendicular,  En,  of  the  triangle  E n m.  To  the  square  of  En 
add  that  of  the  base  n m,  the  result  from  tlie  sine  ( bhvjajy&pkala) ; the 
square  root  of  the  sum  is  the  line  E r/i,  the  hypothenuse : it*is  termed  the 
variable  liypothenuse  (cala  Jcarna ) from  its  constantly  changing  its 
length.  We  have  now  the  two  similar  triangles  Emit  and  Keg.  & 
comparison  of  the  corresponding  parts  of  which  gives  us  die  prbfSSnon 
Km : m n : : Ko ; og\  that  is  to  say,  o* 7,  which  is  the  sine  of  the  equation 
oM,  equals  the  product  of  Eo.  th«?  radius  into  m 11,  the  result  from  the 
bftae*siu<i>,  divided  by  the  variable  hypothenuse,  Em. 

When  the  planet's  mean  place  is  in  the  quadrant  DO.  as  at  M#,  the 
result  from  the  perpendicular  sine  (koiijyaphala)%  or  M'n',  is  subtracted 
from  radius,  and  the  remainder,  Kn\  i»  employed  ns  before  to  find  the 
value  of  Em',  the  variable  hypot  lien  use : and  the  comparison  of  the 
similar  trianirb-H  E in'w'  and  KoV  gives  o y\  the  *ine  of  the  equation, 
o'  M 

It  is  obvimis  that  when  tin-  iiKsin  di-taiic*-  «*f  a planet  from  itsconjunc- 
tinii  is  h*>"»  t i i;iu  a quadrant  in  t-i.l^-r  I’.iii:*-;  a-  at  M,  tin.*  ba*e  Ew  is 
greater  than  radius;  when  that  dMam-i*  is  iiumc  than  a ijuadiuiit,  as  at 
M\  the  base  Kir'  is  than  radius:  rh*  cosine  is  to  In*  added  to  radius  ^ 
in  the  0110  and  siihlisii'P'd  from  it  in  i lie  oilier.  This  is  the  mean* 
ing  of  the  ini**  in  wise  40:  compare  tin1.  n*»te<  to  i.  and  ii.  150. 

in  illustration  of  the  pron-s^  we  w i i]  calculate  the  equation  of  the 
conjunction  of  Mcrrury  for  the  given  time,  or  for  midnight  preceding 
January  Jst,  ItfOU,  at  Washington. 

Since  the  Hindu  system,  lik.»  the  t>reck.  interchanges  in  the  case  of  the 
two  inti-rioi  planets  the  million  and  place  of  the  plain-t  itself  and  of  the 
sun,  giving  to  the  former  as  its  mean  motion  that  which  is  the  mean 
apparent-  motion  of  the  sun,  and  aligning  to  the  conjunction  (riyhrocca) 
a revolution  which  is  actually  that  of  the  planet  in  its  orbit,  the  mean 
position  of  Mercury  at  the  given  time  is  that  found  above  (under  v.  39) 
to’lm  that  of  the  sun  at  the  same  time,  while  to  lind  that  'f  its  conjunc- 
tion we  have  to  add"  the  equation  for  difference  n meridian  (RegAntarar 
pkala , i.  60,  61),  to  the  longitude  given  under  i.  o.‘<  as  that  of  the  planet. 

Longitude  of  Mercury’s  conjunction  (jayAroAtf),  midnight,  at  Ujjaymi,  4-  i5°  i3'  fl" 
add  for  difference  of  meridian,  1 34  >4' 


Longitude  of  conjunction  at  required  time, 
Mean  jftgitude  of  Mercury, 

Mean  commutation  ' 


•4  16  57  33 
8 18  i3  i3 


? a8  4 4 9 


70 


StoyaStidhlfa  [iUS- 

The  position  of  Mercuiy  with  reference  to  the  eomtuiction  i»  accord- 
ingly very  nearly  that  of  M',  in  Fig.  5,  The  arc  which  determines  the 
base-sine  (bhujojyd),  orOM',  is  58°  44',  while  M*D,  its  com  piemen  t| 
from  which  the  perpendicular-sine  (kotijyd)  is  takenv  is  31°  la.  The 
corresponding  sines,  M'  IV  and  M'  G,  are  2038'  and  1784'  respectively. 

The  epicycle  of  Mercury  is  one  degree  less  at  D than  at  6.  Hence 
the  proportion 

3438 : 6o : : 2938 : 5i 

S'ves  51'  as  the  diminution  at  M* : the  circumference  of  the  epicyle  at  M, 
env  is  132°  9'.  The  two  proportions 

36o°  : 132®  9' : : 2938 : 1078,  and  36o°  : 1 3a°  9' : : 17B4 : 655, 
give  us  the  value  of  iw'n'as  1078',  and  that  of  n'M'  as  655'.  The 
commutation  being  more  than  three  and  less  than  nine  signs,  or  in  the 
half-orbit  beginning  with  Cancer,  the  fourth  sign,  n'M' is  to  be  sub- 
tracted from  EM',  or  mdius,  3438' ; the  remainder,  2783',  is  the  perpen- 
dicular En'. 


To  the  square  of  E n \ 

7,745,089 

add  the  square  of  n' 

i,i6a,oS4 

of  their  sum, 

®.9°7.,73 

the  square  root, 

3984 

is  the  variable  liypotlienuse  (culu  JLurna),  Em'.  The  comparison  of  thp - 
triangles  E m*  n'  and  E o //'  gives  t lie  proportion  E mr : w'  n' : : E o' : olg\  or 

1984  : M17R  : : 34%:  1242 

The  value  of  o'//,  the  sine  of  the  equation,  is  accordingly  1242':  the  cor- 
responding arc,  o'  M,  is  found  by  the  process  prescribed  in  verse  33  to  bo 
21°  12;.  The  figure  shows  the  equation  to  be  subtractive. 

The  annexed  table  presents  the  n suits  of  the  calculation  of  the  equa- 
tion of  the  conjunction  (righrakannan)  for  the  live  planets. 


/faults  of  the  First  Process  for  finding  the  True  Plans  of  the  Planets . 


| Lnngitudft  of  M»*an  lime-!  f’orr. 

I Conjunction.  CaimniitHtioiJ.  sine.  jEpicycii 


!lenalt  -Bfnult Va 
from  I from  | fthl 
U aine.  P -iiiM 


5Ufffcury,j8  18  i3  1 3!  4 16  67  22  7 a8  44  fy  29%j  ila  9 1078  855  |2984|-ai  iaj 
Venus,  ;8  r8  i3  i3>ro  21  49  4?i  2 3 36343080  260  i-3  2226  no4  .5o58|+a6  71 
Mara,  15  a4  3o  67!  8 18  il  >3-  a 23  4a  16,3416,  23a  ij  2202  aa5  ;4a74j+3i  1 

Jupiter,  [a  a6  a i4(  6 18  i3  i.3L  5 22  »o  f >9  4681  70  16  91  665  *2774:4.  1 53j 

Saturn,  ;3  20  1a  3!  8 18  i3  x 3,  4 28  i io  i6ao|  39  3a‘  200  32o;3i24j+  3 4o| 


This  is,  however,  only  a first  step  in  the  whole  operation  for  findipg 
the  true  longitudes  of  these  five  planets,  as  is  laid  down- rid  the, next 


4JJ  The  process  of  correction  for  the  apsii^fcetj; 
thp  only  one  required  for  the  sun  and  moon ; ;for 
other  planets  are  prescribed  that  lor  the  cOufend 


: Other  planets  are 
i&frt-ibitbe  apsis 


^oi\j.unction— ienir,  in  sue 


scribed  that  for  jthe  c6qjfan<% 
inda),  again  thafcjbrjhe  apsis, 


are  an 


Thmmtim  land  Notes. 


71 


44.  To  the  mean  place  of  the  planet  apply  half  the  equation 
of  the  conjunctum (ffyhraphdla)}  likewise  half  the  equation  of  the 
apsis;  to  the  mean  place  of  the  planet  apply  the  whole  equation 
of  the  apsis  ( mandaphali ),  and  also  that  of  the  conjunction. 

45.  In  the  case  of  all  the  planets,  and  both  in  the  process  of 
correction  for  the  conjunction  and  in  that  for  the  apsis,  the  equa- 
tion is  additive  (dhana)  when  the  distance  (kmdra)  is  in  the  lialf- 
orbit  beginning  with  Aries;  subtractive  (rmz),  when  in  the  half1 
orbit  beginning  with  Libra. 

The  rule  contained  in  the  last  verse  is  n general  one,  applying  to  all 
the  processes  of  calculation  of  the  equations  of  place,  and  has  already 
been  anticipated  by  us  above.  Its  meaning  is,  that  when  the  anomaly9 
(i mandakerulra ),  or  commutation  ( fhjhrakendnC ),  reckoned  always  forward 
from  the  planet  to  the  apsis  or  conjunction,  is  less  than  six  signs,  the 
equation  of  place  is  additive ; when  the  former  is  more  than  six  signs, 
the  equation  is  subtractive.  The  reason  is  made  clear  by  the  figures  given 
above,  and  by  the  explanations  under  verses  1-5  of  this  chapter. 

It  should  have  been  mentioned  above,  under  verse  where  the  word 
kendra  was  first  introduced,  that,  as  employed  in  thi->  sense  by  the  Hin- 
dus, it  properly  signifies  tin*  position  (>oe  note  to  i.  53)  of  the  u centre” 
Of  the  epicycle — which  coincides  with  the  mean  place  of  the  planet  itself 
-^relative  to  the  apsis  or  conjunction  respectively.  In  the  text  of  the 
Sflrya-Siddhuntu  it  is  used  only  with  this  signification  : the  commentary 
employs  it  also  to  designate  the  centre  of  any  circle. 

Since  the  sun  and  moon  have  bur  a single  in-qurditv,  according  to  the 
Hindu  system,  the  calculation  of  th« -ir  true  places  is  simple  and  easy. 
With  the  other  planets  the  case  is  different,  on  account  of  the  existence 
of  two  causes  of  disturbance  in  their  orbits,  and  the  consequent  necessity 
both  of  applyiug  two  equations,  and  also  of  allowing  tor  the  effect  of  each 
cause  in  determining  the  equation  due  to  the  other.  Tor,  to  the  appre- 
hension of  the  Hindu  astronomer,  it  would  not  be  proper  to  calculate  the 
two  equations  from  the  mean  place  of  the  planet ; nor,  again,  to  calculate 
.cither  of  the  two  from  the  mean  place,  and,  having  applied  it.  to  take 
the  new  position  thus  found  as  a basis  from  which  to  calculate  the  otbw; 
since  the  planet  is  virtually  drawn  away  from  its  mean  place  by  Uio 
divinity  at  either  apex  (urea)  before  it  is  submitted  to  the  action  of  tbe 
other.  The  method  adopted  in  this  Siddhftnta  of  balancing  the  two- 
influences,  and  arriving  at  their  joint  effect  upon  the  planet,  is  stated  in 
verses  43  and  44.  The  phraseology  of  the  text  is  not.  entirely  explicit, 
and  would  bear,  if  taken  alone,  a different  interpretation  from  that  which 
the  common  tary*pfct*  upon  it,  and  which  the  rules  t » be  giwu  later  show, 
to  be  its  true  impelling;  thu  is  as  follows:  first  oak  date  from  the  mean 
' place  of  t)ie  jJjlljet  the  equation  of  the  conjunction,  and  apply  the  half 
of  fcgo  mean  place ; from  the  position  thus  obtained  calculate  the 
6qn«Hn  of  the  apsis,  and  apply  half  of  it  to  the  longitude  as  already 
ondMjMmtad ; ffipm  this  result  find  once  more  the  equation  the  apsis^ 
m^m$3  ft  wMm  original  mean  place  of  the  pirns  It*  and  finally,  calw 
jpply  to*  this Jgst  place  the  whole  j&uation  of  the  eon- 


•v  We  have  wtilcuhited  by  this  method  the  true  pieces  of  the  five  planets,' 
an&jiresentthe  results  of  the  processes  in  the  flowing  tables,  Those 
tjf-  the  fust  process  have  been  already  given  under  the  preceding  pas- 
ftKge*:  the  application  of  half  the  equations  there  found  -to  the  tnesui 
longitude  gives  us  the  longitude  once  equated  as  a basis  for  the  next 
'process. 

. 'JS  ■ / 

Result*  of  the  Second  Process  jor  finding  the  True  Places  of  the  Planets . 


p.  , , Equaled  ' Iningitihlc  ! nqu.il.Ml  j nunc 

; Lott^iiiiili'.  | of  Apri*.  j Anomaly.  rinr. 

I'orwlt’d'  Equation 
Epicycle.,  of  April- 

; 1 « * j i w • ••  h • *i  ■ 

Mercury,  <8  7 3?  j 7 1 0 28  30 . 1 1 3 5 1 1 1 568 
Venn*,  j 9 1 r ,i  19  fu  1-7 j 5 18  35 j 681 

Mars.  1 6 id  1 ■ .{  10  2 4|l'i<1  11  J j 79-- 

Jupiter,  ! a an  ! 5 ?i  ?a  i«;  7 ).f  a.3  1 3470  j 

Saturn,  1 3 73  1 1 7 36  37  34]  4 4 37  j 7879  j 

O.j.. 

29  5 | - 2 7 

1 1 48  1 '+  0 22 

"77  74  ' -IO  2 

3-i  o|+5  5 

48  11  |+  6 »o 

Again,  the.  application  of  half  these  equations  to  the  longitudes  ns 
once  equated  furnishes  the  data  for  the  third  process.  The  longitudes  of 
the  apsides,  being  the  same  as  in  the  second  operation,  are  not  repeated 
in  this  table. 


Results  of  the  Third  Process  for  finding  the  True  Places  of  the  Planets . 


1 Planet. 

1 

Equated 

Longitude. 

JSqualod 

Anomaly. 

Bil  tw- 
ain e. 

. C01  rented 
■ Epicyele. 

Equation 
of  Apala. 

j Merrui  y, 

i* 

i 8 

0 

6 

s i 

34  | 

■ 

rr 

0 

3 

54 

i:>12 

a 

-*9 

■» 

a 

-2 

1 

2 

, Venus, 

■ 9 

1 

28 

5 

18 

24 

691 

11 

48 

•fO 

23 

; Mars, 

6 

5 

O 

in 

■ r» 

3 

2Rf4 

ny 

33 

-9 

3o 

| Jupiter, 

A 

=9 

3i» 

7 

71 

5; 

3 2 

1 

+0 

4 

j Saturn, 

■ 3 

75 

1 1 

: A 

I 

27 

i V-* 

48 

9 

46 

33 

The  original  mean  longitude*  are  now  corrected  by  the  results  of  the 
third  process,  to  obtain  a position  from  which  shall  !*c  once  more  calcu- 
lated the  equation  of  the  conjunction : and  the  application  of  this  to  the 
position  which  furnished  it  viclds.  as  a final  result,  the  true  place  of  each' 
pfamot. 


Results  of  the  Fourth  Process  far  finding  the  Tine  Places  of  the  Planets . 


II  -wine.  P.  Kiniv 


! « 


’■  n 


'Mercury,  8 16  it  : 8 
‘■Venus,  ,8  1 8 if)  , a 
jMftrs,  5 i5  i : 3 J 
Jupiter,  j 3 i 6 5 17  7 
{Saturn,  : 3 76  45 ! 4 9 1 28 


"l" 


o 46  3or*#  I*!?  8 noi  ! fnfi 

3 14  >3069'  v6i»  1 3 7718  ni8 
j 3432  23a  o|  2312  134 

766,  70  271  if)o  ; 61)6 
2 r 4 1 , 39  37 1 * 236  ; 796 


3n?9 

5067 

3984 

2786 

3i5i 


Equation 
of  Couj. 

-2J  20 

+»5  59 
+33  44 
+ 3 *| 
+ 4 17 


True 

Isong  ituda.  | 


7 »4  5i 
9 >4  35 
6 18  45 

3 4 ri 

4 1 a 


We  cangot  furnish  a comparison  of  tlio  Hindu  .dctenninatioagflffiha 
true  pieces  of  the  planets  with  their  actual  petitions  as  ascertwetiT.by 
our  modern  methods,  until  after  the  subject  of  tne  latitp^e  has  bfeadeslt 
see  below,  under  verses  ^ ’ 


TIm  Pind*  nwtba&vf  finding  A.  tw«  toogttofiw  «f  4m  firtplanati 
whow  ipparcnt  pwjtlqa.fc  affeeUdey  A'  parallax  jjf  A*  t«Afaswtta 
having  Aw  b#A  Ally  explained,  we  will  proeeed  to  indicate,  a*  me* 
ninety  m powible,  the  way  in  which  the  mum  problem  k wived  by  At 
greettQrcex  aatronomer.  The  annexed  figure  (Fig.  9)  will  iUnatrate  U» 
- 1 J J*  dm  A.  Syntax*  bn* 


hypoAe 

ical,  not  according  wiA  Ae  actual  element.  of  any  of  Ae  planetary 
orbits. 

Let  B be  Ae  earth’*  place,  and  let  Ae  circle  ApC,  deacribed  about 
B ae  a centre,  represent  the  mean  orbit  of  any  planet,  BA  being  Ae 
direction  of  ita  line  of  apsides,  and  £ C Aat  of  its  conjunction  {ftgkra), 
# called  by  Ptolemy  At 

apogee  of  its  epicycle. 
Let  EX  be  Ae  double 
eccentricity,  or  At 
equivalent  to  Ae  tv 
dius  of  Ae  Hindu 
epicycle  of  the  apeia; 
and  let  EX  be  bi- 
sected in  Q.  Then, 
as  regards  the  influ- 
ence of  the  eccen- 
tricity of  the  orbit 
upon  the  place  of  the 
planet,  the  centre  of 
equable  angular  op- 
tion is  At  X,  but  the  centre  of  equal  distance  is  at  Q:  the  planet  virtu- 
ally describes  the  circle  A'  P,  of  which  Q is  the  centre,  but  at  the  same 
rate  as  if  it  were  moving  equably  upon  the  dotted  circle,  of  which  the 
centre  is  at  X.  The  angle  of  mean  anomaly,  accordingly,  which  in- 


[j2tTjT*Tj*TYT7TTir^r}WJTWXT77Tj»^F^KWtj 


HarBi»T-n»]ruui¥i 


PE  A the  true  anomaly,  and  E P X the  equation  of  place.  The  value 
of  E P X is  obtained  by  a process  analogous  to  that  described  above, 
under  verse  39  (pp.  06,  67) ; EB  and  BX,  and  QD  and  PX,  are 
first  found;  then  DP,  which,  by  subtracting  DX,  gives  XP;  XP 
added  to  B X gives  B P ; and  from  B P and  B E is  derived  EP B,  the 
equation  required;  subtract  this  from  PXA,  and  the  remainder  ia 
REA,  the  planet's  true  distance  from  the  apsis.  About  P describe 
A*  epicycle  of  the  conjunction,  and  draw  the  radius  P T parallel . 
to  EC:  then  T is  the  planet's  place  in  the  epicycle,  p its  apparent 
position  in  the  mean  orbit,  and  T E F the  equatic  n of  the  epicycle,  or 
of  the  conjunction.  In  order  to  arrive  at  the  va<ue  of  this  equation 
Ptolemy  first  finds  that  of  8 E R,  the  corresponding  angle  when  file 
centre  of  the  epicycle  is  placed  at  R,  at  the  mean  distance  E R*  or 
^from  E:  he  then  diminishes  it  by  a complicated  process,  into 
tWfjVhMls  of  which  it  is  not  necessary  here  to  enter,  and  *hicb,  as 
htfjftmeelf  acknowledges,  is  not  strictly  accurate,  but  yields  results  tuffi- 
near  to  the  truth.  Implication  of  tbs  elation  thus  obtained  . 


- 74'  'v  SQrya-Siddhdnta,  [ii.  45.  ■. 

%' the  place  of  the  planet  as  already  once  equated  gives  the  final  result 
Ipught  for,  its  geocentric  place. 

the  case  of  Mercury,  Ptolemy  introduces  the  additional  supposition 
thfct  the  centre  of  equal  distances,  instead  of  being  fixed  at  Q,  revolves 
■ In  a retrograde  direction  upon  the  circumference  of  a circle  of  which  X 
ja  the  centre,  and  XQ  the  radius. 

After  a thorough  discussion  of  the  observations  upon  which  his  data 
and  his  methods  arc  founded,  and  a full  exposition  of  the  latter,  Ptolemy 
proceeds  himself  to  construct  tables,  which  are  included  in  the  body  of 
nit  work,  from  which  the  true  places  of  the  planets  at  any  given  time 
knay  be  found  by  a brief  and  simple  process.  The  Hindus  are  also  ac- 
customed to  employ  such  tables,  although  their  construction  and  use  are 
nowhere  alluded  to  in  this  treatise.  Hindu  tables,  in  part  professing  to 
be  calculated  according  to  the  Sfirva-Skldh&nta,  have  been  published 
by  Bailly  (Trait6  dc  l’Astr.  Ind.  ct  Or.,  p.  335,  etc.),  by  Bentley  (Bind. 
Ask,  p.  219,  etc.),  by  Warren  (Ksila  Sankalita,  Tables),  by  Mr.  lloisiug- 
ton  (Oriental  Astronomer,  p.  til,  etc.),  and,  for  the  sun  and  moon,  by 
Davis  (As.  Res.,  ii.  255,  250). 

We  are  now  in  a condition  to  compare  the  planetary  system  of  the 
BSndus  with  that  of  the  Greeks,  and  to  take  note  of  the  principal  re- 
aemblances  and  differences  between  them.  And  it.  is  evident,  in  the  first 
place,  that  in  all  their  grand  features  the  two  arc  essentially  the  same. 
Both  alike  analyze,  with  remarkable  success,  the  irregularities  of  the 
apparent  motions  of  the  planets  into  the  two  main  elements  of  which 
they  are  made  up,  and  both  adopt  the  same  method  of  representing  and 
calculating  those  irregularities.  Both  alike  substitute  eccentric  circles 
for  the  true  elliptic  orbits  of  the  planets.  Both  agree  in  assigning  to 
Mercury  and  Venus  the  same  mean  orbit  and  motion  as  to  the  sun,  and 
in< giving  them  epicycles  which  in  fact  correspond  to  their  heliocentric 
orbits,  making  the  centre  of  those  epicycles,  however,  not  the  true,  but 
the  mean  place  of  the  sun,  and  also  applying  to  the  latter  the  correction 
due  to  the  eccentricity  of  the  orbit.  Both  transfer  the  centre  of  the 
orbits  of  the  superior  planets  from  the  sun  to  the  earth,  and  then  assign 
to/ each,  as  an  epicycle,  the  earth’s  orbit ; not,  however,  in  the  form  of 
an  ellipse,  nor  even  of  an  eccentric,  but  hi  that  of  a true  circle;  and 
here,  too,  both  make  the  place  of  the  centra  of  the  epicycle  to  depend 
upon  the  mean,  instead  of  the  true,  place  of  riie  sun.  The  key  to  the 
woole  system  of  the  Greeks,  and  liic  determining  cause  both  of  its  nu- 
merous accordances  with  the  actual  conditions  of  things  in  nature,  and 
of  its  inaccuracies,  is  the  principle,  distinctly  laid  down  and  strictly  ad- 
hered te  by  them,  that  the  planetary  movements  arc  to  be  represented 
bv  a combination  of  equable  circular  motions  alone,  none  other  being 
deemed  suited  to  the  dignity  and  perfection  of  the  heavenly  bodies.  By 
. the  Hindus,  this  principle  is  nowhere  expressly  recognized,  so  far  as  we 
. ora  aware,  as  one  of  binding  influence,  and  although  their  whole  system, 

^ no  {ess  than  that  of  the  Greeks,  seems  in  other  respects  inspired  by  it* 

" it  is  in  ^pe  point,  as  wc  shall  note  more  particularly  hereafter,  distinctly 
4>andonea  and  violated  by  them  (see  below,  under  vv.  50,  51).  -We 
. e&opot  but  regard  with  the  highest  admiration  the  acuteness  and  in- 
^'dnstry,'  the  power  of  observation,  analysis,' and  deduction  of  thi^riiks, 
■St*  . ' ' ■ 


ii.  45.] 


Translation  and  Notes. 


75 


that,  hampered  by  false  assumptions,  and  imperfectly  provided  witty 

instruments,  they  were  able  to  construct  a 'science  containing  so  much 
of  truth,  and  serving  as  a secure  basis  for  the  improvements  of  a for 
time  ^whether  wc  pay  the  same  tribute  to  the  genius  of  the  Hindu  will 
depend  upon  whether  we  consider  him  also,  like  all  the  rest  of  the  world, 
to  have  been  the  pupil  of  the  Greek  in  astronomical  science,  or  whether 
wo  shall  believe  him  to  have  arrived  independently  at  a system  SO 
closely  the  counterpart  of  that  of  the  West. 

The  differences  between  the  two  systems  are  much  less  fundamental 
.and  important.  The  assumption  of  a centre  of  equal  distance  differimt 
from  that  of  equal  angular  motion — and,  in  the  ease  of  Mercury,  itself 
also  movable — is  unknown  to  the  Hindus : this,  however,  appears  to  be 
an  innovation  introduced  into  the  Greek  system  by  Ptolemy,  and  un- 
known before  his  time;  it  was  adopted  by  him,  in  spite  of  its  seeming 
arbitrariness,  because  it  gave  him  results  according  more  nearly  with  hu 
observations.  The  moon’s  cvcciion,  the  discovery  of  Ptolemy,  is  equally 
wanting  in  the  Hindu  astronomy.  As  regards  the  combined  application 
of  the  equations  of  the  apsis  and  the  conjunction,  the  two  systems  are 
likewise  at  variance.  Ptolemy  follows  the  truer,  as  well  as  the  simpler, 
method:  he  applies  first  the  whole  correction  for  the  eccentricity  of  the 
orbit,  obtaining  as  a result,  in  the  case  of  the  superior  planets,  the 

Iffanet's  true  heliocentric  place ; and  this  he  then  corrects  for  the  paral- 
ax  of  the  Mirth's  position.  Here,  too,  ignorant  as  he  was  of  the  actual 
relation  between  the  two  equations,  we  may  suppose  him  to  have  been 
guide- 1 by  the  better  coincidence  w ith  observation  of  the  results  of  his 
processes  when  thus  conducted.  The  Hindus,  on  the  other  hand,  not 
knowing  tii  which  of  the  two  supernatural  beings  at  the  apsis  and  con- 
junction should  l»e  attributed  the  priority  of  influence,  conceived  them 
to  art  simultaneously,  and  adopted  the  method  stated  above,  in  verse  44, 
of  obtaining  an  average  plan  whence  their  joint  effect  should  be  calcu- 
lated. This  is  the  only  point  where  they  forsook  the  geometrical  method, 
and  suffered  their  theory  respecting  the  character  of  the  forces  produ- 
cing  the  inequalities  of  motion  to  modify  their  processes  and  results. 
The  change  of  dimensions  of  the  epicycles  is  also  a striking  peculiarity 
of  the  Hindu  system,  and  to  us,  thus  far,  its  most  enigmatical  feature. 
The  virtual  effect  of  the  alteration  upon  the  epicycles  themselves  is  to 
give  them  a form  approximating  to  the  elliptical.  But,  although  the 
epicycles  of  the  conjunction  of  the  inferior  planets  represent  the  proper . 
orbits  ol*.  those  planets,  and  those  of  the  superior  the  orbit  of  the  earth, 
it  is  not  possible  to  see  in  this  alteration  an  unconscious  recognition  of 
the  principle  of  ollipliciiy,  because  the  major  axis  of  the  quasi-ellipse — 
or,  in  the  ease  of  Jupiter  and  Saturn,  the  i-.iuor  axis — is  constantly 
poin&d  toward  the  earth.  Its  effect  upon  the  jrbit  described  by  tho 
planet  is,  as  concerns  the  epicycle  of  the  apsis,  \j  give  to  the  eccentric 
circle  an  ovoid  shape,  flattened  in  the  first  and  fourth  quadrants,  bulging 
iu  the  second  and  third  : this  is,  so  far  as  it  goes,  an  approximation  to- 
ward Ptolemy’s  virtual  orbit,  a circle  described  about  a centre  distant 
ftbni  the  earth’s  place  by  only  half  the  equivalent  of  the  radius  of  the 
qgscyclo  (tho  circle  A?  P in  figure  6) : but  the  approximation 
^^^Vdistant  to  furnish  any  hint  of  ou  explanation  A diminution 


t tpioyvlo  nlfio  efftotfe*  ttirenwaSng  diminution  of  tbtf  equating'  i 
is#  the  planet  forwahf where  tn«  equation  ia  lubtrwtive,  and  badfc^ 
,%bere  it  ia  additive : but  we  hardly  feel  justified  in  aasaminff  ml 

l 1.  . j 1 s__  1 x! !■  J a _ 1 


^ .td  be  regarded  As  An  empirical  correction,”  applied  to  maker  Aft  re^  4 
full*  of  calculation  agree  more  nearly  with  those  of  observation,  3j$Cife*6 
III  amount  and  place  stand  in  no  relation  which  we  have  been  able  to 
Iradb  to  the  true  elements  of  the  planetary  orbits,  nor  is  the  accuracy 
of  either  the  Hindu  calculations  or  observations  so  great  as  to  make 
Mach  slight  corrections  of  appreciable  importance.  We  are  compelled 
Hjieave  the  solution  of  this  difficulty,  if  it  shall  prove  soluble,  to  later 
investigation,  and  a more  extended  comparison  of  the  different  text- 
books of  Hindu  astronomical  science. 

As  regards  the  numerical  value  of  the  elements  adopted  by  die  two 
systems — their  mutual  relation,  and  their  respective  relations  to  the  true 
elements  established  by  modern  science,  arc  exhibited  in  the  annexed 
table.  The  first  part  of  it  presents  the  comparative  dimensions  of  the 
planetary  orbits,  or  the  value  of  the  radius  of  each  in  terms  of  that  of 
the  earth’s  orbit  In  the  case  of  Mercury  and  Venus,  this  is  represented 
tar  the  relation  of  the  radius  of  the  epicycle  (of  the  conjunction)  to  that 
« the  orbit ; in  the  case  of  the  superior  planets,  by  that  of  the  radius 
of  the  orbit  to  die  radius  of  the  epicycle.  For  the  Hindu  system  it 
was  necessary  to  give  two  values  in  every  case,  derived  respectively  from 
the  greatest  and  least  dimensions  of  the  epicycles.  Such  a relative  de- 
termination of  the  moon's  orbit,  of  course,  could  not  be  obtained : its 
Absolute  dimensions  will  be  found  Btated  later  (see  under  iv.  3 and  xii. 
84).  The  second  part  of  the  table  gives,  as  the  fairest  practicable  com- 
tt  of  the  values  assigned  by  each  system  to  the  eccentricities,  the 
equations  of  the  centre.  For  Mercury  and  Venus,  however,  the 
t and  modern  determinations  of  these  equations  are  not  at  all 
le,  the  latter  giving  their  actual  heliocentric  amount,  the  for- 
mer tfcbir  apparent  value,  as  seen  from  the  earth. 

Relative  Dimensions  and  Eccentricities  of  the  Planetary  Orbits , according 
to  Different  Authorities . 

vi  en  icat  Equation  of  the  Ceniro.| 
Modemi. 


llodiua  of  the  Orbit. 


Planet. 

Surya-Ri 
eras  quad. 

ddhiiniu 
odd  quad 

Ptolemy. ; Moderns  j 

SiddJl.rnla.i  • 

6oa, 

1.0000 

1-0000 

1.0000 

1.0000 

• . 11  j 

2 10  3l  | 

• 

2 

93 

Vew, 

HM 

PB 

5 2 46 

5 

r 

Mercury, 

.3694 

.3667 

9 

4 27  35 

a 

52 

Venus, 

.7376 

.722* 

wEmm 

MrffiEl 

1 45  3 

9 

23 

Mars.  - 

1 Ji39 

i.55i3 

1.5190 

1.5237 

11  32  3 

11 

32 

Jupiter,  " 

5.t439 

5 0000 

5.3174 

5.2028 

| 5 5 58  | 

5 

16 

Saturn, 

99308 

9.0000 

9 j3o8 

9.5389 

1 7 39  32 

6 

3a 

i 55  97 
6 17  i3 
*3  4fc  # 
a 47  ‘h 

iai4i  3S'] 
Plni 

6 iS  jii 


4&  Multiply  the  daily  motion  (bhukti)  of„a  placet  by  the  sun's 
Result  from  the  base-sine  (< bdbuphala ),  §p^4ivide*%  the  nupiher 
of  minutes  in  a circle  (bhacaJcra) ; |ra;phu]t,  in  minutdfc^wy 
to  the  planet’s  true  place,  in  the 
«ss  applM  to  the  tua.  * ' • 


ii.  40.] 


Translatio 


ttlito  rule,  allowance  is  matte  for  that  pvt  of  the  equation  of  timet 
the  difference  between  mean  and  apparent  solar  time,  which  k dpi 
r difference  between  the  sun’s  mean  and  true, places.  The  instNKr 
, moVgLemployed  by  the  Hindus  in  measuring  time  are  described,  Ar 
Minted  insufficiently,  in  the  thirteenth  chapter  of  this  Work : in  an 
probability  the  gnomon  and  shadow  was  that  most  relied  upon;  at  any 
rate,  they  can  have  had  no  means  of  keeping  mean  time  with  any  Men- 
recy,  and  it  appears  from  this  passage  that  apparent  time  alone  is  re- 
garded as  ascertainable  directly.  Now  if  the  sun  moved  in  the  equi- 
noctial instead  of  in  the  ecliptic,  the  interval  between  the  passage'  oflHs 
mean  and  his  true  place  across  the  meridian  would  be  the  satne  part  Of 
a day,  as  the  difference  of  the  two  places  is  of  a circle : hence  the  pM- 
portion  upon  which  the  rule  in  the  text  is  founded : as  the  number  of 
minutes  in  a circle  is  to  that  in  the  sun's  equation  (which  is  the  same 
with  his  "result  from  the  base-sine:'1  sec  above,  v.  30),  so  is  the  whole  ' 
daily  motion  of  any  planet  to  its  motion  during  the  interval.  And 
since,  when  the  sun  is  in  advance  of  his  true  place,  he  comes  later  to 
the  meridian,  the  planet  moving  on  during  the  interval,  and  the  reverse^ 
the  result  is  additive  to  the  planet's  place,  or  subtractive  from  it,  accovd- 
ing  as  the  sun's  equation  is  additive  or  subtractive. 

The  other  source  of  difference  between  true  and  apparent  time,  the 
difference  in  the  daily  increment  of  the  arcs  of  the  ecliptic,  in  which 
the  sun  moves,  and  of  those  of  the  equinoctial,  which  are  the  measure* 
of  time,  is  not  taken  account  of  in  this  treatise.  This  is  the  more 
strange,  as  that  difference  is,  for  some  other  purposes,  calculated  and 
allowed  for. 

At  the  time  for  which  wc  have  ascertained  above  the  true  places^ff 
the  planets,  the  sun  is  so  near  the  perigee,  and  his  equation  of  plsetfS 
so  small,  that  it  renders  necessary  no  modification  of  the  placegK 

Sven:  even  the  moon  moves  but  a small  fraction  of  a second  diMqp 
e interval  between  mean  aud  apparent  midnight. 

By  bhukti\  as  used  in  this  verse,  wc  arc  to  understand,  of  course,,  not 
the  mean,  but  the  actual,  daily  motion  of  the  planet : the  commentary 
also  gives  the  word  this  interpretation.  IIow  the  actual  rate  of  mqtsMi 
is  found  at  any  given  time,  is  taught  in  the  next  passage. 

47.  From  the  mean  daily  motion  of  the  moon  subtract  th* 
daily  motion  of  its  apsis  (manda)}  and,  having  treated  the  differ- 
ence in  the  manner  prescribed  by  the  next  rule,  apply  the  result^, 
as  an  additive  or  subtractive  equation,  to  the  daily  motion.  * 

48.  The  equation  of  a planers  daily  motion  is  to  be  calculated 
like  the  place  of  the  planet  in  the  process  for  the  apsis : multi- 
ply the  daily  motion  by  the  difference  of  tabular  sines  corre- 
sponding to  the  base-sine  (dorjyd)  of  anoma.y,  and  then  divide 
by  two  hundred  and  twenty-five ; 

' 49.  Multiply  the  result  by  the  corresponding  epicycle  df  thji 


. Multiply  the  result  by  the  corresponding  epicycle  m 
(mandapatidh i),ftnd  divide  by  the  number  of;  (Agrees  in  a 
the  result^in  minutes,  is: additive  when  in  the 
Manning  wiiji  ttflfcer^and  subtractive  vrhenin  that 
tiit ^Oiiprieorn.  ■ * * * ■' ;9" r'  * ! ■*-. 


78 


[iUft 


, Only  the  effect  of  the  apsis  upon  the  daily  rate  of  motion  is  treated 
of  in  these  verses ; the  farther  modification  of  it  by  the  conjunction  ft, 
tttys  subject  of  those  which  succeed.  ' t.f 

InTerse  47  is  a separate  specification  under  the  general  rule  gteen  inJ 
the  following  verse,  applying  to  the  moon  alone.  The  rate  of  a planet’s* 
motion  in  its  epicycle  being  equal  to  its  mean  motion  from  the  apsis,  or 
its  anomalistic  motion,  it  is  necessary  in  the  case  of  the  moon,  whose 
apsis  has  a perceptible  forward  movement,  to  subtract  the  «aily  amount 
of  this  movement  from  that  of  the  planet  in  order  to  obtain  the  daily 
rate  of  removal  from  the  apsis. 

In  the  first  half  of  verse  48  the.  commentary  sees  only  an  intimation 
that,  as  regards  the  apsis,  the  equation  of  motion  is  found  in  the  same 
general  method  as  the  equations  of  place,  a certain  factor  being  multi- 
pliedhby  the  circumference  of  the  epicycle  and  divided  by  that  of  the 
§yMrbik  Such  a direction,  however,  would  be  altogether  trifling  and  super- 
fluous, and  not  at  all  in  accordance  with  the  usual  compressed  style  of 
the  treatise;  and  moreover,  were  it  to  he  so  understood,  we  should  lack 
any  direction  as  to  which  of  the  several  places  found  for  a planet  in  the 
process  for  ascertaining  its  true  place  should  be  assumed  as  that  for 
.which  this  first  equation  of  motion  is  to  lie  calculated.  The  true  mean* 
ing  of  the  lino,  beyond  ail  reasonable  question,  is,  that  the  equation  is 
to  be  derived  from  the  same  data  from  which  the  equation  of  place  for 
the  apsis  was  finally  obtained,  to  be  applied  to  the  planet's  mean  posi- 
tion, as  this  is  applied  to  its  mean  motion;  from  the  data,  namely,  of 
the  third  process,  as  given  above. 

The  principle  upon  which  the  rule  is  founded  may  be  explained  as 
follows.  The  equation  of  motion  for  any  given  time  is  evidently  equal 
*3$:the  amount,  of  acceleration  or  of  retardation  effected  during  that  time 
M^tie  influence  of  the  apsis.  Thus,  in  Fig.  3 (p.  64),  mn , the  sine  of 
is  the  equation  of  motion  for  the  whole  time  during  which,  the 
%enttis  of  the  epicycle  has  been  traversing  the  arc  A M.  If  that  arc, 
and  the  arc  a'ro,  be  supposed  to  be  divided  into  any  number  of  equal 
portions,  each  equal  to  a day's  motion,  the  equation  of  motion  for  each 
successive  day  will'bc  equal  to  the  successive  increments  of  the  sines  of 
fr.the  increasing  arcs  in  the  epicycle ; and  these  will  be  equal  to  the  sue-? 
cessive  increments  from  day  to  day  of  the  sines  of  mean  anomaly,  rc- 
. duced  to  the  dimensions  of  the  epicycle.  Hot  the  rate  at  which  thp 
sine  is  increasing  or  decreasing  at  any  point  in  the  quadrant  is^spprolct- 
vately  measured  by  the  difference  of  tlm  tabular  sines  at  that  point; 
and" as  the  arcs  of  mean  daily  motion  arc  generally  quite  small — being, 
^except  in  the  case  of  the  moon,  much  less  than  3g  4 o',  the  unit  of  the 
table — wc  may  form  this  proportion : if,  at  the  point  in  the  orbit  occu- 
a pied  by  the  planet,  a difference  of  3°  45'  in  arc  produces  an  increase  or 
■ decrease  of  a given  amount  in  sinfe  what  increase  or  decrease  of  sine 
will  be  produced  by  a difference  of  arc.  equal  to,  the  planet’s  daily, 
^motion ! or,  225  : diff.  of  tab.  sines : : phnefts  dgily  motion  : correspond* 
Hug  diff.  of  sine.  The  reduction  of  the  rese^y^  this  proportion  to  tfie 
dmenjDon^of  the  epicycle  gives  the 
We  will  calculate  by  this  method  ipnnKfouly  motion  of. <4 
which  her  true  loand  ebove.^ 


Moon's  mean  daily  motiofa  (I.  5<fy  790'  35" 

4'v.  deduct  daily  motion  of  apsis  (i.  85),  * ,6  4i  ^ . . 

Moon1!  mean  anomalistic  motion,  78)  S4  f 

r??©M,S®  process  of  calculation  of  the  moon’s  true  place,  given  abotfi, 

we  take 

Moon’s  mean  anomaly,  10*  18°  46'  i5"* 

Sine  of  anomaly  (bhujqjyd).  >966' 

From  the  table  of  sines  (ii.  15-27),  we  find 

GOmsponding  difference  of  tabular  since,  174' 

Hence  the  proportion 

aa5':  174'::  783'  54":GoG'  i3" 

■hows  the  increase  of  tlic  sine  of  anomaly  in  a day  at  this  point  to  bf  > 
606'  13".  The  dimensions  of  the  epicycle  were  found  to  be  31°  47'.  1 
Hence  the  proportion 

36o°  : 3i°  47' : : 606'  i3"  : 53'  3i"  * > 

give  us  the  desired  equation  of  motion,  as  53'  31".  By  verse  40  it  ifc 
subtractive,  the  planet  being  less  than  a quadrant  from  the  apsis,  or  Ha 
anomaly  being  more  than  nine  and  less  than  three  signs.  Therefore, 
from  the 


Moon’s  mean  daily  motion, 
subtract  the  equation, 

Moon's  true  daily  motion  at  given  time, 


790'  35" 
53  3i 

7^7  4 


The  roughness  of  the  process  is  well  illustrated  by  this  example^# 
Had  the  sine  of  anomaly  been  but  T greater,  the  difference  of  tinea 
would  have  been  10'  less,  and  the  equation  only  about  50'. 

The  equation  of  the  sun's  motion,  calculated  in  a similar  manner,  is 
found  to  be  +2'  18",  and  his  true  motion  61'  26". 

The  corrected  rate  of  motion  of  the  other  planets  will  be  given  under 
the  next  following  passage. 

50.  Subtract  the  daily  motion  of  a planet,  thus  corrected  for 
the  apsis  (manefa),  from  the  daily  motion  of  its  conjunction  ^ 
{dghra) ; then  multiply  the  remainder  by  the  difference  between' 
the  last  hypnthenuse  and  radius,  # 

61.  And  divide  by  the  variable  hypothenuse(cafaiaTOa):  t&p  ; 
result  is  additive  to  the  daily  motion  when  the  hypothenuse/Tpf^ 
greater  than  radius,  and  subtractive  when  this  is  less;  if,  when 
subtractive,  the  equation  is  greater  than  ttye  duly  motion,  deduett 
the  latter  from  it,  and  the  remainder  is  the  daily  motion  in  a 
. retrograde  (vakra)  direction. 

, Tho  commentary  gives. po  demonstration  of  the  rule  by  which  we  are 
him  taught  to  calcuhte  ihe  variation  of  the  rate  of  motion  of  a planet 
polled  by  the  action  ct'm conjunction:  the  following  figure,  how- 
^p  7),  will  illu^m^j^.  principle  upon  which  it  uu^tpded. 


fig.  I 


A*  in  ft  previous  figure  (Ffc  5,  p.  08),  C M M'  repnaentc  tbo 
..  orbit  of  a planet,  E toe  earth,  and  M the  planet's  mean  peailiao,  at# 
given  time,  relative  to  ita  conjunction,  C : the  circle  described  tbouwl£r 
Ms  epicycle  of  the  conjunction : it  is  drawn,  in  the  lgot%.ij£  the 
„ ywstive  dimensions  of  that  assumed  _ 

for  Mars.  Suppose  M'  M to  bo  the 
amount  of  motion  of  the  ventre  of 
the  epicycle,  or  the  (equated)  mean 
synoaicu  motion  of  the  planet, 
during  one  day ; m‘  m is  the  arc  of  ( 
the  epicycle  traversed  by  the  planet 
in  the  same  time.  As  the  amount 
of  daily  synodical  motion  is  in  every 
case  small,  these  ares  are  necessarily 
. greatly  exaggerated  in  the  figure, 
being  made  about  twenty-four  times 
too  great  for  Mars.  Had  the  planet 
remained  stationary  in  the  epicycle 
at  os'  while  the  centre  of  tnc  opi- 
Cyde  moved  from  M'  to  M,  its  place 
..'at  the  given  time  would  be  at  s; 
having  moved  to  m,  it  is  seen  at  l : 
hence  s t is  the  equation  of  daily  motion,  of  which  it  is  required  to 
ascertain  the  value.  Produce  E m1  to  it,  making  E n equal  to  E m,  and 
join  m n ; from  M draw  M o at  right  angles  to  E m.  Then,  since  the  are 
mm*  is  very  small,  the  angles  Emu  and  Enm,  as  also  Minin'  and 
M m*  m,  may  be  regarded  as  right  angles ; M m o and  n m m'  are  there- 
■ fore  equal,  each  being  the  complement  of  E m m',  and  the  triangles 
mum'  and  M mo  are  similar.  Uencc 


Mm:mo::mm':mn 
EM:  Mm::  MM':  mm' 
EM  :mo::MM':mn 
t*  :Ef::i»n:Em 


lf:me':MM':Em 


Bnt  . 

. Hence,  by  combining  terms, 

Bat 

^therefore,  since  EM  equals  E f,  1 
by  again  combining,  J 

^aad,  reducing  the  proportion  to  an  equation,  tt,  the  required  equation 
jjfof  redMon,  equals  M M',  the  equated  mean  synodical  motion  in  a dmr, 

^ 4i||Itiplied  by  mo,  and  divided  by  Em,  the  variable  hypothenuae.  This,' 

~ however,  is  not  precisely  the  rule  given  above ; for  in  the  text  of  this 
“ Siddh&nta,  m t,  (lie  difference  between  the  variable  hypothenuse  and 
' jradius,  is  substituted  for  mo,  as  if  the  two  were  virtually  equivalent:  a ■ 
w»»y  inaccurate  assumption,  since  .they  differ  from  one  another  by  the 
▼creed  sine,  o /,  of  the  equation  of  the  conjunction,  M t,  which  equation 
is  sometimes  as  much  as  40° : and  indeed,  the  commentary,  contrary  tg* 
. jta  utoal  habit  of  obsequiousness  to  the  inspil^i  text  with  which  it  halt,'! 
to- deal,  rejqpts  this  assumption,  and  says,  without  even  an  apology  fi*? 
the  liberty  it  is  taking,  that  by  the  word  f radios”  in  verse  50  ie  to  he^ 
understood the  cosine  (kotijyA)  of  the  secoodjiquition  of  the  conjunc||||| 


i L 61.]  2 Ventilation  and  Notes.  81 

~In  illustration  of  the  rule,  we  will  calculate  the  true  rate  of  daily 
potion  wf  the  planet  Mars,  at  the  same  time  for  which  the  previous 
*&IcuWtions  have  been  made. 

-prarpFH  already*  illustrated  under  the  preceding  passage,  the 
equation  of  Mars's  dnilv  motion  for  the  effect  of  the  apsis,  as  derived  from 
the  datfeuf  the  third  process  for  appertaining  his  true  place,  is  found  to 
bo  -S'  41",  the  difference  of  tabular  sines  being  131#.  Accordingly, 


t Aotn  ihe  tneJui  daily  motion  of  Mar»  (i.  a 3i'  26" 
./dSljict  the  eqoation  for  the  apsh,  3 4 1 

v Ibis's  equated  daily  motion,  27  45 

. 25oijpy  to  .find  the  equated  daily  synodical  motion, 

from  the  daily  motion  of  Mars’s  conjunction  (the  sun),  5t/  8f> 

deduct  his  equated  daily  motion,  2-  45 

Man's  equated  daily,  synodical  mot i*  in,  lu  a 3 


The  variable  hypotlicnuso  used  in  t lit*  last  proper  for  finding  the  true 
place  was  3984';  its  excess  above  radius  is  54C»#.  The  proportion 
* 3984,  :546r::3i'23',  :4' iS" 

allows,  then,  that  the  equation  of  motion  due  to  the  conjunction  at  the 
given  time  is  -l'  IS".  Since  the  liypothcnuse  is  greater  than  radius — 
that  is  to  say,  since  the  planet  is  in  the  half-orbit  in  which  the  influence 
of  the  conjunction  is  accelerative — the  equation  is  additive.  Therefore, 

to  Murs'«  equated  daily  motion,  27'  45" 

add  the  equation  for  the  conjunction,  4 *3 


Mars's  true  daily  motion  at  the  given  turn1,  3a  3 

In  this  calculation  wo  have  followed  tin*  rule  stated  in  the  text:  had 
we  accepted  the  amendment  of  the  commentary,  and,  in  finding  the 
second  term  of  our  proportion,  substituted  for  radius  the  cosine  of 
33°  44 the  resulting  equation  would  have  been  more  than  doubled, 
becoming  8'  51"  instead  of  4'  IS";  this  happening  to  be  a case  where 
the  difference  is  nearly  as  groat  as  possible.  We  have  deemed  it  best, 
however,  iu  making  out  the  corresponding  results  for  all  the  five  planets, 
as  presented  in  the  annexed  table,  to  adhere  to  the  directions  of  the* 
text  itself.  The  inaccuracy,  it  may  be  observed,  is  greatest  when  thw** 
equation  of  motion  is  least,  and  the  contrary ; so  that,  although  some*  J 
times  very  large  relatively  to  the  equation,  it  never  comes  to  be  of  t 
great  importance  absolutely.  # 

Jtesuli*  of  the  Processes  for  jlmiituf  the  True  Du  1y  \Totion  of  the  Planets . 


82  ' SQryu-Siddh^ita^  [ii.fil- 

The  final  abandonment  by  the  Hindus  of  the  principle  of  cqnablo  cir- 
cular motion,  which  lies  at  the  foundation  of  the  whole  system  of  eccen- 
trics and  epicycles,  is,  as  already  pointed  out  above  (under  vv.  43-4f|r 
, distinctly  exhibited  in  this  process:  wi'm  (Fig.  7),  the  arc  in  the  epi- 
cycle traversed  by  the  planet  during  a given  interval  of  time,  is  no  fixed 
and  equal  quantity,  but  is  dupi  ndunt  upon  the  arc  AI#  M,  the  value  of 
which,  having  suffered  correction  by  the  result  of  a triply  complicated 
process,  is  altogether  irregular  and  variable.  This  necessarily  follows 
from  the  assumption  of  simultaneous  and  mutual  action  on  the  part  of 
the  beings  at  the  apsis  and  conjunction,  and  the  consequent  impossibility 
of  constructing  a single  conn  voted  geometrical  figure  which  shall  repre- 
sent the  joint  effect  of  the  two  disturbing  influences.  By  the  Ptolemaic 
method  the  principle  is  consistently  preserved : the  fixed  axis  of  the 
epicycle  (see  Fig.  0,  p.  2 17),  to  the  revolution  of  which  that  of  the 
epicycle  itself  is  bound,  is  x P X ; and  as  the  angle  x PT,  liko  arX  A", 
increases  equably,  the  planet  traverses  the  circumference  of  the  epicycle 
with  an  unvarying  motion  relative  to  the  fixed  point  x\  although  the 

S nation  is  derived,  not  from  the  arc  x T,  but  from  e T,  the  equivalent  of 
B,  its  part  ex  varying  with  the  varying  angle  £ P X. 

In  case  the  reverse  motion  of  the  planet  upon  the  half-circumference 
of  the  epicycle  within  the  mean  orbit  is,  when  projected  upon  the  orbit,  ■ 
greater  than  the  direct  motion  of  the  centre  of  the  epicycle,  the  planet 
Will  appear  to  move  backward  in  its  orbit,  at  a rate  equal  to  the  excess 
Of  the  former  over  the  latter  motion.  This  is,  as  the  last  table  show*, 
the  case  with  Jupiter  and  Saturn  at  the  given  time.  The  subject  of  the 
retrogradation  of  the  planets  is  continued  and  completed  in  the  next 
following  passage. 

52.  When  at  a great  distance  from  its  conjunction  (fighrocca)9 
a planet,  having  its  substance  drawn  to  the  left  and  right  by 
alack  cords,  comes  then  to  have  a retrograde  motion. 

63-  Mars  and  the  rest,  when  their  degrees  of  commutation 
(kendra),  in  the  fourth  process,  are,  respectively,  one  hundred 
. and  sixty-four,  one  hundred  and  forty-four,  one  hundred  and 
thirty,  one  hundred  and  sixty-three,  one  hundred  and  fifteen, 

^ 54-  Become  retrograde  (vukrin):  and  when  their  respective 

^commutations  are  equal  to  the  number  of  degrees  remaining 
■ after  subtracting  those  numbers,  in  each  several  ease,  from  a 
^ whole  circle,  they  cease  retrogradation. 

’ 65.  In  accordance  with  the  greatness  of  their  epicycles  of  the 

.^conjunction  (j fighraparidhi),  Venus  and  Mars  cease  retrograding 
in  the  seventh  sign,  Jupiter  and  Mercury  in  the  eighth,  Saturn 
ia  the  ninth. 

j&‘  The  subject  of  the  stations  and  retrogradations  of  the  planets  ia 
P|*thcr€  briefly  and  summarily  disposed  of  in  this  passage,  although 
treated  withes  much  fullness,  perhaps,  aB  is  consistent  with  the  general 
method  of  the  Siddh&nta.  Ptolemy  devotes  to  it  the  greater  part  of 
thi'twalfth  book  of  the  Syntaxis.  ' ■ & 


Tranitaitbn  bid  Afcfer. 


69 


UWJ 

The  fihst  verse  gives  the  theory  of  the  physical  cause  of  the  phenome- 
non : is  to  be  compared  with -the  opening  verses  of  the  chapter, 
particularly  verse  2.  We  note  here,  again,  the  entire  disavowal  of  the 
system  of  epicycles  as  a representation  of  the  actual  movements  of  the 
planets.  llow  the  slackness  of  the  cords  by  which  each  planet  is 
attached  to,  and  attracted  by,  the  supernatural  being  at  its  conjunction, 
furnishes  an  explanation  of  its  retrogradation  winch  should  commend 
itself  as  satisfactory  to  the  mind  even  of  one  who  believed  in  the  super- 
natural being  and  Lhe  cord*,  we  find  it  very  Jiard  to  sec,  in  spite  of  the 
explanation  of  the  commentary : it  might  have  been  better  to  omit 
verse  52  altogether,  and  to  suffer  the  phenomenon  to  rest  upon  the 
simple  and  intelligible  explanation  given  at  the  end  of  the  preceding 
verse,  which  is  a Lnic  statement  of  its  cause,  expressed  in  terms  of  the 
Hindu  system.  The  actual  reason  of  tin1  apparent  retrogradation  is, 
indeed,  different  in  the  rase  of  the  inferior  and  of  the  superior  planets. 
As  regards  the  former,  when  tlu-j  are  traversing  the  inferior  portion  of 
their  orbits,  or  arc  nearlylN-twee.il  the  miii  and  the  ''art h,  their  helio- 
centric eastward  motion  becomes,  of  ■■nurse,  as  seen  from  the  earth, 
westward,  or  retrograde ; by  the  parallax  of  the  earth's  motion  in  the 
same  direction  this  apparent  rein ’gradation  is  diminished,  both  in  rate 
and  in  continuance,  blit  is  not  prevented,  because  the  motion  of  the' 
inferior  planets  is  more  rapid  than  that  nf  the  earth.  The  retrogmda-- 
tion  of  the  superior  planets,  on  the  other  hand,  is  due  to  the  parallax  oT 

the  earths  motion  in  the  Mime  dii ti*»n  when  between  litem  and  the 

sun,  a ml  is  *ncd  by  their  own  mot  imi  in  their  orbit**,  although  not 
done  away  with  altogether,  because  their  motion  i>  less  rapid  than  that 
of  the  earth.  I hit,  in  the  Hindu  system,  ihe  revolution  of  the  planet  in 
the  epicycle  of  the  .■unjuiKiiun  represents  in  tin.-  mie  cie*e  the  proper 
motion  of  the  planet,  in  tin*  other,  that  of  the  earth,  revefsed ; hence. 
Whenever  its  apparent  amount,  in  a contrary  direct  inn,  exceeds  that  of 
the  movement  of  the  centre  uf  the  epicycle— which  is,  in  the  one  case, 
that  of  the  earth,  in  the  other,  that  uf  the  planet  itself— retrogradation 
is  the  necessary  consequence. 

Verses  f)3-.Vi  contain  il  statement  of  the  limits  within  which  retro- 
gradation  takes  place.  The  data  of  verse  .‘>3  belong  to  the  diffeicut 
planets  in  the  order.  Mars  Mercury.  Jupiter.  Venus,  and  Saturn  (see 
above,  under  i.  51.  52).  That  is  to  say.  Mercury  retrogrades,  when  his  * 
equated  commutation,  as  made  use  nt  in  the  fourth  process  for  finding 
his  true  place  (sec  above,  under  w.  -13-45),  is  more  than  144°  and  less 
than  Venus,  when  her  commutation,  in  like  manner,  is  between 

163 3 and  137° ; Mars,  between  164°  and  11*0=:  Jupiter,  between  130^‘ 
and  230°;  Saturn,  between  115J  and  245°.  These  limits  ought  not, 
however,  even  according  to  the  theory  of  this  Siddliauia,  to  be  Iphl 
down  with  such  exactness;  for  the  precise  point  ai  which  the  subtractive 
equation  uf  motion  for  the  conjunction  will  exceed  the  proper  motion 
ol*  the  planet  must  depend,  in  part,  upon  the  varying  rate  of  thfrlatter  * 
at  affected  by  its  eccentricity,  and  must  accordingly  differ  a littlo  .at 
different  times.  We  have  nut  thought  it  worth  while  to  Calculate  tte 
^amount  of.  this  variation,  nor  to  draw  up  a comparison  of  the  Hindu 
iftth  the  Greek  and  the  modern  determinations  of  the  limits  of  retro- 


[ii.  56— 


84*  SHtrya-Siddhdnta, 

gradation,  since  these  arc  dependent  for  their  correctness  upon  the  accu- 
racy of  the  elements  assumed,  and  the  processes  employed,  both  of 
4hich  have  been  already  sufficiently  illnstrnted. 

The  last  verso  of  the  passage  adds  little  to  what  had  been  already 
said,  being  merely  a repetition,  in  other  and  loss  precise  terms,  of  the 
Specifications  of  the  preceding  verse,  together  with  the  assertion  of  a 
relation  between  the  limits  of  rctrngradalion  and  the  dimensions  of  the 
T^pective  epicycles;  a relation  which  is  only  empirical,  and  which,  as 
regards  Venus  and  Mars,  dpos  not  quite  hold  good. 

5G.  To  the  nodes  of  Mars,  Saturn,  and  Jupiter,  the  equation 
of  the  conjunction  is  to  be  applied,  as  to  the  planets  themselves* 
respectively;  to  those  of  Mercury  and  Venus,  the  equation  of 
the  apsis,  as  found  by  the  third  process,  in  the  contrary  direction. 

57.  The  sine  of  the  arc  found  by  subtracting  the  place  of  the 
node  from  that  of  the  planet— or,  in  the  case  of  Venus  and 
Mercury,  from  that  of  the  conjunction — being  multiplied  by  the 
extreme  latitude,  and  divided  by  tin1  last  bypntheuiisr—  -or,  in 
the  case  of  the  moon,  by  radius  -gives  the  latitude  (vikshc/'d). 

58.  When  latitude  and  declination  (apukrtnnn)  arc  nf  like 
direction,  the  declination  (kmuti)  is  increased  by  the  latitude: 
when  of  different  direction,  it  is  diminished  by  it,  to  Unci  the  * 
true  (spashta)  declination:  that  of  the  sun  remains  as  already 
determined. 

IIow  to  find  the  declination  of  n planet  at  ,ain\  given  point  in  the 
ecliptic,  or  circle  nf  decimal  imi  [krantirrtfn),  wa-  height  us  in  verse  ‘JN 
above,  taken  in  coiinertiuii  with  ver-i-s  !•  and  to  nf  the  next  chapter: 
here  we  hate  stated  the  method  nf  finding  the  actual  declination  of  any 
planet,  as  modified  by  its  deviation  in  latitude  from  the  ecliptic. 

The  process  l >\  which  the  amount « «t‘  a planet'*  deviation  in  latitude 
from  the  ecliptic  is  here  di reeled  to  be  found  i>  more  m: n et  than  might 
have  been  expected,  considering  how  far  Ujc  Hindu-  were  from  compre- 
hending the  true  relations  of  the  *olai  si  stem,  '['lie  ihrce  quantities 
employed  as  data  in  the  process  arc,  first,  llio  aiigular  distance  of  the 
planet  from  its  node;  second,  tin*  apparent  mine,  as  latitude,  of  its 
greatest  removal  from  the  ecliptic,  when  *e.on  ♦Yom  the  earth  at  a mean 
distance,  equal  to  the  radius  of  its  mean  orbit : and  lastly,  its  actual 
distance  from  the  earth.  Of  the*,;  quantities  tin*  second  is  stated  for 
each  planet  in  the  concluding  ver»es  of  the  first  chapter;  the  third  is 
correctly  represented  by  the  variable  bvpothcnuse  (min  hirnn)  found  in 
the  fourth  process  for  determining  tin;  planet"*  true  place  (sec  above, 
under  vv.  43-45 j ; the  first  is  still  to  be  obtained,  and  verse  fdi  with  tho 
first  part  of  vernu  57  teach  the  method  of  ascertaining  it.,  'flic  princi- 
ple of  this  method  is  the  same  for  all  the  planets,  although  the  state- 
ment .of  it  U so  different;  it  i.s,  in  effect,  to  apply  to  the  mean  place  of 
the  planet,  before  taking  its  distance  from  the  node,  only  the  equation 
dPthe  apsii,  found  as  the  result  of  the  third  process.  In  the  case  of 
tift'-tguperior  planets,  this  method  has  all  tho  correctness  which  the 
Hindu  system  admits;  for  by  tho  first  three  processes  of  correction  is 


ii.  68.]  Translation  and  Notes . 86 

found,  hr  nearly  as  the  Hindus  are  able  to  And  it,  the  true  heliocentric 
place  of  the  planet,  the  distance  from  which  to  the  node  determine*,  of 
course,  the  amount  of  removal  from  the  ecliptic.  Instead,  however,  of 
taking  this  distance  directly,  rejecting  altogether  the  fourth  equation, 
that  for  the  parallax  of  tlm  earth's  place,  the  Hindus  apply  the  latter 
both  to  the  planet  arid  to  the  node ; their  relative  position  thus  remains 
the  same  ns  if  the  other  method  had  been  adopted. 

Thus,  for  iiihtnim',  the  position  of  Jupiter  s node  upon  the  first  of 
January,  1800,  is  found  from  the  data  already  given  above  (sec  i.  41-44) 
to  be  2“  10°  401;  bis  true  heliocentric.  longitude,  employed  as  a datum  in 
the  fourth  process  (see  p.  218),  is  !JB  1°  O';  Jupiter » heliocentric  dis- 
tance from  the  nolle  b,  accordingly,  i 1°  20'.  Or,  by  the  Hindu  method, 
the  planet's  true,  geocentric  place  is  .‘Js  4°  J I',  and  the  corrected  longi- 
‘"^ftide  of  its  node  is  *JH  22°  4.7 : the  distance  remains  as  before.,  11°  26'. 

In  the  case  of  the  inferior  plain  ly  as  the  assumptions  of  the  Hindus 
respecting  them  were  further  removed  from  1 lie  truth  of  nature,  so  their 
method  of  finding  the  distance  tr> *in  the  node  is  more  arbitrary  and  less 
accurate.  In  their  system  the  lielini-i-iitric  position  of  the  planet  is  rep- 
resented by  the  plan;  « if  its  cniijmii-tioii  (\Ufhra\  and  they  had,  as  is 
shown  above  (m*c  ii.  *).  re.-ngni/ed  the  fact  that  it  was  the  distance  of 
the  latter  from  the  node  which  dr|.*-rmiiicd  the  anionnt  of  deviation  from 
the  ecliptic.  Now.  in  a>ci*i  turning  the  hiTiuecutri**  distance  of  an  infe- 
rior planet  from  its  nude.  allnwunee  needs  to  be  insult1,  of  course,  for  the 

effect  upon  its  portion  of  t lit-  entrieily  of  its  orbit.  But  tbc  Hindu 

equation  of  the  apsU  i-  no  true  lvprcscmative  of  this  effect : it  is  calcn- 
bited  in  order  to  he  applii-d  to  the  mean  jilace  of  the  sun.  the  assumed 
ceiiti o of  the  epii-icle  :!.nl  i-.  of  the  tine  orbit ' it-  value,  as  found,  is 
gooeehlrie,  am  I.  a>  appeal-  bv  the  table  mi  p.  ‘Jiiu,  is  widely  different 
from  its  lielioeentrie  value:  and  \[>  -ign  is  plus  or  minus  according  as 
its  infhicTirc  is  ?n  cany  rise  planet.  .*>  seen  from  the  earth,  eastward  or 
westward;  while,  in  i-ii ln-r  ea-e,  the  true  lieliocciurie  effect  may  be  at 
one  time  to  bring  the  planet  nearer  to.  at  another  time  to  carry  it  farther 
from,  the  unde.  The  Hindu-,  however,  overlooking  these  incongruities, 
and  having,  apparently , tin  distinct  views  of  the  subject  to  guide  them 
to  a eurrecter  nn-tlmd,  follow  with  regard  to  Venn*  and  Mercury  what 
seeing  to  them  the  same  rule  was  employed  in  the  ca&c  of  the  other 
planet?- — they  apply  the  equation  of  the  apsis,  the  result  of  the  third 
process,  to  the  mean  place  of  the  eonjiiiictinn : c*nly  hero,  as  before,  by 
an  indirect  process:  instead  of  applying  it  to  the  conjunction  itself,  they 
apply  it  with  a contrary  sign  to  the.  node,  the.  effect  upon  the  relative 
position  of  the  two  being  the  same. 

Thus,  for  instance,  the  longitude  of  Merer ry\i  conjunction  at  the 
given  time  is  (<co  ]•.  2 141  4*  1*»J  .1 7 ' : from  thissibtract  - 1 2#,  the  equa- 
tion of  the  apsis  found  by  the  third  process  am  its  equated  longitude 
is  4*  14°  .17:  now  deducting  the  longitude  of  the  node  at  tho  same 
time,  which  is  2u'J  1 11,  we  ascertain  the  planet's  distance  from  t^p  node 
to  be  3*  24*  14;.  Or,  by  I he  Hindu  method,  add  the  same  equation  to 
the  mean  position  of  the  node,  and  its  equated  longitude  is  22°  43'; 
subtract  this  from  the  menu  longitude  of  tho  conjunction,  and  the  dis- 
. Unco  is,  aa  before,  3"  24°  14'.  ..  .. 


86 


[ii.  68- 


.planet's  distance  from  the  node  being  determined,  its  latitude 
would  be  found  by  a process  similar  to  that  prescribed  in  verse  28  of 
this  .chapter,  if  the  earth  wore  at  the  centre  of  motion ; and  that  rule  is 
accordingly  applied  in  the  case  of  the  moon ; the  proportion  being,  as 
tadiu  is  to  tho  sine  of  the  distance  from  the  node,  so  is  the  sine  or  ex* 
tfmne  latitude  (or  the  latitude  itself,  the  difference  between  the  sine  and 
the  arc  being  of  little  account  when  the  arc  is  so  small)  to  the  latitude 
ft  the  given  point.  In  the  case  of  the  other  planets,  however,  this  pro- 
portion is  mollified  by  combination  with  another,  namely : as  the  last 
variable  hypothenuso  ( eala  hernia),  which  is  the  line  drawn  from  the 
earth  to  the  finally  determined  place  of  the  planet,  or  its  true  distance, 
is  to  radius,  its  mean  distance,  so  is  its  apparent  latitude  at  the  mean 
distance  to  its  apparent  latitude  at  its  true  distance.  That  is,  with 

Ii  : sin  noil. (list. : : extreme  hit. : actual  lat.  at  dist.  R 
combining  var.  hyp : Ii  : : lat.  at  dist.  Ii : lat.  at  true  dist. 

we  have  var.  hyp : sin  nod. dist. : : extreme  lat. : actual  lat.  at  true  dist. 
which,  turned  into  an  equation,  is  the  rule  in  the  latter  half  of  r.  57. 

The  latitude,  as  thus  found,  is  measured,  of  course,  upon  a secondary 
to  the  ecliptic.  By  the  rule  in  verse  58,  however,  it  is  treated  as  if 
Iliftcuiured  upon  a circle  of  declination,  and  is,  without  modification, 
added  to  or  subtracted  from  the  declination,  according  as  the  direction 
df  the  two  is  the  same  or  different.  The  commentary  tales  note  of  this 
erfor,  but  explains  it,  as  in  other  similar  cases  as  being,  11  for  fear  of 

^11^11  trouble,  and  on  account  of  the  very  slight  inaccuracy,  over- 
by  the  blessed  Sun,  moved  with  companion." 

AVe  present  in  the  annexed  table  the  results  of  the  processes  for  calcu- 
lating the  latitude,  the  declination,  and  the  true  declination  as  affected 
bv.  latitude,  of  all  the  planets,  at  the  time  for  which  their  longitude  has 
ajjpfeady  been  found.  The  declination  is  calculated  by  the  rule  in  verse 
28  of  this  chapter,  the  precession  at  the  given  time  being,  as  found 
under  verses  9-12  of  the  next  chapter,  20°  24'  30".  I'pon  the  line  for 
like  sun  in  the  table  are  given  the  results  of  the  process'!  for  calculating 
hfa  declination,  the  equinox  itself  being  accounted  as  a “ node” : it  is,  in 
fsfiVrttjled,  in  modern  Hindu  astronomy.  krdnfijjfia,  “node  of  declina- 
tion,* although  that  term  does  not  m-ciir  in  this  treatise. 

Results  of  the  Process  for  finding  the  Latitude  and  Declination  of  the 

Planets. 


ftlML 

Longitude  j do.  j I) i ■line* 

of  Node,  'cor reiled  1 Troir  .Nwlr 

1 _ 

ftim.  J l-tiMfe  .Declin.tioa!^”"-^. 

Sun,  , 
Muni; 
Mercury, 
Venus, 

Xriif 

Mum* 

■ • . • 
n ro  *4  38, 

9 34  43  

0 30  40  4l)o  33  43 

1 39  89  33!  1 39  iti 
t 10  3 5ja  i3  47 
1 19  4o  % a 33  45 ! 
3^  10  ao  45j  3 i4  38 1 

■ • ' 

9 8 4o 

1 a3  14 

3 s4  i4 

8 23  34 

4 4 58 

0 11  36 
0 r6  34 

33v7  j ' 

3764  ,3  36  N. 

.1 1 34  ] a 4 N. 
3409  if  21  8. 
a8if>  j 1 4 N. 
68a  jo  i5M. 
970  jo  37  N. 

• * 

33  4i  S. 

4 56  N. 
s3  10  S. 
ao  97  8. 
i4  5*  8. 

; 91  42  N. 
j i4  4o  N 

» . 

8 3a  N. 

31  6 S. 

it  48  S. 
i3  48  «. 
ai  57  N. 

•5  17  N. 

lilllkai*  now  able  to  compare  tho  Hindu  determinations  of  the  Iran 
pfjfljii  uni  mntlnm  of  the  planets  with  their  actual  positions  and  motions* 


Translation  and  Notes. 


Sf 


as  obtained  by  modem  science.  The  comparison  is  made  in  the  anneied 
table.  As  the  longitudes  given  by  the  Stirya-Siddh&nta  contain  a con- 
stant error  of  2°  20',  owing  to  the  incorrect  rate  of  precesAHftjUopted 
by  the  treatise,  and  the  false  position  thence  assigned  to  the  equinox,  we 

S'vc,  under  the  head  of  longitude,  the  distance  of  each  planet  both  from 
e Hindu  equinox,  and  from  the  true  vernal  equinox  of  Jan.  1,  1860. 
The  Hindu  daily  motions  arc  reduced  from  longitude  to  right  ascension 
by  the  rule  given  in  the  m:xt.following  verse  (v.  59).  The  modern  data 
are  taken  from  the  American  Nautical  Almanac. 


Trve  Places  and  Motions  of  the  Planets , Jan.  lx/,  I860,  midnight , at 
Washington,  according  to  the  Surya-Siddhanta  and  to  Modern  Science. 


1 Trim  Longitude. 
Planet.  ! Surya  Siddhuuin  : 

• from  | from  Mo 
'Hindu  cq.|  true  eq.  - 


Declination. 


Daily  Motion 
in  Right  Aiceaik 


Moderns, 


Uddhunta!  Modem..  IsSdEUiaJ  Modefn,r 


+ 66  a 
4-683  5o 
4-  3k  i3 
+ 7*  59 
+ 3i  86 
- 8 si ' 
-33 


+ 66  18 
4-655  i4 


The  proper  subject  of  the  second  chapter,  the  determination  of  the 
true  places  of  the  planets,  being  thus  brought  1q  a close,  we  should  ex- 
pect to  see  the  chapter  concluded  here,  aud  the  other  matters  which  it 
coutains  put  off  to  that  which  follows,  in  which  they  would  seem  more 
properly  to  belong.  The  treatise,  however,  is  nowhere  distinguished  fer 
its  orderly  and  consistent  arrangement. 

59-  Multiply  the  daily  motion  of  a planet  by  the  time  of 
rising  of  the  sign  in  which  it  is,  and  divide  by  eighteen^liua* 
dred ; the  quotient  add  to,  or  subtract  from,  the  numDer  of  respi* 
rations  in  a revolution : the  result  is  the. number  of  xwpmtH&i 
in  the  day  and  night  of  that  planet. 


In  the  first  half  of  this  verse  is  taught  the  method  of  finding  the  in- 
crement or  decrement  of  right  ascension  corresponding  to  the  increment 
or  decrement  of  longitude  made  by  aiiy  planet  during  one  day.  For  Aft 
41  time  of  rising”  ( udayapr&nas , or,  more  commonly,  uday&savas,  liter* 
ally  11  respirations  of  rising'1)  of  the  different  signs,  or  the  time  iovtapfe 
rations  (sec  i.  11),  occupied  by  the  successive  signs  of  the  ecliptiq  i| 
passing  the  meridian — or,  at  the  equator,  in  rising  above  the  honXM|?>*# 
see  verses  42-44  of  the  next  chapter.  The  statement  upon  which  Aft 
rule  is  founded  is  as  follows  r if  the  given  sign,  containing  18001  of  lift 
(each  minute  of  arc  corresponding,  as  remarked  above,  under  i.  14*11, 
to  a respiration  of  sidereal  time),  occupies  the  stated  number  of  reaping 
turn  in  passing  the  meridian,  what  number  of  respirations  will  be  oeco- 
pied  by  Aft  arc  traversed  by  the  planet  on  a given  day  I The  veeftH 
gtvftft  Aft  amount  by  which  the  aay  ef.  each  .planet,  reckoned - im  the 


88  Sarya-SiJdhdnla,  [ii.  60- 

manner  of  this  Siddh&nta,  or  from  transit  to  transit  across  the  inferior 
meridian,  differs  from  a sidereal  day  : the  difference  is  additive  when  the 
.motion  of  the  planet  is  direct ; subtractive,  when  this  is  retrograde. 

Thus,' to  find  the  length  of  the  sun's  day,  or  the  interval  between  two 
successive  apparent  transits,  at  the  time  for  which  his  true  longitude  and 
rata  of  motion  have  already  been  ascertained.  The  sun's  longitude,  as 
corrected  by  the  precession,  is  ii*  8°  41V;  he  is  accordingly  in  the  tenth 
sign,  of  which  the  time  of  rising1  (itdupamvu*),  or  the  equivalent  in  right 
ascension,  is  lft35p.  Uis  rate  of  daily  motion  in  longitude  is  Cl#  20". 
Hence  the  proportion 

180  19J  : f>i'  ?h"  : 

shows  that  his  day  differs  fnm  * true  sidereal  «lay  hy  1 lv  up.O-I.  As 
his  motion  is  direct,  the  difference  is  ndditiw* : the  length  of  the  appar- 
ent day  is  therefore  0Ou  1 1 v (ii\U4,  which  is  equivalent  to  24*1  0n>  27*.5, 
mean  solar  time.  According  to  the  Nautical  Almanac,  it  is  24h  0m  28*.0. 
By  a similar  process,  the  length  of  Jupiter's  day  at  the  sumo  time  is 
found  to  be  59n  58v  4P,  or  2 if11  o.V1  ;U>",8  ; hv  the  Nautical  Almanac,  it 
is  23*  5i>m  30*. 

60.  Calculate  the  sine  and  versed  sine  of  declination : then 
radius,  diminished  by  the  versed-sine,  is  the  dav-radius:  it  is 
either  south  or  north. 

The  quantities  mode  use  of,  and  the  processes  prescribed,  in  this  and 
/the  following  verses,  may  be  explained  an*’  illustrated  bv  means  of  the 
annexed  figure  (Fig.  8). 

Let  the  circle  ZSZ'N  represent  the  meridian  of  a given  place,  C 

hi'ing  the  centre,  tlm 
place,  of  the  observer, 
S N the  .section  of  Lliu 
plane  of  his  horizon — 
S being  the  south,  and 
N the  north  point— Z 
and  Z'  the  zenith  and 
it*  opposite  point, 
the  nadir,  1’  and  1* 
the  north  and  .south 
poles,  and  E and  K' 
the  points  on  the  me- 
ridian cut  by  the 
equator.  Let  El) be 
the  dcclinatiou  of  a 
planet  at  a given  time; 
then  D IV  will  be  the 
diameter  of  the  circle 
of  diurnal  rc\olutiou 
described  by  the 
planet,  and  15  D the 
radius  of  that  circle : 
B D is  the  line  which 

me* 60  is  called  the  “day-radius.”  Draw  DP  perpendicular  to  EC : 


Translation  and  Notes. 


then  it  is  evident  that  B D is  equal  to  E C diminished  by  EF,  which  is 
the  venod  sine  of  ED,  the  declination. 

For  “ radius”  we  have  hitherto  had  only  the  term  trijyA  (or  its  equiv- 
alents, trijtuA,  tribhajiyA , tribkajyA , tribhamfturvikA ),  literally  “ the  sine 
of  three  signs,”  that  is,  of  90°.  That  term,  however,  is  applicable  only 
to  the.  radius  of  a great  circle,  or  to  tabular  radius.  In  this  verse/ 
accordingly,  we  have  for  “day-radius”  the  word  dinavydsadala,  “half- 
diameter  of  the  day  and  other  expressions  synonymous  with  this  are. 
found  used  instead  of  it  in  other  passages.  A more  frequent  name  for 
the  same  quantity  in  modern  Hindu  astronomy  is  dyujyA , “ dav-bine 
this,  although  employed  by  the  commentary,  is  not  found  anywhere  in 
.^ur  text. 

It  is  a matter  for  surprise  that  wc  do  not  find  the  day-mlius  declared 
equal  simply  to  the  cosine  (knfijya)  of  declination.  ” . ■ ; 

In  ii lustration  of  the  rule,  it  will  lie  sufficient  to  find  the  radius  of  the 
diurnal  circle  described  by  the  sun  at  the  time  for  which  his  place  has 
been  determined.  His  declination.  K d (Fig.  s)  was  found  to  be  23°  41*: 
of  this  the  versed  sine,  EF,  is,  by  tin*  table  given  above  (ii.  22-27), 
290':  the  di  He  re  lice  between  lliis  and  radius  EC,  or  3438  , is  3148', 
which  is  the  value  of  ( ' K nr  hi /,  the  day -radius.  The  declination  in 
t-bis  tifcftc  being  south,  tlie  day -rad  ins  is  also  south  of  the  equator. 


61.  Multinly  tin*  sine  of  declination  by  the  equinoctial  shadow, 
and  divide  ny  twelve ; the  result  is  the  earth -sine  (kshitijyd) ; 
this,  multiplied  by  radius  and  divided  bv  the  day-radius,  gives 
the  t-inc  of  the  ascensional  dillerenoe  (cam):  the  number  of 
respirations  due  to  the  ascensional  difference 

62.  Is  shown  by  the  corresponding  arc.  Add  these  to,  and 
subtract  them  from,  the  fourth  pan  of  the  corr 
and  night,  and  the  sum  and  remainder  are,when  < 
north,  the  half-day  and  half-night; 

63.  When  declination  is  south,  the  reverse ; these;  toWS 
by  two,  are  the  day  and  the  night  The  day.  and  the 

- the  asterisms  {hha)  may  be  found  in  like  manner, " 
their  declination,  increased  or  diminished  by  their  latittl 

Wc  were  taught  in  verse  59  how  to  find  the  length  ofl 
of  a planet  at  any  givun  time ; this  passage  gives  <ns  thtfd 
ascertaining  the  length  of  its  day  and  of  its  nighty  or  c*  ' 
day  during  which  the  planet  is  above,  and  that  during.^ 
the  horizon.  « , 

In  order  to  this,  it  is  necessary  to  nsCertai^,  for  the  \ 

4 its  ascensional  difference  (cam),  or  the  difference  V 
oblique  ascension,  the  amount  of-  which  variej^wit 
the  plauct  and  the  latitude  of  the  Observer.  ’ 
fet  stated  in  verse  01 : it  may  be  explar  :J 
(Fig.  8).  First,  the  value  of  the:  line  , 
siitje”  ik&iiijya),  is  found,  by 
CHE,  which  are  similar,  sinefc 

equal  to  the  latitude  of  the  obaerver.]H^|^|gle  CHEis.i 
12 


j 


trUngle  of  whiehia  gnomon  of  twelve  digits  is  the  p&ptn  '* 
/aodit-  eqoinodi&riwjw,  cast  when  the  sun  is  in  tip  eqmjfe# 
jrathe' meridian  (see  die  next  chapter  verse  7,  etc^if  the  briM 
the  proportion  EH  : H C : : B C : A B is  equiyalent^-since  BC 
the  sine  of  declination — to  gnom. : cq.  shg^:  :shi  decl.: 
th-eipe.  But  the  arc  of  which  A B is  sine  is  the  same  part  of  the** 
dfe  6f  diurnal  revolution  as  the  ascensional  difference  is  of  the  equa- 
tor hence  the  reduction  of  A B to  the  dimensions  of  a great  circTfc,  by 
' the  proportion  BD:AB::GE:CG,  gives  the  value  of  C G,  the  sine 
of  the  ascensional  difference.  The  corresponding  arc  is  the  measure  in  . 
tbne  of  the  amount  by  which  the  part  of  the  diurnal  circle  intercepted 
■'  between  the  meridian  and  the  horizon  differs  from  a quadrant,  or  h# 

* Which  the  time  between  sun-rise  or  sun-set  and  noon  or  midnight  differs 
',’lfe  a quarteFof  the  day. 

"''TjSa  illustration  of  the  process,  we  will  calculate  the  respective  length 
If*  the  sun’s  day  and  night  at  Washington  at  the  time  for  which  our  . 
previous  calculations  have  been  made. 

the  latitude  of  Washington  being  38°  54',  the  length  of  the  equi- 
fi4etU  shadow  cast  there  by  a gnomon  twelve  digits  long  is  found,  by 
..  tfio  rule  given  below  (iii.  17),  to  be  9^.88.  The  sine,  rfF  or  4C,  of  the 
sun’s  declination  at  the  given  time,  23°  41'  S,  is  1380'.  Bene£  the 
ntoqportion  '* 

12:9.68::  i38o:  1 1 1.1 

,'^myes  us  the  value  of  the  earth-sine,  a ft,  as  1113'.  This  is  reduced  to 
dimensions  of  a great  circle  by  the  proportion 
3i48  : 3438::  ml:  1216 

The  value  of  C.v,  the  sine  of  ascensional  difference,  is  therefore  1210': 
the  corresponding  arc  is  20°  44',  or  1244',  which,  as  a minute  of  an; 
equals  a respiration  of  time,  is  equivalent  to  311  27v  2p.  The  total 
hmgthof  the  day  was  found  above  (under  v.  59)  to  be  60"  1 1 v ; in- 
Crease  and  diminish  the  quarter  of  this  by  the  ascensional  difference, 
agti Rouble  the  sum  and  remainder,  and  the  length  of  the  night  is  found 
^klje4!)i7B  0V  IP,  and  that  of  the  day  23n  10*  5P,  which  are  equivalent 
iumptively  to  14h  45m  38*.G  and  9"  14in  48\9,  mean  solar  Jme. 

%Of  course,,  the  respective  parts  of  a sidereal  day  during  which  each 
of  the  lunar  mansions,  as  represented  by  its  principal  star,  will  remain 
above  end  below  the  horizon  of  a given  latitude,  may  be  found  in  the 
jegM  manner,  if  the  declination  of  the  star  is  known;  and  this  is  stated 
iadhe  chapter  (ch.  viii)  which  treats  of  the  asterisms. 

^ > m called  JkMlijyA  is  not  easy  to  see.  One  is  tempted 


id  the  term  as  meaning  rather  “sine  of  situation”  than 
Sue,”  the  original  signification  of  kahili  being  te  abode,  rest 
deuce”  ; it  might  then  indicate  a sine  which,  for  a given  declination,  < 
>>‘aS‘i  fAkthis  sHpation  of  the  observer.  But  that  kthni  in  this  com- 
mas to  betaken  in  its  other  acceptation,  of  u earth*”  k at  least 
4 5 indicated* by  the  other  and  more  usual  name  of  the  line  m 
i,  htgyd,  which  k used  by  the  commentary,  although  not  iff  tpb 
which  can  only  mean*4  earth-sine”  • The  word  cure,  usedUo 
si  difference,  means  simply  * variable”  ? we  have 
, mWsiftifa, » variable  pgj yjfffc&ff  tot  k to  mft  to 


ti.60.}  , Translation  and  Note. 

1 41 

con*t*ntly  varying  amount  by  which  the  Apparent  day  in 

day  *t»d  night  of  onehajtfthe  tmt  day  eaeKThc 
gadooMa,  ffafqjliBoctial  shadow,  etc,  are  treated,  of  iithatat  chatat 

' . t - vi*;1  : f ■ * » - 

14  portioh  (bhoga)  o%an  asterism,  (bha)  is  eight  Vqdri$ 
^teinutes^'.oJ^a  lunar  day  ( tithi ),  in  like  manner,  seven  bp#4fo$ 
^nd.twenty.  If  the  longitude  of  a planet,  in  minute^,  be  divided 
by  the  portion  of  an  asterism,  the  result  is  its  position  in  liter 
isms:  by  means  of  the  daily  motion  arc  found  the  days,  etc. 

The  ecliptic  is  divided  (see  cli.  viii)  into  27  lunar  mansions  or  aster* 
ferns,  of  equal  amount ; hence  the  portion  of  the  ecliptic  occupied  by; 
'each  asterism  is  13°  20',  or  800'.  In  order  to  find,  accordingly^,  -4 
winch  afctcrism,  at  a given  time,  the  moon  or  any  other  of  the  pbpjij 
is,  we  have  only  to  reduce  its  longitude,  not  corrected  by  the  preceisjfe^^ 
to  minutes,  and  divide  by  800  : the  quotient  is  the  number  of  asteriaarifc;-!) 
traversed,  and  the  remainder  the  part  traversed  of  the  asterism  in  wl)H&' 
the  planet  is.  The  last  clause  of  the  verse  is  very  elliptical  and  obscure? 
according  to  the  commentary,  it  is  to  be  understood  thus : divide  by  the 
planet's  true  daily  motion  the  part  past  and  the  part  to  coibe  of the 
current  asteri&TU,  ami  the  quotients  arc  the  days  and  fractions  of  a 4jgr 
^hich  the  planet  lias  passed,  and  is  to  pass,  in  that  asterism.  Thiate-* 
terpretation  is  supported  by  the  analogy  of  the  following  verses,  ankt  is 
doubtless  correct. 

The  tnie  longitude  of  the  momi  was  found  above  (under  v.  39)  to  bf? {' 
11*  17°  39',  or  20,859'.  Dividing  by  800,  we  find  that,  at  the  given 
time,  the  moon  is  in  the  27th,  or  last,  asterism,  named  Revati,  of  which 
' it  has  traversed  59',  and  has  741' still  to  pass  over.  Its  dailj  motion 
being  737',  it  has  spent  28l  4P,  and  has  yet  to  continue  Id  0"  19r  in 
the  aateriam. 

The  latter  part  of  this  process  proceeds  upon  the  assumption  that  the 
planet’s  rate  of  motion  remains  the  same  during  its  whole  continuance 
m the  asterism.  A similar  assumption,  it  will  be  noticed,  is  made  in  jM  t 
the  processes  from  verse  59  onward  ; its  inaccuracy  is  greatest  of  uotifae, 
where  the  moon's  motion  is  concerned.  r;,,; 

Respecting  the  lunar  day  (tithi)  see  below,  under  verse  66. 

65.  From  the  number  of  minutes  in  the  sum  of  the  longittxfa 
of  the  sun  and  moon  are  found  the  yogas,  by  dividing  tbit  rtst 
by  the  portion  (bhoga)  of  an  asterism.  Multiply  the  minutes 
past  ana  to  come  of  the  current  yoga  by  sixty,  and  diridrW 
the  sum  of  the  daily  motions  of  the  two  planets:  the  Mfl&tlg 
the  time  in  uadis.  V’ 

What  the  yoga  is,  h evident  from  this  rule  tor  fading  it  \ hjt.fa 

Bof  variable  length,  daring  which  the  joint  motion  in  lenglHgn  Sif 
and  moon  amounto  to  13°  20',  the  portion  of  a lunar  i 
ing  to  Celobrook*  (As.  Boa,  ix.  36 6 ; Buaya,  ii.  3^3,  f 
Hu  jnirsi  is  'chiefly  astrological;  the  occurrence  of.caxti 
UetottivaU  a,  however,  alee  regulatod  by  them,  and  tbagr  < 
ftMnktfy  .ployed  that  *YW7  Hindualu  ! ,J  * 


'M 


SArya-SidcUidntc^  py* . 


She  y^gtt  for  each  d«y,  -vyitli.  the'  time  of  its  tenauihtibh'^  Tfco-^ 
Of  the  twenty-aove^./ogasare  as  follows:  !}'. ' i‘  >! 


f.  Vishkirabha. 

а.  Priti. 

3.  Ayushmant 

4.  SAublidgya. 

5.  £obhana. 

б,  Atignnda. 

7.  Sulrarman. 

8.  Dhfli. 
^fula. 

ere  is  also 


io.  Gapdn. 
it.  VrddbL 


■Sr.. 

ao.  Qii 
ai.  SWdh*. 

33.  S&fcyiv. 
a 3.  Qubha. 

34.  £uk1a. 

a 5.  Brahmau. 
76.  India. 

37.  VAidhrti. 


IP 


' la.  Dhruva. 

1 3.  VyftghAta. 

1 4.  Harahaiio. 

1 5.  Vftjra. 

16.  Siihllii. 

17.  Vyntip&tn. 

18.  Yuriy  os. 

in  use  in  liulia  (sec  (Vdcbrnokc,  ns  above)  another 
of  yogas,  twenty-eight  in  iitiinl»cr1#liuving  for  the  most  part  -, 
ant  names  from  these,  ami  governed  by  other  rules  in  their  succes- 
Of  this  system  the  »Surya-Siddh&uta  presents  no  trace. 

We  will  find  tlie  time  in  yogas  corresponding  to  that  tor  which  the 
previous  calculations  have  been  unde. 

The  longitude  of  the  monn  at  that  time  is  11R  l73  It!)',  that  of  the 
min  is  8B  18°  lo;;  their  sum  is  N*  ,j°  6 R or  14, 754'.  Dividing  by  800,  * 
we  find  that  eighteen  yogas  of  the  series  are  past,  ami  that  the  current 
one  is  the  nineteenth,  Ravi  glia,  of  which  3."»  1'  are  past,  and  446' to 
come.  To  ascertain  the  time  at  whic  h the  current  yoga  began  and  that  '* 
at  which  it  is  to  end,  we  divide,  those  parts  respectively  by  7!)8'4,  the 
jfeum  of  the  daily  motions  «>f  the  >un  ami  moon  at  tlie  given  time,  and 
'ibujltiply  by  60  to  reduce  the  roMilts  to  midis:  ami  we  find  that  1’arigha 
$£gan  26™  36v  before,  and  will  end  33 11  3uv  after  the  given  time. 

The  name  yoyo.  by  which  this  astrological  period  is  called,  is  applied 
it,  apparently,  as  designating  the.  period  during  which  the,  “sum” 
s)  of  the  increments  in  longitude  of  the  sun  and  moon  amounts  to  a 
jiven  quantity.  It  seems  an  entirely  arbitrary  device  of  th^  astrologers, 
neither  a natural  period  nor  a subdivision  of  one,  not  being  of 
' use  that  we  can  discover  in  determining  the  ruative  position,  or 
t aspect,  of  tlie  two  planets  with  which  it  deals,  nor  having  any  assignable 
wtjjif’  R tlie  asterisms,  with  which  it  is  attempted  to  be  brought  into  1 
, v‘dd.  Were  there  thirty  yogas,  instead  of  twenty-seven*  the 
} would  seem  an  artificial  counterpart  to  tlie  lunar  dp,y,  whicteis 
abject  of  the  next  verse ; being  derived  from  the  sum,  as  the  other.' ' 
difference,  of  the  longitudes  of  the  sun  and  moon. 

From  the  number  of  minutes  in  tlie  longitude  of  the  moon 
diminished  by  that  of  tlie  sun  are  found  the  lunar  days  (tithi),  . 
dkrldiDf;  tlie  difference  by  the  portion  (Mtofja)  of  a lunar  day. 
“‘ply  the  minutes  past  and  to  come  of  the  current  lunar  day 
ixty,  and  divide  oy  the  difference  of  the  daily  {potions  of 
planets : the  result  is  the  time  in  nfidis.  ■. 

« fitly, , or  lunar  day,  is  (hoc  i.  13)  one  thirtietii  of  a lunar  Ttpi 
■the  time  during  which  the  moon  gaina  in  longitude  upon  the) 
hole  revolution,  or  300* : it  ia,  therefore,  the  period  tduriqg -whltft 
r'dtgareuce  of  the  increment  of  longitwi?  of  panel, nnjpntsA 


Translation  and  Notes. 


afr; t'  - 

it.  60.] 


^.td  lSfc  tor  7201,  tfhich  arc,  as  stated  in  verge  04,  is  its  portion 
■To 1^5' ^tivw.dnjfrenti.’lunar  day,  we  divide  by  this  amount  the  whole 
c ess"  of  th^^km^tode  of  th^  moon  over  that  of  die  sun  at  the  gww^ 
time;,  ind-t&Hhd  the  part  past  and  to  come  of  the  current  day,  we  con-  4 
vert  longitude  ipto  time  in  a manner  analogous  to  that  employed  in  the 
case  of  the  yoga. 

Tims,  to  find  the  date  in  lunar  time  of  the  midnight  preceding  the 
first  of  January,  I860,  we  first  deduct  the  longitude  of  the  sun  from  that 
of  the  moon;  the  remainder  is  2*  29°  241,  or  53G4#:  dividing  by  720, 

- it  appears  that  the  current  lunar  day  is  the  eighth,  and  that  324'  of  its 
portion  are  traversed,  leaving  3961  to  he  traversed.  Multiplying  these 
numbers  respectively  by  00,  and  dividing  l»v  07o'  38",  the  difference  of  ^ 
the  daily  motions  at  the  time,  we  find  that  28n  4ftv  2i*  have  passed 
the  beginning  of  the  lunar  day,  and  that  it  <till  has  35n  10v  8P 

The  lunar  days  have,  for  tlic  moist  pail,  no  distinctive  names,  \MW 
those  of  each  half  mniitli  ( jtnkxha — see  above,  under  i.  48-51)  alif' 
called  first,  second,  third,  fourth,  etc.,  up  to  fourteenth.  The  last,  or 
fifteenth,  of  each  half  has,  however,  a special  apfYcUation  a:  that  which 
concludes  the  first,  the  light  half,  ending  at  the  moment  ofyopposition, 
is  called  ptlurmmasi,  purnimu , pit  main  a,  -May  of  full  moon;”  that 
which  doses  the  month,  and  ends  with  the  conjunction " of  the  tw:o 
planets,  is  styled  amurfiw a,  “the  day  of  dwelling  together.”  ^ 

Each  lunar  day  is  farther  divided  into  two  halves,  called  karanis^  as 
appears  from  the  next  following  passage. 

4V 

67.  The  fixed  ( dhruva ) hi  rah  ns } namely  cakum\  ndga , mtydi-  ■ 
pada  the  thfrd,  and  kinsiatjhno,  are  counted  from  the  latter  half 
of  the  fourteenth  clav  of  the  dark  half-month. 

68.  After  these,  the  kuriiuas  called  movable  (cam),  namely 
bava,  etc.,  seven  of  them:  caeli  of  these  karanas  occurs  eight 
times  in  a month. 

69.  Half  the  portion  (bhoga)  of  a lunar  day  is  established  "M 
that  of  the  karanas  .... 

Of  the  eleven  karanas,  four  occur  only  once  in  the  lunar  month, 
while  the  other  seven  are  repeated  each  of  them  eight  times  to  fill  out 
tKc  remainder  of  the  month.  Tlicir  names,  and  the  numbers  of  the 
half  lunar  days  to  which  each  is  applied,  are  presented  below : 


i.  Kinatnghna. 

а.  Bays. 

3.  BAlava. 

4*i  EAulava. 

5.  TflitiU. 

б.  Gai* 

7.  BHqJj. 

h 4.VW.IL 
^C.toaL 
*ai  IHgfc 


and,  9th,  i6th,  ?3rd,  3nth,  37ih,  44th,  5ist 
3rd,  volh,  17th,  a4th,  3 ist,  38' ii,  45ili,  5and. 
4th.  nth,  1 8th,  a5tli,  3;nd,  39th  46th,  53rd. 
5th,  lath,  19th,  a6th,  33rd,  4oth,  47th,  54th. 
6th,  1 3th,  aoth,  37th,  34ih,  4 1st,  48th,  55th. 
7th,  i4lb,  *ist,  aflth,  35th,  4and,  49th,  56th. 
8th,  1 5th,  a and,*  29th,  36th,  43rd,  5oth,  57th. 
58th.  • 

59th. 

6oth. 


S&rya-Siddli&nta}  [ii.0<N\ 

k • ' 

cit  of  these  names  are  very  obscure.;  the  last  three  mean  “hawk,"  > 
“serpent,"  an<j  11  quadruped.”  Karaqa  itself  is,  by  derivation,  “fcotay 
cause  in  what  sense  it  is  applied  to.  denote  these  the  . • 

month,  we  do  not  know.  Nor  hare  we  found  anywhere  nreitpfiibation 
of  the  value  and  use  of  the  karanas  in  Hindu  astronomy  orastrblogy. 

■'  The  time  which  wc  have  had  in  view  in  our  other  calculations  being*  ' 
•a  is  shown  under  the  preceding  passage,  in  the  first  half  of  the  eighth 
lunar  day,  is,  of  course,  in  the  fifteenth  karana,  which  is  named  Visnti. 

, The  remaining  half-verse  is  simply  a winding-up  of  the  chapter. 

69 Thus  lias  been  declared  the  corrected  (sphuia)  mo- 

tion of  the  sun  and  the  other  planets. 

v>The  following  chapter  is  styled  the  “chapter  of  the.  three  inquiries" 
(iriprapiddhikdra).  According  to  the  commentary,  this  means  that  it 
is  intended  by  the  teacher  ns  a reply  to  his  pupil's  inquiries  respecting' 
the  three  subjects  of  direction  (c//y),  place  (dfya),  and  time  (Mb). 


chapter  nr. 


OF  DlKElTIOX,  PEACE,  AX I)  TIME. 


Contents: — 1-6,  construction  of  the  dial,  ami  description  of  its  parts;  7,  the 
.measure  of  amplitude;  8,  of  the  gnomon,  liypothciiuse,  and  shadow,  any  two 
being  given,  to  find  the  third;  9—1 2,  precession  of  the  equiqpjcea;  1*2-18,  the 
equinoctial  shadow;  13-14,  to  find,  from  the  equinoctial  shadow,  the  latitude  and 
co-latitude;  14-17,  the  sun's  declination  being  known,  to  find,  from  a given 
shadow  at  noon,  his  zenith-distance,  the  latitude,  and  its  sire  and  cosine : 17,  lati- 
tude being  given,  to  find  the  equinoctial  shadow  ; 17-20,  to  find,  from  the  lati- 
tude and  the  sun's  zenith-distance  at  nr»onp  his  declination  and  his  true  and  mean 
^longitude;  20-22,  latitude  and  declination  being  given,  to  find  the  noon-shadow 
and  hypotlienuse;  22-23,  from  the  sun's  declination  and  the  equinoctial  shadow, 
to  find  the  measure  of  amplitude  ; 23-25.  to  find,  from  the  equinoctial  shadow 
i lilid  the  measure  of  amplitude  at  any  given  time,  the  base  of  the  shadow  ; 26-27, 
to  find  the  liypothenuse  of  the  shadow  when  the  sun  is  upon  the  prime  vertical; 
27-*28,  the  sun's  declination  and  the  latitude  being  given,  to  find  the  sine  and  the 
measure  of  amplitude  ; 28-83,  to  find  the  sines  of  the  Altitude  and  zenith-distance 
of 'the  sun,  when  upon  the  south-east  and  south-west  vertical  circles;  33-34,  to 
* Jpd  the  corresponding  shadow  and  ny  put  hen  use ; 34-36,  the  Bun's  ascensional  dtf- 
■'  Eerence  and  the  hour-angle  >>eii»g  given,  to  find  the  sines  of  his  altitude  and  zenith- 


distance,  jod  the  corresponding  shadow  and  hypotlienuse ; 37-39,  to  find,  by  a 
conffitPf  process,  from  the  shadow  of  a given  time,  the  sun's  altitude  and  oenith- 
distjums,  and  the  hour-angle  ; 40-41,  the  latitude  and  the  sun's  amplitude  being 
known,  to  find  bis  declination  and  true  longitude ; 41-42,  to  draw  the  path  do- 


■Jjribsd  by  the  extremity  of  the  shadow;  42-46,  to  find  the  ares  of  right  and 
ow)^  nsesnsion  corresponding  to  the  several  signs  of  the  ecliptic;  46-40, His 
Sun's  Sffgftude  and  the  time  being  known,  to  find  the  point  pf  the  ecliptic  which 
Pfpos  the  horizon;  49,  thesun'a  longitude  and  the  hour-angle  being  tarjrn, 
j iOl  rtie  point  of  the  ediptie  which  is  upon  the  roedU^ 


4" 


Hi.  5.]  Translation  and  Notts.  $$ 

f 

1.  On  a itofly  surface,  made  vater-level,  or  moon  hard  plaster, 
HHufolevel,  there  draw  an  even  circle,  of  a radios  equal  to  any 
reduitA  number  of  the  digits  (angula)  of  the  gnomon  ($a niu). 

. 2.  JpRts  centre  set  up  the  gnomon,  of  twelve  digits  of  the 
measure  fixed  upon ; and  where  the  extremity  of  its  shadow 
touches  the  circle  in  the  former  and  after  parts  of  the  day, 

ft.  There  fixing  two  points  upon  the  circle,  and  calling  them 
the  forenoon  and  afternoon  points,  draw  midway  between  them, 
by  means  of  a fish-figure  (timi),  a north  and  south  line. 

4.  Midway  between  the  north  and  south  directions  draw,  by 
a fish-figure,  an  east  and  west  line : and  in  like  manner  also,  by 
fish-figures  (mal&ya)  between  the  four  cardinal  directions,  drfiw 
the  intermediate  directions.  ' ■ 

6.  Draw  a circumscribing  square,  by  means  of  the  lines  going  ' 
out  from  the  centre;  by  the  digits  of  its  base-line  (phujasiUrajj 
projected  upon  that  is  any  given  shadow  reckoned.  ’/ 

In  this  passage  is  described,  the  method  of  ronst  ruction  of  the  Hindu 
dial,  if  that  can  properly  lie  called  ;t  dial  which  is  without  hour-lines, 
and  does  not  give  the  time  hv  simple  inspection.  It  is,  as  will  be  at 
once  remarked,  a horizontal  dial  of  the  simplest  character,  with  a verti- 
cal gnomon.  This  gnomon,  whatever  may  be  the  length  chosen  for  it, 
is  regarded  as  divided  into  twelve  equal  parts  called  digits  (angula% 
“finger”).  The  ordinary  digit  is  one  twelfth  of  a span  ( vitasti ),  or  one 
twenty-fourth  of  a cubit  (ftasta) : if  made  according  to  this  measure, 
then,  the  gnomon  would  he  about  nine  inches  long.  Doubtless  the  first 
gnomons  were  of  such  a length,  and  the  rules  of  the  gnomonic  science 
were  constructed  accordingly,  “twelve”  mid  “the-  gnomon”  being  used, 
as  they  are  used  everywhere,  in  this  treatise,  as  convertible  terms:  thus 
twelve  digits  became  the  unvarying  conventional  length  of  the  staff,  and 
all  measurements  of  the  shadow  and  its  hypothemise  were  made  to  cor- 
respond. How  the  digit  was  subdivided,  wc  have  nowhere  any  hint. 
In  determining  the  directions,  the  same  method  was  employed  which  is 
still  in  use;  namely,  that  of  marking  the  points  at  which  the  extremity 
of  the  shadow,  before  and  after  noon,  crosses  a circle  described  about 
the  base  of  the  gnomon ; these  points  being,  if  wc  suppose  the  sun’s 
declination  to  have  remained  the  same  during  the  interval,  at  an  equal 
diatance  upon  either  side  from  the  meridian  line.  Tn  order  to  bisect  the 
line  joining  these  jtoiuts  by  another  at  right  angles  to  it,  which  wilfchw>; 
the  meridian,  the  Hindus  draw  the  figure  which  is  called  here  the  “fish" 
{math rya  or  timi) ; that  is  to  say,  from  the  two  extremities  of  the  line  in 
question  as  centres,  and  with  a radius  equal  to  I le  line  itself  ifps  tf 
circles  arc  described,  cutting  one  another  in  two  points.  The  lentiosiar 
figure  formed  by  the  two  arcs  is  the  14  fish through  the  pohttWM>f 
intersection,  which  are1  called  (in  the  commentary)  the  u mouth  %id 
u tail/’  a line  is  drawn,  which  is  the  one  required.  The  meridian  Stomp  v 
thus  determined, ^hc  east  and  west  line,  and  those  for  the  lnlermedi^, 
points  of  directions,  are  laid  down  from  it*  by  a repetition  of  the  same 
PpeessL  square^^urom,  f having  four  corners”)  is  then  farther 


Ito  Surya-Siddh&nta,  * [Hi.  5- 

».  ' • ft  * 

Ascribed  about  the  general  centre,  or  about  a ciA  drwflrn  about  that< 
r -^entre,  the  eastern  and  western  sides  pf  which  ail  divided  into  digits; 
4fet use  is,  to  aid  in  ascertaining  the  “ base”  (bkuja)  <jif  ahy  givs^J^adow, 

which  is  the  value  of  the  latter  when  projected  upon  a n®5l 

line  (see  below,  w.  23-25);  the  square  is  drawn,  as  explains 
commentary,  in  order  to  insure  the  correctness  of  the  projection,  by  a 
line  strictly  parallel  to  the  cast  and  west  line. 

The  figure  (Fig.  9)  given  below,  under  verse  7,  will  illustrate  the  form 
of  the  Hindu  dial,  as  described  in  this  passage. 

The  term  used  for  “ gnomon”  is  fanku , which  means  simply  u staff”. 
For  the  shadow,  we  have  the  com  in  on  word  cAdyd,  “ shadow,”  and  also, 
in  many  places,  prabhd.  ami  bha%  which  properly  signify  the  very  oppo- 
’fiig^of  shadow,  namely  41  light,  radiance  it  is  difficult  to  see  how  they 
Ud  come  to  he  used  in  this  sense ; so  far  as  we  are  aware,  they  are 
~ to  no  other  shadow'  than  that  of  the  gnomon. 

The  cast  and  west  line  is  called  the  prime  vertical  (mma- 
~ la);  it  is  likewise  denominated  the  east  and  west  hour 
(unmandala)  and  the  equinoctial  circle  ( viahuvanmandala ). 

’ The  line  drawn  cast  and  west  through  tlic  base  of  the  gnomon  may 
bck'lreg&rded  as  the  line  of  common  intersection  at  that  point  of  thred 
great  circles,  as  being  a diameter  to  each  of  the  three,  and  as  thus  enti- 
tled to  represent  them  all.  These  circles  are  the  ones  which  in  the  last 
j.  8,  p;  88)  .are- shown  projected  in  their  diameters  ZZ',  BJgf, 
the  centre  C,  in  which  the  diameters  intersect,  is  itself  the' 
loC the  line'  in  question  here.  ZZ'  represents  the  prime  verfci- 
vamamandala/  literal ly  M even  circle:”  V V'  is  the 
of  declination,  which  passes  through  the  east  and 
w&pbintsjaf  the  observer's  horizon ; it  is  called  unmandala , Uup-cir- 
cle^*r4bft»  to  say,  the  circle  which  in  the  oblique  sphere  is  elevated ; 

. . jf*  the  cquatolr^haB  the  name. of  viahuvanmandala^  orviskuvad - 
„ Of ' -the  equinoxes the  equinoctial  points  themselves 
£ >■  , ^ viihuval,  or  vishuva,  which  may  be  rciidcrcd  44 point 

m ” The  same  line  of  the  dial  might  be  regarded  as 
tiye  in  like  .manner  of  a fourth  circle,  that  of  the  horizon 
^ jested,  ilithe  figure,  in  SN : hence  tlie  commentary  adds 
reotluar  three;  it  is  omitted  in  the  text,  perhaps,  because  it  is 
*by  the  whole  circle  drawn  about  the  base  of  tlic  gnomon, 

: not  by  this  diameter  alone. 

^(jtfbebfipeciiicatioTts  of  tins  verse,  especially  of  the  latter  half  of  it,  are 
-of  little  'practical  importance  in  the  treatise,  for  there  hardly  arises  fa 
- #ease,'an  any  of  its  calculations;1  in  which  the  cast  and  west  axis  of  Hxc 
diaheomes  to  be  taken  as  standing  for  these  circles,  or  any  one  of  them. 
In  drawing  the  base  (i bkvja ) of  the  shadow,  indeed,  it  docs  represent  the 
plane  of  the  prime  vertical  (sec  below,  under  vy.  23-28) ; hut  Jjiis  ia 
fy^bti&istinctly  stated,  and  the  name  of  the  prime  vertical  (ttamatnalldala) 
jflCcuri  in  eitly  one  other  passage  (below,  v.  20) : the  jggst  and  west  hour*  ., 
■iPole  (unmanrlala)  is  nowhere  referred  to  again:  dpi  the  equator,  M 
wfU  be  seen  under  the  next  verse,  is  properly  represented  on  the  d kd, 
not  by  its  east  and  west  axis,  but  by  taulino  o^pn%quinoctial  shade#,  ' 


Translation  and  Notes. 


v .7.  Draw  likewise  an  east  and  west  liae^hrcn^  the'extreTnity 
of  lii&'equuiocttgl  shadow  ( vishuvadbhd ) ; the  interval  between 
awJK^hado#  and"  the  line  of  the  equinoctialBhadow  is  de* 

* nomwNwthe  measure  of  amplitude  (ajrd). 

The  equinoctial  shadow  is  defined  in  a subsequent  passage  (w.  12, 
13);  it' is,  as  we  have  already  had  occasion  to  notice  (under  iL  01-02), 
the  shadow  cast  at  mid-day  when  the  sun  is  at  either  equinox*— that  is 
to  say,  when  he  is  in  the  plane  of  the  equator.  Now  as  the  equator  is 
a drcle  of  diurnal  revolution,  the  line  of  intersection  of  its  plane  #ith 
that  of  the  horizon  will  be  an  east  and  west  line ; and  since  it  is  also  a. 
great  circle,  that  line  will  puss  through  the  centre,  the  place  of  tkerdb? 

• server:  if,  therefore,  we  draw  through  the  extremity  of  the  eqiiittgMjiji 

shadow  a line  parallel  to  the  cast  and  west  axis  of  the  dial,  it  will  MMtfjf 
sent  the  intersection  with  the  dial  of  an  equinoctial  plane  pamttg' 
through  the  top  of  the  gnomon,  and  in  it  will  terminate  the  lines  dttirft- 
through  ■ that  point  from  any  point  in  the  plane  of  the  equator gBa 
hence,  it  will  also  coincide  with  the  path  of  the  extremity  of  the  emjpRt 
on  the  day  of  tlic  equinox.  Thus,  let  the  following  figure  (Fig.  tpifepr* 
resent  the  plane  of  the  dial,  X 8 and  E W being  its  tw^ascs,  and  £tbe 
base  of  the  gnomon : and  let  the  shadow  cast  at  noon  wheu  the  SM-.  ip 
upon  the  equator  lie,  * 

in  n given  latitude,  ■ 1 *■  9‘ 

jkf.  then  Ac  is  the 
equinoctial  shadow, 
and  QQ',  drawn 
tJi rough  e and  paral- 
lel to  EW,  is  the 
path  of  the  equinoc- 
tial shadow,  being 
the  line  in  which  a 
ray  of  the  sun,  from 
any  point  in  the  plane 
of  the  equator,  pass- 
ing through  the  top 
of  the  gnomon,  will 
meet  the  face  of  the 
dial.  In  the  figure 
ns  given,  the  circle 

is  supposed  to  be  described  about  the  base  of  the  gnomon  with  a'tiiSSjjl 
-of  forty  digits,  and  the  graduation  of  the  eastern  and  westo&P  aidea  a&| 
the  circumscribing  square,  used  in  measuring  the  base  (bhvja)  of  iiggJj 
shadow,  is  indicated : the  length  given  to  the  equit  ictial  shadM'dMw^* 
aponds  to  that  which  it  has  in  the  latitude  of  Washington. 

It  is  not,  bow  overtoil  account  of  the  coincidence  of  QQf  withilha 
psthof  the  equinoctial. shadow  that  it  is  directed  to  be  pen^RWmyv 
drawn  upon  the  dial-face : its  use  is  to  determine  for  any  pfeabhidip^ 
its  qprd,  or  mejfitarc  of  uinplitude.  Thus,  let  «/,4  d\  bk%  tf,  b 
shailowa  cfist  by  the  gnomon,  under  various  conditions  of  time  and  dec- 
lination • then  the?dSs|ance  frop  the  extremity  of  each  Of  them  to  the 
s'  - '''is*-  13 


S&rya-SiddJi&nta, 


[iii.7- 


Hpe  of  the  equinoctial  shadow,  or  d e,  d'i , id,  l «*,  m tfu  respectively,  is 
denominated  the  agr&  of  that  shadow  or  of  that  time.  ' 

term  a grA  we  have  translated  “measure  of  amplitude,? .-^ecause 
it  does  in  fact  represent  the  sine  of  the  sun’s  amplitude — undmmding 
by  “amplitude"  the  distance  of  the  sun  at  rising  or  setting  from  tlic 
east  or  west  point  of  the  horizon — varying  with  the  hvpothcnuse  of  the. 
dmdow,  and  always  maintaining  t<>  that  hypothenusc  the  fixed  ratio  of 
-the  sine  of  amplitude  to  radius.  That  this  is  so,  is  assumed  by  the  text 
in. its  treatment  of  the  nyrd,  but  is  nowhere  distinctly* stated,  nor  is  the 
commentator  at  the  pains  of  demonstrating  the  principle.  Since,  how- 
ever, it  is  not  an  immediately  obvious  one,  we  will  take  the  liberty  of 
giving  the  proof  of  it. 

/ the  annexed  figure  (Fig.  10)  let  C represent  the  top  of  tl&e  guouiou, 
*a$  let  K be  any  given  position  of  the  sun  in  the  heavens.  From  K 
KB7  at  right  angles  to  the  plane  of  the  prime  vertical,  meeting  that 

Fi£f.  10.  a 


'plane  in  IV,  and  let  the  point  of  its  intersection  with  the  plane  of  the 
equator  be  in  H7.  Join  kC,  YJ O,  and  JVC.  Then  KO  is  radius,  and 
E7Kia  equal  to  the  sine  of  the  sun’s  amplitude:  for  if,  in  the  sun’s 
daily  revolution,  the  point  K is  brought  to  the  horizon,  Er  IV  will  disap- 
. -pear,  K Er  C will  Income  a right  angle,  K OE'  will  he  the  amplitude, 
irfD K its  sine;  but,  with  a given  declination,  the  value  of  re- 
^lilaiia  always  the  same,  since  it  is  a line  drawn  in  a constant  direction 
bSftrifen  two  parallel  planes,  that,  of  the  circle  of  declination  and  that  of 
thwfeqiwtbr.  Now  conceive  the  three  lines  intersecting  in.C  to  bb  pro- 
ducad  until  they  meet  the  plane  of  the  dial  in  b\  c7,  and  k respectively; 
the&  three  points  will  be  in  the  same.  straight  line,  being  in  the  lino  of 
„ intersection  with  the  horizon  of  die.  plane  K IV  C produced,  and  this 
^ line,  V Jr,  will  be  at  right  angles  to  IV  b\  since,  it  is  the  line  of  intersQ1^ 
;tion  of  two  planes,  each  of  which  is  at  right  angles  to  the  plane  of  the 
‘ prime  vertical,  in  which  IV  ft7  lies.  K IV  and  k & are  therefore  parallel, 
and  the  triangles  C Ef  K and  C e7  k arc  similar,  and  e7  k : C k : : E7  K : C K. 

’ But  C k is  the  hypothenusc  of  the  shadow'  at  thf  given  time,  andL^i  it 
4*fchfc  oyrd,  or  measure  of  amplitude,  since  e7,  by  what  was  said  abbve,  in 
*'.IW  of  the  equinoctial  shadow ; therefore  meas.  ampl. : hyp.  * 
qKU L: : sin  ampl.  :dL  Hence,  if  the  declination  and  we  latitude,  which 
together  determine  the  sine  of  amplitude,  be  given,  tp)?  measure,. tf  ■ 
amplitude  will  vary  with  the  faypothenuse  of  the  shadow,  and 

i.  fcrVfS 


Translation  and  Notes. 


iii.  10.] 


.Hf 


.rf 


measure  of  amplitude  of  any  given  shadow  will  be  to  that  of  any  other, 

. as  the  hypothennse  of  the  former  to  that  of ‘the  lsttfcri';;  ' W4  - ■ 

Thedettering  of  the  above  figure  is  made  to  correspond  ? a*  nearly  as 
may  flu  it  of  the  one  preceding,  and  also  with  that  of  ttt;One 

given  filter,  under  venes  13  and  14,  in  either  of  which  the  relations  of 
the  problem  may  be  farther  examined. 

There  are  other  methods  of  proving  the  constancy  of  the  ratio  bdVM 
by  the  measure  of  amplitude  to  the  hypothennse  of  the  shadow,  but  we 
have  chosen  to  give  the  one  which  seemed  to  us  most  likely  to  be  thrit 
by  which  the  Hindus  themselves  deduced  it.  Onr  demonstration  ie+in 
one  respect  only  liable  to  objection  as  representing  a Hindu  procaOS  1 
it  is  founded,  namely,  upon  the  comparison  of  oblique-angled  trii 
which  elsewhere  in  this  treatise  are  hardly  employed  at  all.' 
although  the  Hindus  bad  no  methods  of  solving  problems  c:  ” 
in  right-angled  trigonometry,  it  is  hardly  to  be  supposed  that 
frained  from  deriving  proportions  from  the  similarity  of  oblique* 
triangles.  The  principle  in  question  admits  of  being  proved  by 
of  right-angled  triangles  alone,  but  these  would  be  situated  in  dil 
planes. 

Why  the  line  on  the  dial  which  thus  measures  the  son’s 
^called  the  agrd,  we  have  been  unable  thus  tar  to  discover^ 

*a  feminine  adjective  (belonging,  probably,  to  rriAd,  “line/*  hi 
literally  means  44  extreme,  first,  chief.”  Possibly  it  may  be  in  . . _wji  . ^ 
connected  with  the  use  of  anfyd, 14  final,  lowest,”  to  de»igEi*t& 

By  or  EG  (Fig.  8,  p.  88) : see  below,  under  v.35.  The 
tude  itself,  aC.or  AC  (Fig.  8),  is  called  below  (vv. .27^80)  ^ 

8.  The  square  root  of  the  sum  of  the  squares  of 
and  shadow  ia  the  hypothenuse : if  from  the  square  oft 
the  square  of  the  gnomon  be  subtracted,  the  square  root  of 
remainder  is  the  shadow : the  gnomon  is  found  by  the  convene 
process.  - . 

This  in  simply  an  application  of  the  familiar  rule,  that  in  a .iMht- 
angled  triangle  tlic  square  of  tho  hypothcnusc  is  equal  to  the  nun  of  ’ 
the  Squares  of  the  other  two  sides,  to  the  triangle  produced  by  tbe 
gnomon  as  perpendicular,  the  shadow  as  base,  and  the  hypothenoai  of 
the  shadow,  the  line  drawn  from  the  top  of  the  gnomon  to  the  extrem- 
ity of  the  shadow,  ns  hypothemise.  . " 

Tho  subject  next  considered  is  that  of  the  precession  of  the  equingyas. 

h 9.  In  an  Age  ( yuga ),  the  circle  of  the  aslcrisms  (iha) 

■back  eastward  thirty  score  of  revolutions.  Of  the  result 
- tnined  after  multiplying  the  sum  of  days  {di  ugand ) by  thijfenui 
ber,  and  dividing  by  the  number  of  natural  days  in  an  Age, 

^0.  Take  the  part  which  determines  the  sine,  multiply^  ijt,;by 
thkfte,  and  divide  by  ten ; thus  are  found  the  degrees  caUedthoae 
of  the  precosgion  (ayana).  From  the  longitude  of  a planet ijps 
corrected  by  these  are  to  be  calculated  the  declination,  shadow, 
.wuwensioual^diiference  (caradala),  etc. 

M'  ■«-  * 


SArya-Siddh&ntOy 


[iii.  11- 


Jjk/.Tbe  circle,  as  thus  corrected,  accords  with  its  observed 
pace  at  the  solstice  (aydnu)  and  at  either  equinox ; it  has  moved 
^fcastward,  when  the  longitude  of  the  sun,  21s  obtained  by  calcu- 
<t*tk>ri,  is  less  than  that  derived  from  the  shadow, 

12.  By  the  number  of  degrees  of  the  difference ; then,  turning 
, back,  it  has  moved  westward  by  the  amount  of  difference,  when 
the  calculated  longitude  is  greater 


Nothing  could  well  be  more  awkward  and  confused  than  this  mode  of 
stating  the  important  fad  of  tlm  precession  of  the  equinoxes,  of  de- 
scribing its  method  and  rate,  and  of  directing  how  it-s  amount  at  any 
time  is  to  be  found.  The  theory  which  the  passage,  in  its  present  form, 
is  actually  intended  to  put  forth  is  as  follows : the  vernal  equinox  lihrates 
westward  and  eastward  from  the  fixed  point,  near  s Piscium,  assumed  as 
the  commencement  of  the  sidereal  sphere — the  limits  of  the  lilmitory 
movement  being  27°  in  either  direction  from  that  point,  and  the  time 
of  4 complete  revolution  of  libration  being  the  six -hundredth  part,  of 
the  period  called  the  l! rent.  Age  (see  above,  under  i.  15-17),  or  7200 
. years;  so  that*  the  annual  rate  of  motion  of  the  equinox  is  r»4,/.  We 
' will  examine  with  some  r are  the  language  in  whieli  this  theory  is  e.on- 
' veyed,  as  important*  results  are  believed  to  bn  deductible  from  it. 

The  first  half  of  verse  9 professes  to  teach  the  fundamental  fact  of  the 
v motion  in  precession.  The  words  bh6.na.rn  cakram , which  wc  have  ren- 
dered “circle  of  the  nstcrisins,”  i.  c.,  the  fixed  zodiac,  would  admit  of 
Japing  translated  “circle  of  the  signs,'1  i.  <\,  the  movable  zodiac,  an 
reckoned  from  the  actual  equinox,  since  hha  is  used  in -this  treatise  in 
either  sense.  Rut.  our  interpretation  is  shown  to  be  the  correct  one  by 
the  directions  given  in  verses  1 1 and  12,  which  teach  that  when  the  sun’s 


^calculated  longitude — which  is  his  distance  from  the  initial  point  of  the 
* fixed  sphere — is  less  than  that  derived  from  the  shallow  by  the  process 
. tb  be  taught  below  (vv.  17-19) — which  is  his  distance  from  tlic  equinox 
-r-the  circle  has  moved  eastward,  and  Ihc  contrary:  it  is  evident,  then, 
^ VRt  the  initial  point,  of  the  sphere  is  regarded  as  the  movable  point, 
^ISdthc  equinox  ns  the  fixed  one.  Now  this  is  no  less  strange  than  in- 
^nfrbsistcnt  with  the  usage  of  the  rest,  of  the  treatise.  Elsewhere  { Pis- 
ciujp  is  treated  as  the  one  established  limit,  from  which  all  motion  com- 
menced at  the  creation,  and  by  reference  to  which  all  motion  is  reckoned, 
while  here  it  is  made  secondary  to  a point  of  which  the  position  among 
theaters  is  constantly  shifting,  and  width  hardly  has  higher  value  thtm 
a node,  as  which  the  Hindu  astronomy  in  general  treats  it  (see  p.  86). 
The  word  used  to  express  the  motion  (lambaie)  is  the  same  with  that; 
.-employed  in  a former  passage  (i.  25)  to  describe  the  eastward  motion  gf 
the  planets,  and  derivatives  of  which  (as  larnba , lamhana , etc.)  are  not 
ilifjfequent  in  the  astronomical  language ; it  means  literally  to  “lag,  lianjf 
. rack,  fall  behind here  we  have  it  farther  combined  with  the  prefix 

■ jpar^  “about,  round  about,”  which  seems  plainly  to  add  the  idea^uf  a 

■ complete  revolution  in  the  retrograde  direction  jijdicatecl  by  it,  and  we 
- .Eta e translated  the  line  accordingly.  This  venfiTtiicn^Aonteins  no  hint 

dna  libratory  movement,  but  rather  the  distinct  atetemei&M  a contin- 
uous cifcttfaid  revolution.  It  should  th 


Translation  and  Notes . 


iii.  12.] 

circumstance  is  one  of  less  significance,  that  the  form  in  vhicl 
number  of  revolutions  is  stated,  trinfatkrlyai , “ thirty  twenties,*)) asfnb 
parallel  in  the  usage  of  this  Sidclhdmtn  elsewhere.  ' , ) 

We  may  also  mention  in  this  connection  that  Bhfakara,  thp  great  ■* 
Hindu  astronomer  of  the  twelfth  century,  declares  in  his  Sidclhanta- 
^irornuni  (Gol&dli.,  vi.  1?)  that  the  revolutions  of  the  equinox  are  given 
by  the  Sftrya-Siddh&nta  as  tJiirty  in  an  Age  (see  Colebrooke,  As.  Res., 
xii.  209,  etc.;  ISssays,  ii.  374,  etc.,  for  a full  discussion  of  this  passage 
and  its  bearings);  thus  not  only  ignoring  the  theory  of  bbration, but  . 
giving  a very  different  number  of  revolutions  from  that  presented  by  Our 
text.  As  regards  this  latter  point,  however,  tin;  change  of  a single  letter, 
in  the  modern  reading  (substituting  trinffitkrtvax,  “thirty  times,”  fof 
trinrulkrtyax , “thirty  twenties”)  would  make  it  accord  with  Rh&sbar&’s 
statement.  We.  shall  return  again  to  this  subject. 

The  number  of  rcvolutiontfof  whatever  kind  lhc\  may  bo,  being  000'. 
in  an  Ago,  the  position  at  any  given  time  of  the  initial  point  of  tb#'1.- 
sphere  with  reference.  t«»  the  equinox  is  found  by  a proportion,  as  follows* 
as  the  number  of  days  in  :m  Age  is  to  the  number  of  revolutions  in  the 
same,  period.  >n  is  the  given  “sum  of  <ln\V'  (see  dhow,  under  i.  48-51)  ’ 
to  the  revolutions  and  parts  of  a revulutinn  .lo-omptishod  down  to  the 
given  time.  Thus,  let  us  find,  in  illustration  or  the  process,  the  amount 
of  ^precession  on  the  first  of  January.  18GU.  Since  the  number  of  years 
elapsed  before  the  beginning  of  the-  present  Iron  Age  [kali  yiufa)  is  di- 
visible by  720(1,  it  is  unnecessary  t«»  make  our  calculation  from  the  com-  . 
men  cement  of  the  present  order  of  things:  we  may  take  the  sum  df 
days  since  the  current  Age  began,  which  is  (see  above,  under  i.  58) 
1,81 1,045.  lienee  the  proportion 

1.577.91  T.B'jK'l  : ;;  1.81  l yj1}*!  : (»rev  >48°  8".t) 

gives  us  the  portion  umpi  1 pi ished  of  the  cui+cnt  revolution.  Of  this 
■we  are  now  directed  (v.  Ill)  to  take  the  part  which  determines  the  sinq 
(dovj  or  bfotja — for  the  origin  ami  nn  aning  of  the  phrase,  see  above, 
under  ii.  2!),  .10).  This  direction  determines  the  character  of  the  mot^rin^ 
as  lihratorv.  For  a motion  of  91°,  92°,  93°,  etc.,  gives,  bj  it,  a prqcJ^  ] 
siou  of  89°,  88°,  87°,  etc.;  so  that  the  movable  point  virtually  return*^ 
upon  its  own  track,  and,  after  moving  ISO0,  lias  reverted  to  its  starting- 
place.  So  its  farther  motion,  from  180°  to  270°,  gives  a precession.  In- 
creasing from  0°  to  90°  in  the  opposite  direction ; and  this,  again,  is 
reduced  to  0°  by  the  motion  from  270°  to  300°.  Ft  is  as  if  the  second 
and  third  quadrants  were  folded  over  upon  the  first  and  fourth,  so  that 
the  movable  point  can  never,  in  any  quadrant  of  its  motion,  be 
than  90°  distant  from  the  fixed  equinox.  Thus,  in  the  instance 
the  bhvja  of  248°  2*  8".9  is  its  supplement,  or  08°  2#  B".9 ; the  fi?f£ ' 
%p0°  having  only  brought  the  movable  point,  bacl  to  its  original,  post 
tibn,  its  present  distance  from  that  position  is  the  excess  ovei^URf* 
of  the  arc  obtained  as  the  result  of  the  first  process.  But  tills  distance 
we-TOre  now  farther  directed  to  multiply  hy  three  and  divide  by  tepi 
this  is  equivalent  to  reducing  it  to  the  measure  of  an  arc  of£7^,  instead 
;of  90°,  as  the  quadrant  of  libration,  since  3:10::  27  : 00.  Tt»m% 
done,  we  lajhtbe  actual  distance  of  the  initial  point  x>f  the  npherc  from 
.f  equino^  the  fi||£of  JahQary,  1860,  to  be  20°  24'  38"j'7l;  *’ 


SCtrya-Siddh&nta, 


[iii.  12. 


■•*k. question  now  arises,  in  which  direction  is  the  precession,  thus' 

^^tlUHu  1 * 1 1 Ja  a-j  i ■ ii  ■ i _i_x  i„  mu 


a&ert&ned,  to  be  reckoned  ? And  here  especially  is  brought  to  light 
the  awkwardness  ami  insufficiency,  and  even  the  inconsistency,  of  the 

{Process  as  taught  in  the  text-.  Not  only  have  we  no  rule  given  which 
urnishea  us  the  direction,  along  with  the  amount,  of  the  processional 
movement,  but  it  would  even  be  a fair  and  strictly  legitimate  deduction 
from  verse  9,  that  that  movement  is  taking  place  at  the  present  time  in 
an  opposite  direction  from  the  actual  one.  We  have  already  remarked 
above  that  the  last  complete  period  of  lihratory  revolution  closed  with 
the  dose  of  the  last.  Hrazen  Age,  and  the  process  of  calculation  has 
shown  that,  we  arc  now  in  the  third  quarter  of  a new  period,  and  in  tho 
third  quadrant  of  tho  current  revolution.  Therefore,  if  the  revolution 
is  an  eastward  one,  as  taught  in  the  text,  only  taking  place  upon  a folded 
circle,  so  as  to  be  made  lihratory,  the  present  position  of  the  movable 
point,  ; Piscium,  ought  to  he  to  the  wesffof  the  equinox,  instead  Of  to 
the  cast,  as  it  actually  is.  It  was  probably  on  account,  of  this  unfortu- 
nate flaw  in  the  process,  that  no  rule  with  regard  to  the  direction  wan 
given,  excepting  the  experimental  one  contained  in  verses  11  and  12, 
which,  moreover,  is  not  properly  supplementary  to  ttjp  preceding  rules, 
Jsiut  rather  an  independent  method  of  determining,  from  observation,  both 
the  direction  and  the.  amount  of  the  precession.  In  verse  12,  it  may  be 
remarked,  in  the  wuid  arrtyu,  “turning  hack,"  is  found  the  only  distinct 
intimation  to  he  discovered  in  tho  passage  of  the  character  of  the  motion 
as  lihratory. 

y.  We  have  already  above  (under  ii.  2rt)  hinted  our  suspicions  that  the 
phenomenon  of  the.  precession  was  made  no  account  uf  in  the  original 
composition  of  the  Suryu-Siildhanta,  and  that  the  notice  taken  of  it  by 
the^ treatise  as  it  is  at  present  is  an  afterthought:  we  will  now  proceed 
to  expose  the  grounds  of  those  suspicions. 

It  is,  in  the  first  place,  upon  record  (see  Colehrooke,  As.  lies.,  xii.  215 ; 
Essays,  ii.  380,  etc.)  that  sonic;  of  the  earliest  Hindu  astronomers  were 
ignoraut  of,  or  ignored,  the  periodical  motion  of  the;  equinoxes;  Brabma- 
~-  j&Qpta  himself  is  mentioned  among  those  whose  s\>tenis  Look  no  account 
'*of  it;  it  is,  then,  not  at  all  impossible  that  the  Surya-Siddhanta,  if  an 
ancient  work,  may  originally  have  done  the  same.  Among  the  positive 
^.evidences  to  that  effect,  we  would  first  direct  attention  to  the  significant 
fact  that,  if  the  versos  at  the  head  of  this  note  were  expunged,  there 
would  not  be  found,  in  the  whole  body  of  the  treatise  besides,  a single 
Hftt  of  the  precession.  Now  it  is  not  a little  difficult  to  suppose  that  a 
phenomenon  of  so  much  consequence  as  this,  and  which  enters  as  an 
Jnement  into  so  many  astronomical  processes,  should,  had  it  been  borne 
^distinctly  in  mind  in  the  framing  of  the  treatise,  have  been  hidden  away 
thus  in  a pair  of  verses,  and  unacknowledged  elsewhere — no  hint  being 

S"vep,  in  connection  with  any  of  the  processes  taught,  as  to  whether 
e correction  for  precession  is  to  be  applied  or  not,  arid  only  the  gen- 
^rpl  .directions  contained  in  the  latter  half  of  verse  10,  and  ending^ith 
“etc.,”  being  even  here  presented.  It  lias  much  more  the  aspect  of 
jp,  after-thought,  a correction  found  necessary  at  a date  subsequent  to.. 
*vp|  original  composition,  and  therefore  inserted,  with  orders  to  “ apply 
itwaererer  it  is  required.”  The  place^here  fyg  subjects  introduce^ 


Translation  and  Notes. 


iii.  1S.J 

looks  the  same  way : as  having  to  do  with  a revolution,  a a enterin^H^to 
the  calculation  of  mean  longitudes,  it  should  have  found  a place  whete  . . 
such  matters  are  treated  of,  in  the  first  chapter;  and  even  in  the  second  • 
chapter,  in  connection  with  the  rule  for  finding  the  declination,  it  would  ■ 
have  been  better  introduced  than  it  is  here.  Again,  in  the  twelfth 
chapter,  where  the  orbits  of  the  heavenly  bodies  are  given,  in  terms 
dependent  upon  their  times  of  revolution,  such  an  orbit  is  assigned  to 
the  asterisms  (v.  88)  as  implies  a revolution  onec  in  sixty  rears:  it  u, 
indeed,  very  difficult  to  sec  what  can  have  been  inteuded  by  such  a reso- 
lution as  this;  but  if  the  doctrine  respecting  the  revolution  of  die 
asterisms  given  in  verse  0 of  this  chapter  had  been  in  the  mind  of  the 
author  of  the  twelfth  chapter,  he  would  hardly  have  added  another  and 
a conflicting  statement  respecting  the  same  or  a kindred  phenomenon. 

It  appeal's  to  us  even  to  admit  of  question  whether  the  adoption  by  the 
Hindus  of  the  sidereal  year  as  the  unit  of  time  does  not  imply  a failure 
to  recognize  the  fart  that  the  equinox  was  variable.  We  should  expect, 
at  any  rate,  that  if,  at  the  outset,  the  ever-increasing  discordance  be- 
tween the  solar  and  the  sidereal  year  had  been  fully  taken  into  account 
by  them,  they  would  have  more  thoroughly  established  and  defined  the  - 
relations  of  the  two,  and  made  the  precession  a more  conspicuous  feature 
of  their  general  system  than  they  appear  to  have  done.  In  the  con- 
struction of  their  rosmical  periods  they  have  reckoned  by  sidereal  years 
only,  at  the  same  time  assi  ninir  (as  for  instance,  above,  i.  13,  14)  that  . 
the  sidereal  year  is  roiiipn-  d of  the  two  <njnna$,  “ progresses n of  lh|/ 
sun  from  solstice  to  solMice  The  supposition  of  an  iifier-eorrectieg^ 
likewise  seems  to  furnish  tlx*  most  satisfactory  explanation  of  tlio  forrii 
given  to  the  theory  of  the  preressinn.  The  system  having  been  first 
constructed  on  the  assumption  of  the  equality  »»f  the  tropical  and  side- 
real years,  when  it  began  later  to  appear,  t««o  plainly  to  be  disregarded, 
that  the  equinox  had  changed  its  place,  the  question  was  how  to  intro- 
duce the  new  clement.  Now  to  assign  to  the  equinox  a complete  revo-  " 
lut-ioii  would  derange  the  whole  system,  acknowledging'  a different  nuift- 
berof  solar  from  sidereal  years  in  the  chronological  periods;  if,  howeveS*,  . 
a libratnrv  motion  were  assumed,  the  equilibrium  would  be  maintained, 
since  what  the  solar  year  lost  in  one  part  of  the  revolution  of  libration 
it  would  gain  in  another,  and  so  the  tropical  and  sidereal  years  wonldS 
coincide,  in  nunihcr  and  in  limits,  in  each  great  period.  The  circum- 
stance which  determined  the  limit  to  be  assigned  to  the  libration  jrc 
conceive  to  have  bceu,  ns  suggested  bv  Bentley  (Hind.  Ask,  p.  132),  Cnat 
the  earliest  recorded  Hindu  year  had  been  made  to  begin  when  the  sun 
entered  the  asterism  Krttikk,  or  was  20°  40'  west  of  the  point  fixed . 
upon  as  the  commencement  of  the  sidereal  sphere  for  all  time  (stije 
above,  under  i.  27),  on  which  account  it  was  desi  'able  to  make  the  arc 
of  libration  include  the  beginning  of  Krttik&. 

Besides  these,  considerations,  drawn  from  the  general  history  of  the 
Hiriflii  astronomy,  and  the  position  of  the  element  of  the  precession  (a 
the  system  of  the  Sflrya-Siddh&nta,  we  have  still  to  nrge  tge  blind  art 
^incoherent,  as  well  as  unusual,  form  of  statement  of  the  phenomenon, 
as  ftilly  exposed  above.  There  is  nothing  to  compare  With  it  in  this 
Respect  in  adjyother  ggrf  of  the  treatise,  and  we  are  unwilling  to  believe 


M Shya-SuW&nta,  [Hi.  «- 

tb*t  in  the  original  composition  of  tho  Siddh&nta  a clearer  explanation! 
and  one  more  consistent  in  its  method  and  language  with  those  of  tho 
treatise  generally,  would  not  have  been  found  for  the  subject.  We  even 
discover  evidences  of  more  than  one  revision  of  the  passage.  The  first 
half  of  verse  9 so  distinctly  teaches,  if  read  independently  of  what  follows 
it,  a complete  revolution  of  the  equinoxes,  that,  especially  when  taken  in 
connection  with  Bh&skara's  statement,  as  cited  above,  it  almost  amounts 
to  proof  that  the  theory  put  forth  in  the  S&rya-Siddh&ntA  was  at  one 
time  that  of  a complete  revolution.  The  same  conclusion  is  not  a little 
strengthened,  farther,  by  the  impossibility  of  deducing  from  verse  0, 
through  the  processes  prescribed  in  the  following  verses,  a true  expres- 
sion for  the  direction  of  the  movement  at  present : we  can  see  no  reason 
why,  if  the  whole  passage  came  from  the  same  hand,  at  the  same  time, 
this  difficulty  should  not  have  been  avoided ; while  it  is  readily  explain- 
able upon  the  supposition  that  the  libratory  theory  of  verse  10  was 
added  as  an  amendment  to  the  theory  of  verse  9.  while  at  the  same 
time  the  language  of  the' latter  was  left  as  nearly  unaltered  as  possible. 

There  seems,  accordingly,  sufficient  ground  for  suspecting  that  in  the 
Sfirya-Siddh&nta,  as  originally  constituted,  no  account  was  taken  of  the 
precession;  that  its  recognition  is  a later  interpolation,  and  was  made 
at  first  in  the  form  of  a theory  of  complete  revolution,  being  afterward 
pdtered  to  its  present  shape.  Whether  the  statement  of  Kluiskara  truly 
represents  the  earlier  theory,  :is  displayed  in  the  Surva-Siddh&uta  of  his 
time,  wa  must  leave  an  undetermined  question.  The  very  slow  rate 
:«tsignea  by  it  to  the  movement  of  the  equinox — onlv It"  a year — throws 
a doubt  upon  the  matter : hut.  it  must  be  borne  in  mind  that,  so  fur  as 
we  can  see,  the  actual  amount  of  the  prcccssWii  sin’r  about.  A.  I>.  o70 
(sea; above,  undir  i.  27)  might  by  that  first  theory  have  been  distributed 
over  the  whole  duration  of  the  present  Ago,  since  H.  <\  3102. 

In  his  own  astronomy.  Bluisknia  teaches  the  complete  revolution 
of  the  equinoxes,  giving  the  number  of  revolutions  in  an  iEon  (of 
4,320,000,000  years)  as  100,009 ; this  makes  the  time  of  a single  revo- 
lution to  be  21, 03o.8073  years,  and  the  yearly  rare  of  precession 
. $9'#.9007.  It  is  not  to  bo  supposed  that  lie  considered  himself  to  have 
determined  the  rate  with  such  exactness  as  would  give  precisely  the  odd 
number  of  199,009  revolutions  to  the.  -.Eon ; the  number  doubtless 
Stands  in  6omc  relation  which  we  do  not  at  present  comprehend  to  the 
other  elements  of  his  astronomical  system.  Bh&skara’s  own  coinmenta- 
tdte,  however,  reject  his  theory,  and  hold  to  that  of  a lihration,  which 
has  been  ami  is  altogether  the.  prevailing  doctrine  throughout  India,  and 
aecma  to  have  made,  its  way  thence  into  the  Arabian,  and  even  into  tho 
early  European  astronomy  (see  Colebrookc,  as  above). 

Bentley,  it  may  be  remarked  here,  altogether  denies  (Hind.  Ast.,  p. 
130,  etc.)  that  the  libration  of  the  equinoxes  is  taught  in  the  Siirva- 
Siddh&nta,  maintaining,  with  arrogant  and  unbecoming  depreciation  of 
those  who  venture  to  hold  a different*  opinion,  that  its  theory  is  tlVnt  of 
a'continimqs  revolution  in  an  epicycle,  of  which  the  circumference  is 
equal  to  108°  of  the  zodiac.  In  truth,  however,  Bentley’s  own  theory^ 
derive*  no  color  of  support  from  the  text  of  the  Siddh&nta,  and  is  besides 
in  itself  utterly  untenable.  U is  not  a little  strange  that  he  should  notj. 


lit  13,]  -''ESI  Trvtndation  andlfbtet 

" . i • 

Mw*  perceived  that,  if  the  {recession  were  to  be  explained  bjra 
tiin  in  an  epicycle,  its  rate  of  increase  would  not  be  equable,  but  aa  the 
increment  of  the  sine  of  the  arc  in  the  epicycle  traversed  by  the  mover' 
ble  point,  farther  varied  by  the  varying  distance  at  which  it  would  be  ' 
seen  from  the  centre  in  different  parts  of  the  revolution ; and  also  that, 
tiie  dimensions  of  the  epicycle  being  108°,  tlio  amount  of  precession  ; 
would  never  conic  to  equal  27°,  but  would,  when  greatest,  fall  ahovb.of 
18°,  being  determined  by  tbc  radius  of  tlie  epicycle.  Bentley’s  .whole  . 
treatment  of  the  passage  shows  a thorough  misapprehension  of  ita-iaMit-  _ 
ing  and  relations:  lie  even  commits  the  blunder  of  understanding. the  ■■ 
first  half  of  verse  0 to  refer  to  the  motion  of  the  equinox,  instead  of  to 
that  of  the  initial  point  of  the  sidereal  sphere. 

Among  the  Greek  astronomers,  Hipparchus  is  regarded' as  the  first 
who  discovered  the  precession  of  the  equinoxes;  their  rate  of  motion, 
however,  seems  not  to  have  been  confidently  determined  by  him,  . 
although  lie  pronounces  it  to  be  at  any  rate  riot  less  than  36"  yearly. 
For  a thorough  discussion  of  the  subject  of  the  precession  in  Greek 
astronomy  sen  JJclainbro’s  History  of  Ancient  Astronomy,  ii.  247,  etc.  . 
Front  the  observations  reported  as  the  data  whence  Hipparchus  made  .3 
his  discovery,  1 Jclambre  deduces  very  nearly  the  true  rate  of  the  preees-  * 
sion.  Ptolemy,  however,  was  so  unfortunate  as  to  adopt  for  tixQ^iruo 
rate  Hipparchus’s  minimum,  of  30"  a year : the  subject  is  treated* 
him  in  the  seventh  book  of  tlic  Syntax  is.  The  actual  mot  km;  of  tSe. 
equinox  at  the  present -time  is  50 ".25  ; its  rate  is  slowly  on  the  increase, 
having  been,  at  the  epoch  of  the  Greek  astronomy,  somewhat  less  tlmji 
50".  How  the  Hindus  succeeded  in  arriving  at  a determination  of  it  so 
much  more  accurate  than  was  made  by  the  great  Greek  astronomer,  or 
whether  it  was  anything  more  than  a lucky  hit  on  tlieir  part,  we>will 
not  attempt  here  to  discuss. 

The  term  by  which  the  precession  is  designated  in  this  passage  is 
ayavdnfa,  “ degrees  of  the  ayana ."  The  latter  word  is  employed;  in*' 
different  senses:  by  derivation,  it  moans  simply  “going,  prognss^Uind  * 
it  seems  to  have  been  first  introduced  into  the  astronomical  language  to  - 
designate,  the  half-revolutions  of  the  sun,  from  solstice  to  solstice;  theftfe  " 
being  called  respectively  (sec  xiv.  0)  the  uttar&yam  and  daknlunayana^ 
“northern  progress”  and  “southern  progress."  From  this  uae  thewordk; 
was  transferred  to  denote  also  tin1  solstic.es  themselves,  as  we  have  tra ay 
latod  it  in  the  first  half  of  verse  11.  In  the  latter  sense  we  conceive 
it  to  bo  employed  in  the  compound  ayananga  ; although  why  the  nfime 
of  the  precession  should  be  derived  from  the  solstice  we  are  unable 
dearly  to  sec.  The  term  kranlipatayati,  “movement  of  the  node  of 
declination,”  which  is  often  met  with  in  modern  works  on  Hindu  astron- 
omy, does  not  occur  in  the  S&rya-Siddh&nta. 

12. . . . In  like  manner,  the  equatorial  shadow'  which  is  cost 
aVtoid-day  at  one’s  place  of  observation  s ^ 

IS.  Upon  the  north  and  south  line  of  the  dial — thatjp  die 
h equinoctial  shadow  (vishuvatprabhti)  of  that  place. . 

The  equinoctial  shallow  lias  been  already  snfiicieutiv  explained,  in 
; connection  with  a preceding  passage  (above,  v.  7).  In  this  treatise?  it  is 
’*  14 


■ jftjfe,.  S&rya-Siddhdnta,  j pii.13- 

1 „ ’ r 

Known  only  by  names  formed  by  combining  ono  of  ilio  words  for 
shadow  (ch&y&%  hhtt , prabhd),  with  vishuvat , M equinox”  (see  above, 
under  v.  6).  In  modern  Hindu  astronomy  it  is  also  called  akshabhd , 
“shadow  of  latitude” — i.  o.,  which  determines  the  latitude — and  paflff- 
fthft,  of  which,  as  used  in  this  sense,  the  meaning  is  obscure. 

13. .  . . Radius,  multiplied  respectively  by  gnomon  and  shadow, 
and  divided  by  the  equinoctial  hypothesise, 

14.  Gives  the  sines  of  co-latitude  (lambn)  and  of  latitude 
(alssha):  the  corresponding  arcs  arc  co-latitude  and  latitude, 
always  south. . . . 

The  proportions  upon  which  these  rules  are  founded  are  illustrated 
by  the  following  figure  (Pig.  1 1),  in  which,  ns  in  a previous  figure  (Fig. 

8,  p.  88),  Z S represents  a quadrant  of  the  meridian,  Z being  die  zenith 
and  8 the  south  point, 

C being  the  centre, 
and  EG  the  projec- 
tion of  the  plane  of 
the  equator.  In  order 
to  illustrate  the  eor- 
reppatuKog  relations 
ot  we  have 

conceived  the  gno- 
mon, 0 ft,  to  be  placed 
at  the  centre.  Then, 
when  the  sun  is  on 
the  meridian  and  in 
the  equator,  at  E,  the 
shadow  cast,  which  is 
the  equinoctial  sloid- 

■ owfejiiftr,  while.  <lc  i?»  the  corresponding  liypothemisc.  But,  by  simi- 
larity Of  triangles, 

Cr:6c::CE:  UK 
and  Cc:(J6::<:K:CK 

and  asBEistlic  sine  of  HZ,  which  equals  the  latitude,  and  CBthe 
vftinc  of  ES,  itn  complement,  the  reduction  ot  these  proportions  to  the 
form  of  equations  giws  the  rules  of  the  text. 

14. .  . . The  mid  day  shadow  i»  the  base  (hhuja) ; if  radius  be 
multiplied  by  that, 

15.  And  the  product  divided  by  the  corresponding  hypothc- 
nuse,  the  result,  converted  to  arc,  is  the  sun’s  zenith-distance 
(nato),  in  minutes:  this,  when  the  base  is  south,  is  north,  and 
when  the  base  is  north,  is  south.  Of  the  sun’s  zenith-distance 
and  his  declination,  in  minutes, 

16*.  Take  the  sum,  when  their  direction  is  different — the  dif- 
ference, when  it  is  the  same;  the  result  is  tho  latitude, 
minute*  From  this  find  the  sine  of  latitude;  subtract  its™' 
square  from  the  square  of  radius,  and  the  square-root  of  the  re- 
mainder 


Fiff.  11. 


Translation  and  Notes. 


iii.  SO.] 


17.  Is  the  sine  of  co-latitude. . . . 


This  passage  applies  to  cases  in  which  the  sun  is  not  upon  the  equator, 
but  has  a certain  dccliuation,  of  which  the  amount  and  direction  aro 
known.  Then,  from  the  shadow  cost  at  noon,  may  be  derived  his  zenith- 
distance  when  upon  the  meridian,  and  the  latitude.  Thus,  supposing 
the  sun,  having  north  declination  E D (Fig.  11),  to  be  upon  the  meridian, 
at  D:  the  shallow  of  the  gnomon  will  be  b e/,  and  the  proportion 
CtI:rf6::CI):  D1V"' 

gives  Dli"",  the  sine  of  the  sun’s  zenith-distance,  ZD,  which  is  found 
from  it  by  the  conversion  of  sine  into  are  by  a rule  previously  given 
(ii.  3.3).  Z D in  this  ease  being  south,  and  E D being  north,  their  sum, 
EZ,  is  the  latitude:  if,  the  declination  being  south,  the  sun  were  at  TV, 
the  difference  of  E !)'  and  Z IV  would  be  EZ,  the  latitude.  The  figure 
floes  not  give  an  illustration  of  north  zenith-distance,  being  drawn  for 
the  latitude  of  Washington,  where  that  is  impossible.  The  latitude 
being  thus  ascertained,  it  is  easy  to  find  its  sine  and  cosine:  the  only 
tiling  which  deserves  to  be  noted  in  the  process  is  that,  to  find  the  co- 
sine from  the.  sine,  resort  is  had  to  the  laborious  method  of  square*, 
instead  of  taking  from  the  table  the  sine  of  the  complementary  arc,  fir 
the  kotijyA. 

The  sun’s  distance  from  the  zenith  when  he  is  upon  the  meridian  is 
called  natas , “deflected,”  an  adjective  belonging  to  tin-  noun  liptfo,  “min- 
utes,” or  bh&giLs,  anras^  u degrees”  The  same  term  is  also  employed,  as 
will  be  seen  farther  on  (vv.  34-30),  to  designate  the  lmur-angle.  For 
zenith-distance  off  the  meridian  another  term  is  lined  (see  below,  v.  33). 

17. . . . The  sine  of  latitude,  multi  plied  by  twelve,  an<l  divi- 
ded by  the  sine  of  co-latitude,  gives  the  equinoctial  shadow. . . . 

That  is  (Fig.  II), 

l\C:\\K::Cb:he  - 

the  value,  of  the  gnomon  in  digits  being  .substituted  in  the  fuloltaf  the 
gnomon  itself. 


17. . . . The  dilUnvncc  «>f  the  latitude  of  the  place  of  observa- 
tion and  the  sun’s  meridian  zenith-distance  in  degrees  (nuta-, 
bhfhjdd ),  if  their  direction  he  the  same,  nr  their  sum, 
ltf.  If  their  direction  be  different,  is  the  sun’s  declination:  if 
the  sine  of  this  latter  be  multiplied  by  radius  and  divided  by  the 
sine  of  greatest  declination,  the  result,  converted  to  arc,  will  be 
the  sun’s  longitude,  if  he  is  in  the  quadrant  commencing  with 
Aries ; 

19.  If  in  that  commencing  with  Cancer,  s ’btract  from  a half- 
circle; if  in  that  commencing  with  Libra,  add  a half-circle;  if  in 
that  commencing  with  Capricorn,  subtract  from  a circle:  the  re- 
sult, in  each  ease,  is  the  true  (sphutt i)  longitude  of  the  sun  at 
juiid-day.  # 

" 20.  To  this  if  4hc  equation  of  the  apsis  (mdnda  phala)  be. 
repeatedly  applied;  with  a contrary  sign,  the  sun’s  mean  longi- 
tude will  be  found. . . . 


Mrya-Suldhdnta,  [iii.20- 

■ ' passage  teaches  how,  when  the  latitude  of  the  observer  is 
known,  tiic  sun’s  declination,  and  his  true  and  mean  longitudes,  may  be- 
found  by  observing  his  zenith-distance  at  noon.  The  several  parts  of' 
the  process  are.  all  of  them  the  converse  of  processes  previously  given, 

• and  require  no  explanation.  To  find  the  sun’s  declination  from  his 
meridian  zenith-distance  and  the  latitude  (reckoned  as  south,  by  v.  14), 
the  rule  given  above,  in  versos  15  and  16,  is  inverted ; the  true  longitude 
is  found  from  the  declination  by  the  inversion  of  the  method  taught  in 
ii.  28,  account  being  taken  of  the  quadrant  in  which  the  sun  may  be 
according  to  the  principle  of  ii.  30:  and  finally,  the  mean  may  be  do- 
rived  from  the  true  longitude  by  a method  of  successive  approximation, 
applying  in  reverse  the  equation  of  the  centre,  as  calculated  by  ii.  80. 

It  is  hardly  necessary  to  remark  that  this  is  a very  rough  process  for 
ascertaining  the  sun’s  longitude,  and  could  give,  especially  in  the  liands 
of  Hindu  olmcrvers,  results  only  distantly  approaching  to  accuracy. 

20.  . . . The  sum  of  the  latitude  of  the  place  of  observation 
and  the  sun’s  declination,  if  their  direction  is  the  same,  or,  in  tho 
contrary  case,  their  difference, 

21.  Is  the  sun’s  meridian  zenith-distance  (nntduals) ; of  that 
find  the  base-sine  (Uihv/yd)  and  the  perpendicular-sine  (Icotijyd). 
If,  then,  the  base-sine  and  radius  be  multiplied  respectively  by 
the  measure  of  the  gnomon  in  digits, 

22.  And  divided  by  the  perpciulicular-sine,  the  results  arc  the 
shadow  and  hypothemiso  at  mid-day. . . . 

The  problem  lien;  is  In  determine,  the  longlli  of  the  shadow  which 
will  be  cast  at  mid-day  when  the  sun  has  a given  declination,  the  latitude 
of  the  observer  being  also  known.  First,  the  sun’s  meridian  zenith-dis- 
tance is  found,  by  a process  the  converse  of  that  taught  in  \erses  15  ami 
16;  then,  the  corresponding  sine  and  cosine  having  been  calculated,  a 
Butiplb  proportion  gives  the;  desired  result.  Thus,  let  us  suppose  the  sun 
to  be  at  IV  ( Fig.  1 1 . p.  106);  the  sum  of  his  south  declination,  K.IV, 
and  the  north  latitude,  KZ,  gives  the  zenith-distance,  ZJ)#:  its  sine 
\hkujajyd)  is  IFIF",  and  its  cosine  (ko/ijytt)  is  ClF".  Then 

and 

which  proportions,  reduced  to  equations,  give  the  value  of  bd',  the 
shadow,  and  C </',  its  hypothcmisc. 

22. . . . The  nine  of  declination,  multiplied  by  the  equinoctial 
hypothenusc,  and  divided  by  the  gnomon-sine  (cankujiv fi), 

23.  Gives,  when  farther  multiplied  by  the  hypothenuse  of  any 
given  shadow,  and  divided  by  nidius  (madhyakama),  the  sun’s 
measure  of  amplitude  (arlcdgrd)  corresponding  to  that  shadow. . . 

. Iif  this  passage  wo  arc  taught,  the  declination  being  known,  how  to 
find  the  measure  of  amplitude  (ayrd)  of  any  given  shadow,  as  prepara- 
tory to  determining,  by  the  next  following  rule,  the  base  W*§m  of  thdfi 
shadow,  by  calculation  instead  of  measurement.  The  first 
the  line  of  the  sun’s  amplitude ; iu  order  to  tins,  wo  comparolfto  triaa- 


HI  4&]  Translation  and  Nbte$. 


glos  ABC  and  CE1I  (Fig.  13,  p.  110),  which  are  similar,  since  the. 

angles  ACB  and  C Eli  arc  each  equal  to  the  latitude  of  the  observer. 

Hence  EU:EC::BC:AC 

But  the  triangles  CKI1  (Fig.  13)  and  C be  (Fig.  11)  arc  also  similar; 

and  EJr:EC::C6:C0 

Hence,  by  equality  of  ratios,  06:  Ce: : B C : A C 

and  AC,  the  sine  of  the  sun’s  amplitude,  equals  13  C — which  is  the  sine 

of  declination,  being  equal  to  UF — multiplied  by  Cf,  the  equinoctial 

liypothcuuso,  and  divided  by  0 6,  the  gnomon.  The  remaining  part  of 

the  process  depends  upon  the  principle  which  we  have  demonstrated 

above,  under  verse  7,  that  the  measure  of  amplitude  is  to  the  hypothe- 

nusc  of  the.  shadow  as  the  sine  of  amplitude  to  radius. 

Why  the  gnomon  is  in  this  passage  called  the  “gnomon-sine,”  it  is 
not  easy  to  discover.  Verse  23  presents  also  a name  tor  radius,  madhya - 
kaina , “ half-diameter,”  which  is  not  found  again;  nor  is  karna  oflU.il 
employed  in  the  sense  of  “diameter”  in  this  treatise. 

23.  . . . The  sum  of  the  equinoctial  shadow  and  the  sun’s 
measure  of  amplitude  (arkagrti),  when  the  sun  is  in  the  southern 
hemisphere,  is  the  base,  north ; 

24.  When  the  sun  is  in  the  northern  hemisphere,  the  base  is 
found,  if  north,  by  subtracting  the  measure  of  amplitude  from 
the  equinoctial  shadow ; ifLsuulli.  by  a contrary  process — accord- 
ing to  the  direction  ofVio  interval  between  the  end  of  tho 
shadow  and  the  oast  and  west  axis. 

25.  The  mid-day  base  is  invariably  the  midday  shadow. . . . 

\VTc  have  already  had  invasion  tu  notice,  in  connection  with  the  first 
verses  of  this  chapter,  that  the  hast*  (hbujn)  «»f  the.  shadow'  is  its  projec- 
tion upon  a north  and  south  lino,  or  the  distance  of  its  extremity  from 
the  east  and  west  axis  of  the  dial.  It  is  that  lino  which,  as  shown 
above  (under  v.  7),  corresponds  to  and  represents  the  perpendicular  let 
fall  from  the  atm  upon  the  plane  of  the  prime  vertical.  Thus,  if  (Fig. 
11,  p.  100)  K,  L,  IV,  I.)  be  different  positions  of  the  sun — K and  L 
being  conceived  to  be  upon  the  surface,  of  the  sphere — the  perpendicu- 
lars KIV,  L IV',  IV  IV",  1)13""  arc  represented  upon  the  dial  by  X:6,  /&, 
d#6,  db,  or,  in  Fig.  9 (p.  241),  by  kb1,  lh'\  d*  6,  d b.  Of  these,  the  two 
latter  coincide  with  their  respective  shadows,  the  shadow  cast  at  noon 
being  always  itself  upon  n north  and  south  line.  The  base  of  any 
shadow  may  be  found  by  combining  its  measure  of  amplitude  (agrA) 
with  the  equinoctial  shallow.  When  the  sun  is  in  the  southern  hcinia- 

Ehere,  as  at  1)'  or  Iv  (Fig.  1 L),  the  measure  of  amplitude,  ed1  or  eft,  is  to 
e added  always  to  the  cquinoetial  shadow,  6*,  in  order  tn  give  the  base, 
bd ' or  bk.  on  the  contrary,  the  sun’s  dcclinu.  *on  be  north,  a differ- 

ent method  of  procedure  will  be  necessary,  according  as  lie  is  north  or 
south  from  the  prime  vertical.  If  he  be  south,  as  at  D,  the  shadow,  bd, 
will  be  thrown  northward,  and  the  base  will  be  found  by  subtracting  tho 
measure  of  amplitude,  d e,  from  the  equinoctial  shadow,  6% : if  he  be 
Snqrth,  aa  at  L,  tho  extremity  of  the  shadow,  I,  will  be  south  from  the 
east  and.  West  axis,  and  the  base,  6/,  will  be  obtained  by  subtracting  tho 
equinoctial  shadow,  dr,  from  tho  measure  of  amplitude,  le. 


8&rya-8iddliu7ita,  [iu.25- 

25. . . . Multiply  the  sines  of  co-latitude  and  of  latitude  re- 
spectively by  tlic  equinoctial  shadow  and  by  twelve, 

26.  And  divide  by  the  sine  of  declination ; tho  results  are  the 
hypothenusc  when  the  sun  is  on  the  prime  vertical  (samaman- 
Add).  When  north  declination  is  less  than  the  latitude,  then 
the  mid-day  hypothenusc  (?rtwa), 

27.  Multiplied  by  the  equinoctial  shadow,  and  divided  by  the 
mid-day  measure  oif  amplitude  (agrd\  is  the  hypothenuse. . . . 

Here  we  have  two  separate  and  independent  methods  of  finding  the 
hypothenusc  of  the  east  and  went  shadow  cast  by  the  sun  at  the  moment 
when  lie  is  upon  the  prime  vertical.  In  connection  with  the  second  of 
the  two  are  stated  the  circumstance!*  under  which  alone  a transit  of  the 
sun  across  the  prime  vertical  will  take  place : if  his  declination  is  south, 
or  itj  being  nortli,  it  is  greater  than  the.  latitude,  his  diurnal  revolution 
will  be  wholly  to  the  south,  or  wholly  to  the  north,  of  that  circle. 

Thu  first  method  is  illustrate*  1 hv  the  tV»  owing  figures.  Let  V C' 
(Fig.  12)  be  iui  arc  of  the  prime  ver- 
tical, V being  the  point  at  which  the 
sun  crosses  it  in  liis  daily  revolution ; 
and  let  C'  be  the  centre ; then  V i'S 
is  radius,  and  YV  the  sine  of  the 
sun’s  altitude;  and,  Cb  being  the 
gnomon,  6 v will  Ik*  the  shadow,  and 
C'  v its  Iivpothenufic.  But,  by  ninii- 
laritv  of  triangles, 

V(  : ChU'/v 

Again,  in  tlm  other  figure  (Fig.  13) — of  which  the  general  relations 
arc  those  of  Fig.  8 ...  , „ 

(p.  88) — A I)  being  **’ J* 

the  projection  of  the 
circlo  of  llit:  sun's 
diurnal  revolution, 
and  the  {mint  at 
which  it  crosses  the 
prime  vertical  being 
seen  projected  in  1', 

V C is  the  sine  of  the 
sun’s  nltjtnde  at.  that 
point.  But  VCII 
and  ECU  nrc  simi- 
lar triangles,  the  an- 
gles B V ( 1 and  C EU 
being  each  equal  to 
the  latitude;  hence 
VC:EC::IJr:riI 

JS'ow  thq  first  of 
tli£HC  ratios  is — since 
E jpcqual*  V C',  both 
befbig  radius — the 
same  with  the  first 


Fig.  IB. 


: uTi  Sl<]  TranslaStm  and  Notes.  lit 

in  die  former  proportion ; and  therefore 

HC:Clt::C‘b:Qv 

or  sin  decl. : sin  lat. : : gnom. : liyp.  pr.  vert.  uliad. 

hilt.  sin  lat. : cos.  lat. : : cq.  shad. : gnom. 

therefore,  by  combining  terms, 

ain.  decl. : cos.  lat. : : cq.  shad. : hyp.  pr.  vert.  shad, 
and  die  reduction  of  the  first  and  third  of  these  proportion! ■ to  the 
form  of  equations  gives  the  rules  of  the  text. 

The  other  method  of  finding  the  same  quantity  is  an  application  of 
the  principle  demonstrated  above,  under  verse  7,  that,  with  a given  dec- 
lination, the  measure  of  amplitude  of  any  shadow  is  to  that  of  any  other 
shadow  as  the  hypotlieimsc  of  the  former  to  that  of  the  latter.  Now 
when  the  sun  is  upon  the  prime  vertical,  the  shadow  falls  directly 
eastward  or  directly  westward,  and  hence  its  extremity  lies  in  the  east 
and  west  axis  of  the  dial,  ami  its  measure  of  amplitude  is  equal  to' 
tiic  equinoctial  shadow.  The  noon  measure  of  amplitude  is,  accord- 
ingly, to  the.  hypotheniise  of  the  noon  shadow  ns  the  equinoctial  shadow 
to  the  hypotlieimsc  of  tin1  shadow  east  when  the  sun  is  upon  the  prime 
vertical. 

27. ...  If  the  sine  of  declination  of  a given  time  be  multiplied 
by  radius  and  divided  by  the  sine  of  co-latitude,  the  result  is  the 
sine  of  amplitude  (agranvl unil.a ). 

28.  And  this,  being  farther  multiplied  by  the  hypothenuse  of 
a given  shadow  at  that  time,  and  divided’ by  radius,  gives  the 
measure  of  amplitude  (uyrd),  in  digits  (< lingula ),  etc. . . . 

The  sine  of  the  sun's  amplitude  is  found — his  declination  and  the 
latitude  being  known — by  a compare  »n  of  the  similar  triangles  ABC 
and  CE1I  (Fig.  in),  in  which 

1I.E:  EC::BC:CA 

or  cos.  lat. : U : : sin.  decl. : sin.  nmpl. 

And  the  proportion  upon  which  is  founded  the  rule  in  verse  28 — name- 
ly, that  radius  is  to  the  sine  of  amplitude  as  the  hypothenuse  of  a given 
shadow  to  the  corresponding  measure  of  amplitude — lias  been  demon- 
strated under  verse  7,  above. 


28 If  from  half  the  square  of  radius  the  square  of  the 

sine  of  amplitude  {agrajyd)  be  subtracted,  and  tbe  remainder 
multiplied  by  twelve, 

20.  And  again  multiplied  by  twelve,  and  then  farther  divided 
by/tke  square  of  the  equinoctial  shadow  increased  by  half  the 
square  of  the  gnomon — the  result  obtained  by  tbe  wise 

SO,  Lt  celled  the  “surd”  (faro?!) : this  let  the  wise  man  set 
doWnintfrQ  places.  Then  multiply  the  equinoctial  shadow  by 
twelvfe,  and  again  by  the  sine  of  amplitude 

§And.divide  as  before:  the  result  it  styled  the  “fruit” 
i ' Add  its«uare -ta  the  square  root 

tr tocrts^  by  die  “fruit,”  for 
ithemand  - - 


^PlL^Is'ihe  mne  of  a]tititi!^.(9an&ii).of  the  southern  intemedkte 
, ^dmetioas  (virftf) ; and  equally,  whether  the  sun’s  revoluiwjp 
Mllkd  place  to  the  south  or  to  the  aorth  of  the  gnomon  foanftu)*- 
only,  in  the  latter  case,  the  sine  of  altitude  is  that  of  the  north* 
em  intermediate  directions. 

33.  The  square  root  of  the  difference  of  the  squares  of  that 
' and  of  radius  is  styled  the  sine  of  zenith-distance  (off.)  If)  then, 

the  sine  of  zenith-distance  and  radius  be  multiplied'  respectively 
by  twelve,  and  divided  by  the  sine  of  altitude,  . - 

34.  The  results  are  the  shadow  and  hypothenuse  at  the  anjglea, 
{bona),  under  the  given  circumstances  of  time  and  place. ...  ■ 


The  method  taught  in  this  passage  of  finding,  with  a given  declina- 
tion and  latitude,  the  sine  of  the  sun’s  altitude  at  the  moment  when  he 
crosses  tlic  south-east  and  south-west  vertical  circles,  or  when  the  shadow 
of  the  gnomon  is  thrown  toward  the  angles  (lum)  of  the  circumscribing 
square  of  the  dial,  is,  when  stated  algebraically,  as  follows: 
(iR»-1ia»ampI)Xgn.»=gurti; 

ign.a4-eq.  »li.* 
eq.  ih.  X gn.  X Bin  nmpl.  _ 

ten.»+eq.s1  ..*"  “lrUlL 

\/ surd  + fruit*  -f-  fruit  = sin  nit.,  declination  being  north. 

V^Bunl+  fruit*  — fruit  =sin  nit.,  declination  Ix/iiig  hiuIIi. 


i It  is  at  once  apparent  that  a problem  is  here  presented  more  compli- 
cated and  difficult  of  solution  than  any  with  which  we  have  heretofore 
had  to  do  in  the  treatise.  The  commentary  gives  a demonstration  of 
it,  in  which,  for  the  first  time,  the  notation  ami  processes  of  the 
Hindu  algebra  are  introduced,  and  witli  these  wc  arc  not  sufficiently 
familiar  to  be  able  to  follow  the  course  of  the  demonstration.  The 

Emblem,  however,  admits  of  solution  without  the  aid  of  mathematical 
owlcdge  of  a higher  character  than  has  been  displayed  in  the  pro- 
cesses already  explained ; by  means,  namely,  of  the  consideration  of 
right-angled  triangles,  situated  in  the  same  plane,  and  capable  of  being 
represented  by  a single  figure.  Wc  give  heJow  such  a solution,  which, 
-■  we  ere  persuaded,  agrees  in  all  its  F*rf  14 

main  features  with  the  process  by  °* 

which  the  formulas  of  the  text  were 

stern 

5th,  z, 

|ts  in- 
)nd  D 
ltd  let 

-;C$i,represent  the  gnomon, 
s*'  fSibce  e is in  the  line  of  the  equi- 
noctial shadow  (see  above,  v.  7), 

' MbA  mnce  be  makes  an  angle  of  46° 

4|th4r  axis  of  the  dial;  we 

iEVtaid 

^'$b*+b&^$to*+2  oq.sh.9 


118 


iii,  &] 


TVanelaiion  and  Notes* 


In  like  manner,  =2  mass,  ampl.*  But  the  iimilar  triangles 
Ode  and  CDE'  give  Cda:iea::CI)2:DE'a;  which,  by  halving 
the  two  consequents,  and  observing  the  constant  relation  of  Cd  to  the 
measure  of  amplitude  (see  above,  under  v.  7),  gives  R*  : sin  ampl.2  : : 
R2  : E'2  : whence  JD  E'2=  sin  ampL2,  or  D E'2=  2 sin  ampl.2 

Now  the  required  sine  of  altitude  is  I)  G,  and  D G=D  H4-II  G= 
DH+IJ.  And,  obviously,  the  triangles  Dill,  D IEX,  EFC,  IJ  C, 
and  C b e arc  all  similar.  Then,  from  Dll  T and  0 b e,  we  derive 
DH:DI::i«:Ce 
from  DIE'  and  Cde,  DI : DE' : : Cb  : Ce 
and,  by  combining  terms,  D H : D E1 : : b r XC  b : C e2 

whence  D U = — fnut, 
gn.*  + 2 eq.  eh*  4jfu.a  -|-  eq.  th.* 

Again,  from  D H 1 and  E F C,  we  derive 

111* : 1) I*  : : E F*  : E C* 
from  I JC  and  EFC,  I J*  : 1C*  : : EF»  : EC* 
whence,  by  adding  tlie  terms  of  the  equul  ratios,  and  observing  that 
1II*+IJ*=JII*,  and  Di»+IC»=DC*=EC*,  we  have 
J 11*  : EC* : : E F* : EC* 

or  J H*=EF».  Hence  IJJ=J  H»-I  H*=EF*-IH*=EF*-i)I*+DH* 
But  from  E F C and  C be  ai'e  derived 


from' DTE'  and  V be, 


Ce*  : C4*  : : EC2  : EF* 
C e*  : C 6*  : : 1>  E'*  : D I* 


whence  EF*=^,»d  and  EF*-DI*=^^f 


C e4 


Ce* 


that  is  to  say, 

F i«  rn*_(R,--iin  «"pl  9)X  gn.*  _ (*R»  - sin  ampl.*)  Xgu*  _ 

" ‘ gn.»+2eq.ah.*  ' ~~  *gu*+  eq.  sh.*  ✓ 

But,  as  was  shown  above,  I J2=E  F2  — D Ia+D  H2=surd+frnit2 
and  */surd + fruit2  + fruit=  1 J + D 1I=D  G = sine  of  altitude. 


When  declination  is  south,  so  that  the  sun  crosses  the  circle  of  alti- 
tude at  1>,  1 II1,  the  equivalent  of  D 11,  is  to  be  subtracted  from  I J,  to 
give  D'  ti#,  the  sine  of  altitude. 

The  correctness  of  the  Hindu  formulas  may  likewise  be  briefly  and 
succinctly  demonstrated  by  means  of  our  modern  methods.  Thus,  let 
PZS  (Fig,  15)  be  a spherical  triangle,  Fig.  15. 

pf . which  the  three  angular  points  arc 
P,  the  pole,  Z,  the  senith,  and  S,  the 
{face  of  the  sun  when  upon  the  south- 
east or  the  south-west  vertical  circles; 

JJZ,  then,  is  the  co-latitude,  ZB  the 
zenith-distpiice,  or  co-altitude,  P S 
ihd  oordedhiation ; and  thi  angle  PZS  is  135° ; the  problem  is,  to  And 
^Bmi  sine  of  the  complement  of  ZS,  or  of  tho  sun’s  altitude.  By  s^heri- 
c^t^gi^ometry, cos  SPscos  ZS  cos  ZP-f  sin  ZS  sin  ZPnos  Z.  Di- 
IP,  and  observing  that  cos  S P-j-sin  ZP=ain  decL-f-cos 
jitade,  webave  sin  arapL=sin  alt  tan  laL+ooa  altoos 
U,  Ve  repretojst  sin  ampl.  byia,  tan  lat  by  ft,  oos  lSfl0  by 
‘ 13  ...  i 


(DQ  nit  by  z,  Mi(l  coe  alt.  hy  l — **,  W0  bmvfl  «a-9ai*+ia  *?^5 

Wr**):  and,  by  reduction,  xa—  Representing, 

'■  '■  a a jt6  t+o 

again,  ^-j-^-  by  /,  and*  - by  «,  and  reducing,  we  have  *=/+ 

yp+i.  But/  is  evidently  the  same  with  the  “ fruit,"  since  8,  ot  tan 
, . , , . . o 8 eq.sh.Xgn-Xsin.ampl. 

ntad  « is  also  the  same  with  the  “surd,”  for  ttx=~~T~~~~U 

£+6*  |gnoin.*+eq.  sh.' 


If,  the  latitude  being  north,  wc  consider  the  ntorth  direction  na  posi- 
tive! b will  be  positive.  The  value  of  /,  given  above,  will  then  Evidently 
be  positive  or  negative  as  the  sign  of  a is  plus  or  minus.  But  a,  the 
sine  of  amplitude,  is  positive  when  declination  is  north,  and  negative 
when  declination  is  south.  Hence  / is  to  be  added  to  or  subtracted 


from  the  radical,  according  as  the  sun  is  north  or  south  of  the  equator, 
-as  prescribed  by  the  Hindu  rule.  A minus  sign  before  the  radical  would 
fmreSpond  to  a second  passage  of  tlic  sun  across  the  south-east  and 
liorth-west  vertical  circle ; which,  except  in  a high  latitude,  would  take 
place  always  below  the  horizon. 

The  construction  of  the  last  part  of  verse  32  is  by  no  means  clear,  yet 
we  cannot  question  that  the  meaning  intended  to  be  conveyed  bjjflt  is 
truly  represented  by  our  translation.  When  declination  is  greater  than 
north  latitude,  the  sun's  revolution  is  made  wholly  to  the  north  of  the 
prime  vertical,  and  the  vertical  circles  which  he  crosses  are  the  liorth- 
east  and  the  north-west.  The  process  prescribed  in  the  text,  however, 
gives  the  correct  value  for  the  sine  of  altitude  in  this  ease  also.  For, 
in  the  triangle  8 Z V (Fig.  1 5),  all  the  parts  remain  the  same,  excepting 
that  the  angle  PZS  becomes  45°,  instead  of  135°:  but  the  cosine  of 
the  former  is  the  same  as  that  of  the  latter  arc,  with  a difference  only 
'“of  sign,  which  disappears  in  the  process,  the  cosine  being  squared. 

The  sine  of  altitude  being  found,  that  of  its  complement,  or  of  zenith- 
distance,  is  readily  derived  from  it  by  the  method  of  squares  (as  above, 
in  vv.  16,  17).  To  ascertain,  farther,  the  length  of  the  corresponding 
Shadow  and  of  its  bypothenuse,  we  make  the  proportions 
sin  alt. : sin  zen.  dist. : : gnom. : shad, 
and  sin  alt : It : : gnom. : hyp.  shad. 

In  this  passage,  m in  those  that  follow,  the  sine  of  altitude  is  called 
by  the  same  name,  fanku , 44  staff,”  which  is  elsewhere  given  to  the 


gnomon : the  gnomon,  in  fact,  representing  in  all  cases,  if  the  hypothe- 
nuse  be  made  radius,  the  sine  of  the  sun’s  altitude.  The  word  is  fre- 
.^ouentlr  used  in  this  sense  in  the  modern  astronomical  language : thus 
WG  (Fig.  13,  p.  110),  die  sine  of  the  sun’s  altitude  when  upon  the 
jprime  vertical,  is  called  the  samamandalafanku,  “ prime  vertical  staff,” 

* and  BT,  tfye  sine  of  altitude  when  the  sun  crosses  the  unmandala,  or 
east  and  west  hour-circle,  is  styled  the  unmandalafaitku : of  the  lattes 
.liaeyrhbwever,  the  S&rya-Siddn&nta  makes  ;&6  account  We  are  np^ 
*prftbd,  however,  not  to  fipdsB  distinct  haij#for  the  altitude,  as  for  ittf 
complement,  the  zenith-distance : the  sine  of  the  latter  might  with  very 


■v  rv 


iii.$&]  ..  iMmfafy n and  Notes.  '?  li^; 

nearly  the  same  propriety  be  called  the  “ shadow,  ” as  that  ofthe  former 
the  ^ gnomon.*1  The  particular  sine  of  altitude  which  is  the  result  of 
the  present  process  is  commonly  known  as  the  konapanku^  from  the 
word  Aono,  which,  signifying  originally  “ angle,”  is  used,  in  connection 
with  the  dial,  to  indicate  the  angles  of  the  circumscribing  square  (see 
Fig.  9,  p.  97),  and  then  the  directions  in  which  those  angles  lie  from 
the  gnomon.  The  word  itself  is  doubtless  borrowed  from  the  Greek 
ywWa,  the  form  given  to  it  being  that  in  which  it  appears  in  the  com- 
pounds Tf/yoiiw  (Sanskrit  irikona  etc.  Lest  it  seem  strange  that  the 
Hindus  Bbould  have  derived  from  abroad  the  name  for  so  familiar  and 
elementary  a quantity  as  an  angle,  we  would  direct  attention  to  the 
striking  fact  that  in  that  stage  of  their  mathematical  science,  at  least, 
whieh  is  represented  by  the  Stirya-Siddh&nta,  they  appear  to  have  made  - 
no  use  whatever  in  their  calculations  of  the  angle:  for,  excepting  in 
this  passage  (v.  34)  and  in  the  term  for  “square”  employed  in  a pre- 
vious verse  (v.  5)  of  this  chapter,  no  word  meaning  “angle”  is  to  be 
met  with  anywhere  in  the  text  of  this  treatise.  The  term  drp,  used  to 
signify  “zenith-distance” — excepting  when  this  is  measured  upon  the 
meridian;  see  above,  under  vv.  14-16 — means  literally  “sight,  in  this 
sense,  it  occurs  here  for  the  first  time  : we  have  had  it  more  than  once 
above  with  the  signification  of  “observed  place,”  as  distinguished  from 
a position  obtained  by  calculation.  In  verse  32,  fanku  might  be  under- 
stood as  used  in  the  sense  of  “ zenith,”  yet  it  has  there,  in  truth,  its  own 
proper  signification  of  “gnomon the  meaning  being,  that  the  sun,  in 
the  cases  supposed,  makes  his  revolution  to  the  south  or  to  the  north  of 
the  gnomon  itself,  or  in  such  a manner  as  to  cast  the  shadow  of  the 
latter,  at  noon,  northward  or  southward.  One  of  tlie  factors  in  the  cal-  ' 
culatkm  is  styled  karanit  “ surd ” (see  Colobrookes  Hind.  Alg.,  p.  145^. 
rather,  apparently,  as  being  a quantity  of  wliir.li  the  root  is  not  required 
be  taken,  than  one  of  which  an  integral  root  is  always  impossible;  or,  it 
may  be,  as  being  the  square  of  a line  which  is  not,  and  cannot  be,  drawn. 
The  term  translated  “fruit”  ( phala ) is  one  of  very  frequent  occurrence 
elsewhere,  aa  denoting  “ quotient,  result,  corrective  equation,”  etc. 

The  form  of  statement  and  of  injunction  employed  in  veroes  29  and 
90,  in  the  phrases  “the  result  obtained  by  the  wise,”  and  “let  the  wise 
man  set  down,”  etc.,  is  so  little  in  accordance  with  the  style  of  our 
treatise  elsewhere,  while  it  is  also  frequent  and  familiar  in  other  works 
of  a kindred  character,  that  it  fumishes  ground  for  suspicion  that  this 
passage,  relating  to  the  kona fanku,  is  a later  interpolation  into  the  body 
of  the  text;  and  the  suspicion  is  strengthened  by  the  fact  that  the  pro- 
cess prescribed  here  is  so  much  more  complicated  than  those  elsewhere  & 
presented  in  this  chapter.  . 


84. . . . If  radius  be  increased  by  the  sine  cf  ascensional  differ- 
ence (cara)  when  declination  is  north,  or  diminished  by-' thi-s&me, 
when  declination  is  south,  ^ * 

36,  The  result  is  the  day-measure  (< antyd ) ; this,  diminished  - 
by  the  versed  sine  (uikramajyd)  of  the  hop^angle  (bate),  then 
Multiplied  by  the  day?gadius  and  divided  by  radiu^  is  the  11  di- 
Jgrisor”  (chedaji  the  latfin^ain,  being  mpljbplied  by  thg  sine  of 
platitude  (iamba\  and  divided  ■-  'f  : . 


116 


V 

f8®.  By  fadius,  gives  the  (tine  06  altitude  (pan  £u) : sabtrac^ts 
sine  from  that  of  radius,  and  the  Square  root  .of  the  remainder1  is 
the  sine  of  zenith-distance  (Af) : the  shadow  and  its  hypothe- 
nudb  are  found  as  in  the  preceding  process. 

Tbe  object  of  this- process  is,  to  find  the  sine  of  the  sun’s  altitude  at 
any  given  hour  of  the  day,  when  his  distance  from  the  meridian,  his 
declination,  and  the  latitude,  are  known.  The  sun’s  angular  distance 
from  the  meridian,  or  the  hour-angle,  is  found,  as  explained  by  the  com- 
mentary, by  subtracting  the  time  elapsed  since  sunrise,  or  which  is  to 
elapse  before  sunset,  from  tbe  half  day,  as  calculated  by  a rule  previously 
given  (ii.  61-63).  Prom  ’the  declination  and  the  latitude  the  sine  of 
ascensional  difference  (i carajya ) is  supposed  to  have  been  already  derived, 
by  the  method  taught  in  the  same  passage ; as  also,  from  the  declina- 
tigjf  (by  ii.  60),  the  radius  of  the  diurnal  circle.  The  successive,  steps 
of  She  process  of  calculation  will  be  made  clear  by  a reference  to  the 
annexed  figure  (Fig.  16),  taken  in  connection  with  Fig!  13  (p.  110),  witb 
which  it  corresponds  in  dimensions  and  lettering.  Let  GG'CVE  repre- 
sent^ portion  of  the  plane  of  the  equator,  C being  its  centre,  and  GE 
intersection  with  the  plane  of  the  me-  1A 

flqjati ; and  let  A A#  IV 1)  represent  a cor-  s' 

responding  portion  of  the  plane  of  the 
diurnal  circle,  as  seen  projected  upon  the 
other,  its  centre  and  its  line  of  intersection 
upth  the  meridian  coinciding  with  those 
of  the  latter.  Let  C G cciind  the  sine  of 
fcjMKWpsional  difference,  ana  A B its  corrc- 
5 sntohdeut  in  the  lesser  circle,  or  the  carth- 
£jfett jkjj&jyb  or  kshitijyb  ; see  above,  ii.  61). 

Voy  let  O'  be  the  place  of  the  sun  at  a 

S‘yen  time;  the  angle  O' CD,  measured 
r the  arc  of  the  equator  Q'E,  is  the 
$ hour-angle : from  Q'  draw  Q'Q  perpendic- 
ular to  C E ; then  Q'  Q is  the  sine,  and 
QEis  the  versed  sine,  of  Q'  E.  Add  to 
radius,  EC,  the  sine  of  ascensional  difference,  CG;  their  sum,  E O— 
which  is  the  equivalent,  in  terms  of  a great  circle,  of  IF  A,  that  part  of 
thft:4hvieter  of  the  circle  of  diurnal  revolution  which  ».  above  the 
horaon,  and  which  consequently  measures  the  length  of  tha^day^-is 
the  day-measure  (an-tyi).  From  EG  deduct  E Q,  the  versed,v$ne  of  the 


the  day-measure  (antyd).  From  EG  deduct  E Q,  theversed.'fne  of  the 
hour-angle ; the  remainder,  G Q,  is  the  same  quantity  in  terms  of  a great 
’ circle  wnich  A O is  in  terms  of  the  diurnal  circle : hence  the  reduction 
of  G Q to  thus  dimensions  of  the  lesser  circle,  by  the  proportion 
CE.-BD: :GQ: AO  ’ , -g-:*  < 

Sires  vi  the  value  of  AO;  to  this  the  tcit  gives  the  technical  name  of 
divisor”  (ckeda).  But,  by  Fig.  13,  • y'y*  -fab' 

**  CE:EH::AO:OR  ■’ 

hence  OB.  which  ia'the  sine  of  the  sun’s  altitude  i&ihe  given  tims.. 


L Which  is  tfae  sine  of  the  sun’s  altitude  a£tbe  given ’t 
j^tto!  “ divisof”  multiplied  bytfE^tbe  cosh^f  latitude; 


iii.  4|i| 


. undNotu 


zenith- 
and  its 


distance,  and  from  both  the  length  of  the  correspohd»g  shadow  and  its 
hjpqthennse,  are  precisely  the  same  aa  in  the  last  problem. 

For  the  meaning  of  anted— whidi,.  for,  lack  of  a better  term,  we  have 
translated  “ day-measure ”-*kec  above,  under  verse  7.  The  •word  nata, 
by  which  the  hour-angle  is  designated,  is  the  same  with  that  employed 
above  with  the  signification  of  “ meridian  zenith-distance  see  the  note 
to  veiaea  14-17. 


87.  If  radius  be  multiplied  by  a given  shadow,  and  divided 
by-  the  corresponding  liypothenuse,  the  result  is  the  sine,  of 
zenith-distance  ( dre ) : the  square  root  of  the  difference  between 
the  square  of  that  and  the  square  of  radius 

88.  Is  the  sine  of  altitude  (r/tnJcv) ; which,  multiplied*  by 
radius  and  divided  by  the  sine  of  co-latitude  (lamba),  gives  pie  ^ 
4/ divisor"  (cheda) : multiply  the  latter  by  radius,  and  divide Try  K 
the  radius  of  the  diurnal  circle, 

39.  And  the  quotient  is  the  sine  of  the  sun’s  distance  from  thfc 
horizon  (jinrutla) ; this,  tlu-n,  being  subtracted  from  the  day- 
measure  (antyt ?),  and  the  remainder  Mrned  into  arc  by  means 
the  table  of  versed  sines,  the  final  rmPIt  is  the  hour-angle  (note), 
id  respirations  (asu),  east  or  west. 

. The  ptafate  tauglit  in  these  verses  is  precisely  the  converse  of  the 
(pie  described  in  tlic  preceding  passage,  'flic  only  point  which  calls  for 
fortherramark  in  connection  with  it  is,  that  the  lino  O Q (Fig.  10)  is  in  , 
verfNtf  called  the  usine  of  the  tin  nata.''  15v  this  latter  term  is  desig-’4^ 
natemtbe.oj^XMte  of  the  hour-angle  (nata) — that  is  to  say,  the  anna 
angdarjisisiw  from  the  horizon  upon  his  own  circle,  O'  A',*  reduced  t#  . 
..time,  or  measure  of  a great  circle.  Thus,  when  the  sun  is  ift  0*, 
•Ik  houwmj^e.^nata),  or  the  time  till  noon,  is  O’  E ; his  distance  from 
the  hprkpn  (winaXd),  or  the  time  since  sunrise,  is  O'  ( But  G Q'u. 
with  uo^Cb|riety  styled  the  sine  of  G'Qf;  it  is  not  itself  a sine  bfap£& 
and  t|p  sw&daine  of  tlie  arc  in  question  would  have  a very  different 
value. 


40.  Multiply  the  sine  of  co-latitude  by  any  given  measure  of 

amplitude-  (agrd),  and  divide  by  the  corresponding  hypotbmnue 
in  uigits;  the  result  is  the  sine  of  declination.  This,  agtfzn,  is 
to  be  multiplied  by  radius,  and  divided  by  the  sine  of  greatest 
declination;  , , $ 

41.  The  quotient,  converted  into  arc,  is,  i.i  signs,  etc.,  the  sun’s”  ’ 

place,  inthe  qufc&tant;  by  means  of  the  qua*  rants  is  then  found 
the  actual,  longitude  of  the  suh  at  that  point. ...  & 


Bj&tho  •method  taught  in  this  passage,  the  aun’s  declination,  and, 
thretgh  thaft,  his  true  and  mean  longitude,  may,  the  latitude  of  the  ob*'*U4 
server  being  known,  bo  found  from  a single  observation  np M$f the  shadow 
hoar  izLthe  day, . The  declination  ia  obtained  ms  tt&smpre 
ofamplitude^bd  the ‘hypbthehuae  of  the 


U8  SC^8MMtnti%:  , ' #81.41- 

vy  » 

\ 

manner : first,  u was  shown  in  connection  with  verm  Y of  this  rjygrter, 
hyp.  shad. : meas.  ampl. : : EC : C A (Fig.  13,  p.  «0) 
but  EC:CA::EH:B,C 

therefore  hyp.  shad. : meas.  ampl. : : E H : B C 

BC,  the  sine  of  declination,  being  thus  ascertained,  the  longitude  is  de- 
duced from  it  as  in  a previous  process  (see  above,  vv.  17-20). 


41. .  . . Upon  a given  day,  the  distances  of  three  bases,  at 
noon,  in  the  forenoon,  and  in  the  afternoon,  being  laid  off, 

42.  From  the  point  of  intersection  of  the  lines  drawn  betweep 
them  by  means  of  two  fish-figures,  ( maisya ),  and  with  a radios 
touching  the  three  points,  is  described  the  path  of  the  shadow. 

This  method  of  drawing  upon  the  face  of  the  dial  the  path  which 
will  be  described  by  tbe  extremity  of  the  shadow  upon  a given  day  pro- 
ceeds upon  the  assumption  that  that  patli  will  be  an  arc  of  a circle — an 
dfeoneoiu.. assumption,  since,  excepting  within  the  polar  circles,  the  path 
k shadow  is  always  a hyperbola,  when  the  sun  is  not  in  the  cmi&tor. 

, however,  the  difference  between  tbe  arc  of  the  nypor- 
1 not  too  br  from  the  gnomon,  and  the  arc  of  a circle, 
H is  not  vdMsurprising  that  the  Hindus  should  have 
\ ft,  The  path  being  regarded  as  a true  circle,  of  course  it 
T wn  if  any  three  points  in  it  can  be  found  by  calculation : and 
^ I difficult  since  the  rules  above  given  furnish  means  of  aBcer- 
r-if  the  sun's  declination  and  the  observer's  latitude  be  known, 
of  the  shadow  and  the  length  of  its  base,  or  the  distance  of 
" f tram  tbe  east  and  west  axis  of  the  dial,  at  different  times 
l ay.  One  pert  of  the  process,  however,  has  not  been  provi- 
|4  tibe-rulee  hitherto  given.  Thus  (Fig.  0,  p.  97),  supposing 
i f to  be  three  points  in  the  same  daily  path  of  the  shadow,  we 
^teqiiirc,  in  order  to  lay  down  l and  m,  to  know  not  only  the  bases  1 6% 
f,v  but  also  the  distances  b 6",  b b,u.  But  these  are  readily  found 
n the  shadow  and  the  base  corresponding  to  each  are  known,  or 
r may  .be  calculated  from  the  sines  of  the  respective  hour-angles, 
he  three  points  being  determined,  the  mode  of  describing  i circle 
through  them  is  virtually  the  same  with  that  which  we  should  employ : 
lines  are  drawn  from  the  noon-point  to  each  of  the  others,  which  are 
t&ep,^y  fish-figures  (see  above,  under  vv.  1-5),  bisected  by  other  lines,  at 
rigWaiigles  to  them,  and  the  intersection  of  the  latter  is-tho  centrtfof 
the  repaired  circle. 

$ 42. . . . Multiply  by  the  day-radius  of  three  pggns,  and  divide 
by  their  own  respective  day-radii,  ,B 

48.,  £ol  succession,  the  sines  of  one,  of  twoj'tad  of 
the  (tobtients,  converted  into  arc,  being  subtracted^  each  T_._ 
one  rmbwing,  yvo,  beginning  with  Aries,  t^e  tithes  at  ijsing 


/sixteen  hundred  and  seventy,  seventeen  hundred 
nineteen  hundred 


iii.  4 


Ih&aht&iand  Notes. . 


119 
art  tlft 


difflppoe  (edfmUuufa),  as  calculated 
times  af  ntbg  at  that  place. 

46.  Invert  them,  and  add  their  own  portions  of  ascennanai 
difference  inverted,  and  the  sums  are  the  three  signs  beginning 
with  Cancer : and  these  same  six,  in  inverse  order,  are  the  other 
six,  commencing  with  Libra. 

The  problem  here  is  to  determine  the  “ times  of  rising”  (udaydtaoat) 
of  the  different  signs  of  the  ecliptic — that  is  to  say,  the  part  of  die  5400 
rtfpirations  (atavas)  constituting  a quarter  of  the  sidereal  day,  which, 
each  of  the  three  signs  making  up  a quadrant  of  the  ecliptic  will  occupy 
in  rising  (« daya)  above  the  horizon.  And  in  the  first  place,  the  times 
r<ot  rising  at  the  equator,  or  in  the  right  sphere — which  are  the  equiva- 
lents of  the  signs  in  right  ascension — are  found  as  follows : . -,r 

Let  ZN  (Fig.  17)  he  a quadrant  of  the  solstitial  colure,  AN  the  pro- 
of the  equinoctial  colure,  A Z of  the  equator,  asiL 


jection  upon  its  plane 


upon  its  plane  ot  the  equinoctial  coll 
the  ecliptic ; and  let  A,  T,  0,  and 
C be  the  projections  upon  A (!  of  the  initial 
points  of  the  first  four  signs ; then  A T is 
the  sine  of  one  sign,  or  of  30°,  A G of  twp 
signs,  or  of  60°,  and  A C,  which  is  radius, 
the  sine  of  three  signs,  or  of  00°.  From 
T,  (i,  and  C,  draw  T /,  G y,  C c,  perpendicu- 
lar to  A N.  Then  A T t and  A C c arc  simi- 
lar triangles,  and,  since  A C equals  radius, 

K:Cc::AT:Tf 

But  the  arc  of  which  T t is  sine,  is  the 
same  part  of  the  circle  of  dinrnal  revolu- 
tion of  which  the  radius  is  1 1\  as  the  re-  

quired  ascensional  equivalent  of  one  sign  is 

of  the  equator:  hence  the  sine  of  the  latter, fwhich  we  may  call 
found  by  reducing  T*  to  the  measure  of  a grcat^circle,  which  is 
the  proportion 

t V : R : : T t : sin  x 

Combining  this  with  the  preceding  proportion,  we  have, 

If : C e : : A T : sin  x 

Again,  to  find  the  ascensional  equivalent  of  two  signs,  which  weirlH 
cally,  we  have  first,  by  comparison  of  the  triangles  A Gy  and  AC  ft 

R:Cc::AG:Gy 

and  gg1  :R::Gy  :siny 

thtrefbre,  as  before,  yy1  : Ce : : A G : sin  y 
Henm^fto  .sines  of  the  ascensional  equivalents  of  • ne  and  ofteoqgni 
reaMprajfv  are  eqw  to  the  unes  of  one  an£.  of  two  signs,  Aff  and, 
AO,  multiplied  by  the  day-radius  of  three  signs,  Ce,  and  diridijBL'eqch.^ 
by  itt  own  day-radirt,  t if  and  gtf ; and  the  conversion  of  thesrags  thus 
obtained  hito  arc  gifts  the  ascensional  equivalents  thiemjj|ftyM^-tTfr»  :• 
rtUbOTAe  m »J»des  also  tiic , eqniyaient'of  ^»igt§P;thi.1sjo  «, 
jlwip)  equaltM$a  quadrant  that  it  u up 
proeaw,  nil  tha^Hna  in  the  prqgggtyWi”- 


120 


[ifi.  15- 


9 

111 


Upon  working  out  the  process,  by  means  of  the  table  of  sines  given 
in  the  second  chapter  (w.  15-22),  and  assuming  the  inclination  ofvthe 
plane  of  the  ecliptic  to  bo  24°  (ii.  28),  we  find,  by  the  role  given  above 
(ii.  60),  that-  the  day -radii  of  one,  of  two,  mid  of  three  sines,  or  t gg\ 
Cc,  are  3366',  3216',  and  3140'  respectively,  and  that  the  sines  of  x and 
y are  1604'  and  2007',  to  which  the  corresponding  arcs  are  27°  50'  and 
57°  45',  or  1670'  and  3405'.  The  former  is  the  ascensional  equivalent 
of  the  first  sign ; subtracting  it  from  the  latter  gives  that  of  the  second 
sign,  which  is  1795',  and  subtracting  3405'  from  a quadrant,  5400' 
gives  the  equivalent  of  the  third  sign,  which  is  1935' — all  us  stated  iu 
the  text. 

These,  then,  are  the  periods  of  sidereal  time  which  the  first  three 
sigus  of  the  ecliptic  will  occupy  in  rising  above,  the  horizon  at  the  equa-' 
tor,  or  in  passing  the  meridian  of  unv  latitude.  It  is  obvious  that  the 
same  quantities,  in  inverse  order,  will  lie  the  equivalents  in  right  ascen- 
sion of  the  three  following  signs  also,  and  that  the  series  of  six  equiva- 
lents thus  found  will  belong  also  to  the  six  signs  of  the  other  half  of  the 
ecliptic.  In  order,  now,  to  ascertain  the  equivalents  of  the  signs  in 
taMIqne  ascension,  or  the  periods  of  sidereal  time  which  they  will  occupy 
in  rising  above  the  horizon  of  a given  latitude,  it  is  necessary  first  to 
calculate,  for  that  latitude,  the  ascensional  difference  (card)  of  the  three 
points  T,  G,  and  C (Fig.  17),  which  is  done  by  the  rule  given  in  the  last 
chapter  (vv.  61,  62).  We  have  calculated  these  quantities,  in  the  Hindu 
metnod,fbrthc  latitude  of  Washington,  38°  54',  and  find  the  ascensional 
difference  of  T to  be  578',  that  of  ( J 1001',  and  that,  of  C 1263'.  The 
manner  in  which  these  are  combined  with  the  equivalents  in  right 
ascension  to  produce  the  equivalents  in  oblique  ascension  may  bo  ex- 
plained by  the  following  figure  (Fig.  18),  which,  although  not  a true 
projection,  is  sufficient  for  the  purpose 
of  illustration.  Let  ACS  be  a semi- 
circle of  the  ecliptic,  divided  into  its 
^successive  signs,  and  A S a semicircle 
of  the  equator,  upon  which  A T' , T'  O', 

;e to,  are  the  equivalents  of  those  signs 
iu  right  ascension ; and  let  f,  g,  etc.,  be 
the  points  which  rise,  simultaneously 
withT,  G,  etc.  Then  t T'  and  ?>V',  the 
ascensional  difference  of  T and  V,  are 
678',  gQ/  and  11/  arc  1001',  and  cC' 
is  1263'.  Then  A t f,  the  equivalent  in 
oblique  ascension  of  A T,  equals  A T'  - 
t T',  or  1092'.  To  find,  again,  the  value 
of  i9t  the  second  equivalent,  the  text 
directa  to  subtract  from  T'  G'  the  differ- 
ence Between  IT  and*pG',  which  is 
caUed^the  carakhanda,  M portion  of  ascensional  difference”— that  is  to 
«ay,  th£  increment  or  decrement  of  ascensional  difference  at  the  point 
G at  compared  with  T.  Thus 

-Sii 

jfa  * O'  O'— (cWjtp  O')  sb  G'.0*4y  O'— e 0'*»^iPwO'B=1783' 


Fig.  18. 


.ISfcrtlior,  to  find  the  oblique  equivalents  in  the  second  quadrant  we 
a#* directed' to  invert  the  right  equivalent*,  and  to  add  to  each  ite  own 
carakhanda,  decrement  of  ascensional  difference.  Thus 

= W V+(eV-lV)=cV-lL'=mV 
lv=zU  V,+  (ILr-»V,)=slVf- vV'=22W 
and  finally,  i»S*V'S  + vV'=  2248'. 

It  is  obvious  without  particular  explanation  that  the  arcs  of  oblique 
ascension  thus  found  as  tin*  equivalents,  in  a given  latitude,  of  the  first 
six  signs  of  the  ecliptic,  arc  likewise,  in  inverse  order,  the  equivalents  of 
the  other  six.  We  have,  then,  the  following  table  of  times  of  rising 
[uday  teams),  for  the  equator  and  for  the  latitude  of  Washington,  of  all 
■the  divisions  of  the  ecliptic  : 

Equivalents  in  Right  and  Oblique  Ascension  of  the  Signs  of  the  Ecliptic. 


No. 

Sign. 

Name. 

j Ki|iii  v-ila-ul 

| in 

(Right  Ancnnsion. 

I. 

Aries,  mrs/fa, 

i ’ or  p. 

i iflTU 

9. 

Tuurus,  w/mn, 

i 

3. 

Gemini,  mithnno, 

■ *»» 

4. 

Cancer,  karkatn , 

; ■ 

5. 

Leo,  si  a ha. 

. ryr» 

6. 

j 

Virgo,  kmn/ii, 

iA-rfflii. 1 Equiv.  in 

i Obi.  Asreiirtion- 


Sis'll. 


Name 


iHf 


or  ft  , 

<5-8 
infir 
I jf>3 
wrfii 
ri?B 


1 or  p. 
11*92 
i.3 1 u 

1733 
a 1 37 
22-8 
a a 48 


Places,  mina, 
Aquarius,  humbha, 
[Capricomus,  ninkata, 
Sagittarius,  dhamt», 
Scorpio,  alt, 

| Libra,  tula. 


li 

«u 

IO-I 

9 

8. 

7- 


For  tlie  o-xjn-csiidii  *■  at  L-uika " employe)!  in  verso  43  to  designate 
the  equator,  see  above.  under  i.  fill. 

46.  From  the  longitude  of  the  sun  at  a given  time  are  to  be.-, 
calculated  the  ascensional  equivalents  of  the  parts  past  and  to' 
come  of  ihe  sign  in  which  lie  is:  they  are  equal  to  the  number 
ofdegrecs  traversed  and  to  br  traversed,  multiplied  by  the  as- 
censional equivalent  (udaydsavas)  of  the  sign,  and  divided  by; 
thirty; 

Then,  from  the  given  time,  reduced  to  respirations,  sub-’* 
tfijritfbe  equivalent,  in  respirations,  of  the  part  of  the  sign  to 
Qpri&and  also  the  ascensional  equivalents  (hgndsavas)  of  ihe 
^Uevritvg  signs,  in. succession— so  likewise,  subtract  the  equiva- 
'Tofthepart  past,  and  of  the  signs  past,  in  inverse  order; 

‘vif  there  he  a remainder,  multiply  it  ^)y  thirty  and  divide 
1 equivalent  of  the  Ansubtracteu  sign ; add  the  quotient^  in  , 
to  the  whole  signs,  or  subtract  it  from  them the  result : 
rinlofthe.  eqlipbo  (lagna)  which  is  at  ihat  time  upon  the 

% from  the'east  or  west  hour-angle  (mta)  of  the.Jnn,  in 
nagis,  having  made  a similar  calculation,  by  means  of  the.$quiv- 
alwnte  ixx  right  ascension  (lankodaydsavas),  apply  the  Militias  an 
additive  or  anbhHOtive  equation  to  the  suns  longitude : the -re- 
sult is  the  poij^p  the  ecliptic  then  upon  the  meridian  (^rnadhya- 


122  S&rya-Siddhdnla,  [iii-  4®- 

The  word  lagna  means  literally  u attached  to,  connected  with,”  and 
hence, 11  corresponding,  equivalent  to.”  It  is,  then,  most  properly,  and 
likewise  most  usually,  employed  to  designate  the  point  or  the  arc  of  the 
equator  which  corresponds  to  a given  point  or  arc  of  the  ecliptic.  In 
such  a sense  it  occurs  in  this  passage,  in  verse  47,  where  lagndsavas  is 
precisely  equivalent  to  udayAsava#,  explained  in  connection  with  the 
next  preceding  passage;  also  below,  in  verse  50,  and  in  several  other 
places.  In  verses  48  and  40,  however,  it  receives  a different  significa- 
tion, being  taken  to  indicate  the  point  of  the  ecliptic  which,  at  a given 
time,  is  upon  the  meridian  or  at  the  horizon ; the  former  being  called 
lagnam  kxhitije , “ lagmi  at  the  horizon  " — or,  in  one  or  two  cases  else- 
where, simply  lamia — the  other  receiving  the  name  of  madhyalagna, 
u mcridiati-fayfia.” 

The  rules  by  which,  the  sun’s  longitude  and  the  hour  of  the  day  being 
known,  the  points  of  the  ecliptic  at  the  horizon  and  upon  the  meridian 
are  found,  arc  very  elliptically  and  obscurely  stated  in  the  text;  our 
translation  itself  has  been  necessarily  made  in  part  also  a paraphrase  and 
explication  of  them.  Their  farther  illustration  may  be  best  effected  by 
.means  of  ail  example,  with  reference  to  the  last  figure  (Fig.  18). 

• At  a given  place  of  observation,  as  Washington,  let  the  moment  of 
local  time — reckoned  in  the  usual  Hindu  manner,  from  sunrise — be  18n 
J2*  3P,  and  let  the  longitude  of  the  smi,  as  corrected  by  the  precession, 
be,  by  calculation,  42°,  or  l3  12°  : it  is  required  to  know  the  longitude 
of  the  point  of  the  ecliptic  (lagna)  then  upon  the  eastern  horizon. 

Let  P (Fig.  18)  be  the  place  of  the  sun,  and  II  k the  line  of  the  hori- 
zon, at  the  given  time;  and  lit  p be  the  point  of  the  equator  which  rose 
'.with  the  sun;  then  the  arc  j) h is  equivalent  to  the  time  since  sunrise, 
18n  12v  3P.  oi  6555P.  The  \aluc  of  tg , the  equivalent  in  oblique  ascen- 
sion of  the  second  sign  TO,  in  which  the  sun  is,  is  given  iu  the  table 
presented  at  the  end  of  the  note  upon  the.  preceding  passage  as  1312**. 
To  find  the  value  of  the  pail  of  it  pg  we  make  the  proportion 

TfJ : 1MJ : : tg  : pg 

or  30°  : 18°  ::  lai-ji':  78> 

Sr  i 

From  ph,  or  G555P,  we  now  subtract  p g%  787p,  and  then,  in  succession, 
the  ascensional  equivalents  of  the  following  si^ns,  («C  and  CL — that  is, 
gc,  or  1733P,  and  cl,  nr  2137P — until  there  is  left  a remainder,  lh,  or 
1898P,  which  is  less  than  the  equivalent  or  the  next  sign.  To  this  re- 
mainder of  oblique  ascension  the  corresponding  arc  of  longitude  is  theu 
found  by  a proportion  the  reverse  of  that  formerly  made,  namely 

Iv:ZJk::LV:LH 

or  2278P  : 1898P : : 30°  : 25° 

The  result  thus  obtained  being  added  to  A L,  or  4B,  the  sum,  4B  25°,  or 
145°,  is  the  longitude  of  If. 

The  arc  pg  is  called  in  tlic  text  bkogy&mvas,  “the  equivalent  in  respi- 
rations of  the  part  of  the  sign  to  be  traversed,”  while  tp  is  styled  hhuk- 
tAmwu,  “t^e  respirations  of  the  part  traversed.” 

It  op  the  other  hand,  it  were  desired  to  arrive  at  the  same  result  by 
reckoning  in  the  opposite  direction  from  the  sun  to  (he  horizon,  either 
oil  account  of  the  greater  proximity  of  the  two  iu  tbit  direction,  or  for 


Translation  and  Notes. 


in.  61.] 


12a 


sin*  other  reason,  the  manner  of  proceeding  would  be  somewhat  differ- 
ent Tittle,  if  A H (Fig.  18)  were  the  son’s  longitude,  and  p P the  line 
of  the  eastern  horizon,  we  should  first  find  hpy  by  subtracting  the  part 
of  tlie  day  already  elapsed  from  the  calculated  length  of  the  day  (this  • 
step  is,  in  the  text,  omitted  to  be  specified) ; from  it  we  should  then 
subtract  the  bhuktAsava*,  l hy  and  then  the  equivalents  of  the  signs 
through  which  the  sun  has  already  passed,  in  inverse  order,  until  there 
remained  only  the  part  of  an  equivalent,  p //,  which  would  be  converted 
into  the  corresponding  arc  of  longitude,  PCS,  in  the  Ramc  manner  as 
before:  and  the  subtraction  of  ]Mi  from  A<*  would  give  A I1,  the 
longitude  of  the  point  P. 

But  again,  if  it  be  required  to  determine  the  point  of  the  ecliptic 
which  is  at  any  given  time  upon  the  meridian,  the  general  process  is  the 
same  as  already  explained,  excepting  that  for  the  time  from  sunrise  is 
substituted  the.  time  until  or  sinee  noon,  and  also  for  the  equivalents  in  . 
oblique  ascension  those  in  right  us'viis-inn.  or,  in  the  language  of  the  * 
text*  the  “times  of  rising  at  Lanka"  f itntAtxtuyastn'a*)]  since  the  me- 
ridian, like  the  equatorial  horizon,  nits  the  equator  at  right  angles. 

It  will  be  observed  that  all  the**-  calculations  assume  the  increments 
longitude  of  to  be  proportional  t»>  tln^o  of  an-i-usion  throughout,  each 
sign;  in  a process  of  greater  prctruMniis  to  accuracy,  this  would  lead  to 
errors  of  some  consequence. 

The  use  and  value  of  the  methods  here  taught,  and  of  the  quantities 
found  as  their  results,  will  appear  in  the  sequel  (see  eh.  1-tJ;  vii.  7; 
ix.  r»-11 ; x.  J). 

The  term  kxhitljt i,  by  which  the  horizon  is  designated,  mnv  be  under- 
stood, according  to  the  nn  lining  attributed  t"  kshUl  (sec  above,  under 
ii.  61-63),  either  as  the  M circle  * *f  >ituaii>inM — that  is.  the  one  which  is 
dependent  upon  the  .situation  of  the  observer,  varying  with  every  change 
of  place  on  his  part—  or  as  the  ‘■earth-em-lc,"  the  one  produced  by  the 
intervention  of  the  earth  below  the  observer,  or  drawn  bv  the  earth 
upon  the.  skv.  Probably  the  latter  i.-  its  inn-  interpretation. 

50.  Add  together  the  asmisinnal  equivalents,  in  respirations, 
of  the  part  of  the  sign  to  be.  traversed  hy  the  point  having  less 
longitude,  of  the  part  traversed  hy  that  having  greater  longitude, 
and  of  the  intervening  signs — thus  is  made  tlu-  ascertainment  of 
time  ( hSlumdhmui ). 

51.  When  the  longitude  of  the  point  of  the  ecliptic  upon  the 
horizon  ( laynu ) is  less  than  that  of  the  sun,  the  time  is  iu  the 
latter  part  of  the  night;  when  greater,  it  is  iu  the  day-time; 
when  greater  than  the  longitude  of  the  sun  inci^ased  by  half  n 
revolution,  it  is  after  sunset. 

The  process  taught  iu  those  versos  is,  iu  a manner,  the  convene  of 
that  which  is  explained  iu  the  preceding  passage,  its  object  being  t ft  find 
the  instant  of  local  time,  when  a given  |>oiut  of  the  ecliptic  wj)l  Mtapon 
the  horizon,  the  longitude  of  the  sun  being  also  known.  Thus  (Fig.  16), 
supposing  the  sun’s  longitude,  A 1\  to  be,  at  a given  time,.  Is  12°  ;.4it  it 
required  to  know  at  what  time  the  point  II,  of  which  the  longitude  is 


124  Stirya-Siddhduta,  {Hi.  51- 

4*  25°,  will  rise.  The  problem,  is,  virtually,  to  alccrtain  the  arc  of  the 
fequator  intercepted  between  jd,  the  point  which  rose  with  the  sun,  and 
A,  which  will  rise  with  1 T,  since  that  arc  determines  the  time  elapsed 
between  sunrise  and  the  rise  of  11,  or  the  time  in  the  day  at  which  the 
latter  will  take  place.  In  order  to  this,  we  ascertain,  by  si  process  simi- 
lar to  that  illustrated  in  connection  with  the  hist  passage,  the  hhogyh- 
saveuf,  11  ascensional  equivalent  of  llir  part  of  the  sign  to  be  traversed,” 
of  the  point  having  less  longitude — or  pg—  ami  the  bhuktasavas,  “as- 
censional equivalent  of  the  part  trnt  ersed,”  helonging  to  H,  the  point 
having  greater  longitude — or  Ih — and  add  the  sum  of  both  to  that  of 
the  ascensional  equivalents  of  the  intervening  whole  signs,  g c and  c /, 
which  the  text  calls  nuturalagnasams,  “equivalent  respirations  of  the 
interval the  total  is,  in  respirations  of  time,  corresponding  to  minutes 
of  arc,  the  interval  of  tune  required  : it  will  be  found  to  be  65551’,  or 
. 1811  12v  3P;  and  this,  in  the  ease  assumed,  is  the  time  in  the  day  at 
' which  the  rise  of  11  take*  place.:  were  II,  mi  the  other  hand,  the  posi- 
tion of  the  atm,  18”  12V  3P  would  he  llie  time  before  sunrise  of  the  same, 
event,  and  would  require  to  be  subtracted  fit  mi  the  calculated  length  of 
day  to  give  the  instant  of  local  time, 
v It  is  evident  that  tin?  main  use  «»f  this  process  must  he  to  determine 
'the  hour  at  whirli  a given  plaiu-l,  or  a star  of  which  the  longitude  is 
known,  will  pass  the  horizon,  or  at. "which  its  14 day  M (see  above,  ii.  59- 
63)  will  eonimenee.  A like  method  — substituting  only  the  equiva- 
lent* in  right,  for  tlio-c  in  oblique  ascension — might  be  employed  in 
determining  at  what  instant  of  h eal  time  the  complete  day,  aJior&tra , 
of  any  of  the  heavenly  bodies,  reckoned  from  transit  to  transit  across 
the  lower  meridian,  would  cnmm.ure:  and  this  is  perhaps  to  be  re- 
garded as  included  also  in  the  terms  of  verse  50;  even  though  the 
following  verse  plainly  has  reference  to  the  time  of  rising,  and  the  word 
fagnat  as  used  in  it,  means  only  the  point  upon  the  horizon. 

The  last  verse  we  take,  to  be  simply  an  obvious  and  convenient  rule 
for  detenu  ini  ng  at  a glance  in  which  part  nf  the  civil  day  will  take 
.place  the  rising  of  an\  gi\cn  point  nf  the  ecliptic,  or  of  a planet  occu- 
pying that  point.  If  the  longitude  of  a planet  he  less  than  that  of  the 
tun,  while  at  the  same  time,  they  are  imt  more,  than  three-  signs  apart — 
this  ami  the  other  corresponding  restrictions  hi  point  of  distance  arc 
plainly  implied  in  the  different  specifications  of  the  verse  as  compared 
with  one  another,  and  are  accordingly  explicitly  stated  by  tlic  commen- 
tator— the  hour  when  that  planet  comes  to  assume  the  position  called 
in  tlic  text  lagnu,  or  to  pass  the  eastern  horizon,  will  evidently  be 
between  midnight  and  sunrise,  or  in  the  after  part  (pesha,  literally  “re- 
mainder”) of  the  night.:  if,  again,  it  he  more  than  three  ami  less  tjtuui 
six  signs  behind  the  sun,  or,  which  is  the  same  thing,  more  than  six^d 
less  than  nine  signs  in  advance  of  him,  its  time  of  rising  will  be  between 
sunset  and  midnight : if,  once  more,  it  be  in  advance  of  the  sun  by  loss 
than  six  signs,  it  will  rise  while  the  sun  is  above  the  horizon. 

• 

The  next  three  chapters  treat  of  the  eclipses  of  the  sun  and  moon,  the 
fourth  being  devoted  to  lunar  eclipses,  and  the  fifth  to  solar,  and  the 
«KXth>  containing  directions  for  projecting  an  eclipse! 


Translation  and  Note*. 


125 


fir.  l.J 


CHAPTER  IV. 

OF  ECLIPSES,  A Nil  ESPECIALLY  OF  LUNAR  ECLIPSES. 

Coirrnm: — 1,  dimensions  of  the  sun  and  moon;  2-3,  measurement  of  their  apparent 
dimensions ; 4-6,  measurement  of  the  earth’s  shadow ; 6,  conditions  of  the  occur- 
rence of  an  eclipse ; 1-8,  ascertainment  or  longitude  at  the  time  of  conjunction  or 
of  opposition;  9,  causes  of  eclipses;  10-11,  to  determine  whether  there  will  be 
an  eclipse,  and  the  amount  of  obscuration;  12-15,  to  find  half  the  time  of  dump* 
Cion  of  the  eclipse,  and  half  that  of  total  obscuration;  16-17,  to  ascertain  the 
times  of  contact  and  of  separation,  and,  in  a total  eclipse,  of  immersion  and 
• emergence;  18-21,  tu  (Ic.ti'rmiiip  the  amount  of  obscuration  at  a given  time; 
22-23,  to  find  the  time  uorresjamding  to  a given  amount  of  obscuration;  24-26, 
measurement  of  the  deflccLion  of  the  ecliptic,  at  the  point  occupied  by  the, 
eclipsed  body,  from  :ui  cast  and  west  line ; 20,  currccLion  of  the  scale  of  project 
tion  for  difference  of  altitude. 

1.  Tl\c  diameter  of  the  sun's  disk  is  six  thousand  five  hun- 
dred yojanas ; of  tlio  moon’s,  four  hundred  and  eighty. 

AVe  shall  see,  in  rnniuMinii  with  th  * n«*xt  p:i<«af_re,  that  tlic  diameters 
of  the  sun  nwl  muon,  a*  thus  Mated,  ire  Mihji'i-T  io  a «“iiri« ms  modifica- 
tion, dependent  upon  :m«l  representing  tin*  gs  alcr  «*r  less  distance  of 
those  oodies  from  tin:  earth : >»■>  lliat,  in  a ■■oil  in  sense,  we  hai  chore 
only-  their  mean  diameters.  These  represent,  mwever,  in  the  Hindu 
theory — which  atl'er.ts  to  reject  the.  supposition  nf  other  orbits  than  such 
as  arc  circular,  and  dcMTibed  at  equal  distances  about  the  earth — the 
true  absolute  dimensions  of  iho  sun  and  moon. 

Of  the  two, ■only  that  for  the  moon  is  obtnine  y a legitimate,  pro- 
cess, or  presents  any  near  approximation  to  the  It  The  diameter  of 
the  earth  being,  a*  stated  above  (i.  "ill).  IflOu  ynjaua^,  that  of  the  moon, 
480  yojanas  in  of  it  : while  the  true  value  of  the  moon's  diameter  in 
terms  of  the.  earth's  is  .2710,  «»r  only  about  a tenth  less.  An  estimate 
so  nearly  correct,  supposes,  of  course,  an  equally  eorreet  determination 
of  the  moon's  horizontal  parallax,  distance  from  the  earth,  and  mean 
apparent  diameter.  The  Hindu  valuation  of  the.  parallax  may  be  de- 
duced from  the  value  given  just  below  (v.  3),  of  a minute  on  the  moon's 
orbit)  as  15  yojauas.  Since  the  moon's  horizontal  parallax  :s  equal  to 
the  angle  subtended  at  her  centre  by  the  earth's  radius,  and  since,  at 
the  moon's  mean  distance,  l' of  are  equals  1.7  yojanas,  and  the  earth's  , 
radius,  800  yojanas,  would  accordingly  subtend  -m  angle  of  53'  20* — the 
latter  angle,  53#  20",  is,  according  to  the  system  r f the  Surya-Siddhftnta^ 
tfie  moon's  parallax,  when  in  the  horizon  and  . t her  mean  distance. 
This  is  considerably  less  than  the  actual  value  of  the  quantity,  as  deter- 
mined by  modern  science,  namely  R 7f/  1J;  and  it  is  practically,  in  the 
calculation  of  solar  eclipses,  still  farther  lessened  by  3'  51*  the  excess 
of  the  value  assigned  to  the  sun's  horizontal  parallax,  as  wc  shall  see 
farther  on.  Of  the  variation  in  the  parallax,  due  to  the  varying  distance 
of  the  moon,  the  Hindu  system  makes  uo  account : the  variation  is  actu- 

. " * n . 

J7  .*  1 

- I Wlf 


126  S&rya-Slddh&nta , pr.  1-1 

ally  nearly  8',  being  from  53'  48 ",  at  tlie  apogee,  to  6V  24",  at  the 
perigee. 

lLow  the  amount  of  the  parallax  was  determined  by  the  Hindus — if, 
indeed,  they  had  the  instruments  and  the  shill  in  observation  requisite 
for  making  themselves  an  independent  determination  of  it — we  arc  not 
informed.  It  is  not  to  be  supposed,  however,  that  an  actual  estimate  of 
the  mean  horizontal  parallax  as  precisely  53'  20"  lies  at  the  foundation 
of  the  other  elements  which  scorn  to  rest  upon  it.;  for,  iu  the  making 
up  of  the  artilicinl  lliudu  system,  all  these  elements  have  been  modified 
and  adapted  to  one  another  in  suck  a manner  as  to  produce  certain 
whole  numbers  as  their  results,  and  so  to  be  of  more  convenient  use. 

From  tills  parallax  the  moon's  distance  may  be  deduced  by  the  pro- 
portion 

Bin  53'  •iO,r : It : : crirtbs  rail. : muon  a dist. 
or  53 : 3 13S ' : : 8r.t »y ; 5 1 £-oy 

The  radius  of  the  moon's  orbit,  then,  is  51,57i)  \ojanas,  or,  in  terms  of 
the  earth's  radius,  04.47.  The  true  value  of  the  moon's  mean  distance 
is  59.96  radii  of  the  earth. 

The  farther  proportion 

3438* : 54oi »f : : 5-l570y  : hr, cony 

would  give-,  as  the  value  of  a •|ii:i«lr:int  «»f  tin-  iinxm'*  orbit,  81,000  yoja- 
nas,  and,  as  the.  whole  orbit,  niM.nnn  \ . This  is.  in  find,  the  cir- 
cumference. «»f  the.  orbit  assimifl  by  1 1 1 ' ■ >y<t:-m,  and  .stated  in  another 
place  (\ii.  Since,  howewr.  the  iimon's  distance  is  nowhere  assumed 
as  an  element  in  any  of  the  proi-e^vs  of  the  »\  stain,  and  is  own  directed 
(xii.  84)  to  be  found  from  the  em:iimfrrcijro  of  the  orbit  by  the  false 
ratio  of  1 :*/|o,  it  is  probable  that  it  was  also  made  no  account  of  iu 
constructing  the.  msIiiii,  and  tlisil  tin-  relation*,  of  (.ho  moon’s  parallax 
and  orbit  were  fixed  by  some,  such  pmp.irtion  as 
53#  20"  : 3<in° ::  ■ 39.f.o>ioy 

The.  moon’s  orbit,  being  321,000  \ ojanas,  the  assignment  of  480  voja- 
nm  as  her  diameter  implies  a detanuiiiutiun  of  Jicr  apparent  diameter 
at  her  mean  distance  as  32';  since 

3n.'jv  : 3a# : : 3*»4Ioni  >y  : /ft*  ▼ 

The  moon’s  mean  appan nl  diameter  is  actually  3V  7". 

In  order  to  understand,  farther,  how  tin.*  dimensions  of  the  sun’s  orbit, 
and  of  the  sun  himself  arc  determined  ta,  tin:  Hindus,  we  have  to  notice 
tli at,  the  moon’s  orbit  being  324,000  y.ijanas,  and  her  time  of  sidereal 
revolution  27d.32 167416,  the  nm-uirit  of  her  mean  daily  motion  is 
11,858r.7l  7.  The  Hindu  s\>tam  now  assumes  that  this  is  the  precise 
amount  of  the  actual  menu  daily  motion,  in  space,  of  all  the  planets, 
and  ascertains  the  dimensions  of  their  several  orbits  by  multiplying  it 
by  the  periodic  time  of  revolution  of  each  (see  below,  xii.  80-90).  The 
length  of  the  sidereal  year  being  3G5/1 .25875648,  the  sun’s  orbit,  is,  ;ls 
state/1  elsewhere,  (xii.  80),  4,331,500  yojanas.  From  a quadrant  of  this, 
by  the  ratio1 5400' : 3438',  we.  derive  tlie  sun’s  distance  from  tlie  earth, 
689,430  yojanas,  or  861.8  radii  of  the  earth.  This  is  vastly  less  than 
his  true  distance,  which  is  about  24,000  radii.  His  horizontal  parallax 


Translation  and  Holes. 


127 


iv.  3.] 

is,  of  course,  proportionally  over-estimated,  being  made  to  bo  nearly  4# 
(more  exactly,  3;  C9".4),  instead  of  8".G,  its  true  value,  an  amount  so 
small  that  it  should  properly  have  been  neglected  as  inappreciable. 

It  is  an  important  property  of  the  parallaxes  of  the  sun  and  moon, 
resulting  from  the  manner  in  which  the  relative  distances  of  the  latter 
from  tlic  earth  are  determined,  that  they  arc  to  one  another  as  the  mean 
daily  motions  of  the  planets  respectively  : that  is  to  say, 

53'  ao" : 3'  59" : : 790'  35" : 59'  B" 

Each  is  likewise  very  nearly  one  fifteenth  of  the  whole  mean  daily 
motion,  or  equivalent  to  the  amount  of  arc  traversed  bv  each  planet  in 
4 nfrdis ; the  difference  being,  for  the  1110011,  about  38",  for  the  sun, 
about  3".  AVc  shall  sec  that,  in  the.  calculations  of  the  next  chapter, 
these  differences  are  neglected,  and  the  parallax  taken  as  equal,  in  each 
case,  to  the  mean  motion  during  A 11  fid  is. 

Tlic  circumference  of  the  sun’s  orbit  being  4,331, r?00  yojanas,  the 
assignment  of  lioOO  yojanas  as  his  diameter  implies  that  his  mom  appar- 
ent diameter  was  considered  to  be  24".8 ; for 

: 3a'  24".R : : 4.3'Jr,  W : GW 

Tlic  true  value  of  the  sun’s  apparent  diaiiictir  at  his  mean  distance  is 
32'  3".0. 

The  results  arrived  at  by  the  bivek  astronomers  relative  to  the  paral- 
lax, distance,  and  magnitude  of  the  sun  and  menu  are  not  greatly  dis- 
cordant with  those  line  presented.  Hipparchus  found  the  moon’s  hori- 
zontal parallax  to  be. IT':  Arislarvlms  lia>l  piv\  imidy,  b\  «>l nervation 
upon  the  angular  dUlnnce  of  the  miii  and  moon  when  tin*  latter  is  half- 
illuminated,  made  llieir  relatiw  •lislainic<  to  1 e a»  19  to  1 ; this  gave 
ilipparehus  3'  as  the  sun*?,  parallax.  Ptolemy  makes  tlic  mean  dis- 
tauees  of  the.  sun  and  moon  from  the  earth  equal  to  1210  and  59  radii 
of  the.  earth,  and  their  parallaxes  2'  51"  and  08'  14"  respectively  : he 
also  states  the  diameter  of  the  moon,  earth,  ami  sun  to  be  as  MS-  18t, 
while,  the  Hindus  make  them  as  1,3 1,  and  13JJ,  and  their  true  values, 
as  determined  by  modern  science,  are  as  1,3!J,  and  412^,  nearly, 

2.  These  diameters,  each  multiplied  by  the  true  motion,  and 
divided  by  the  mean  motion,  of  its  own  planet,  give  the  cor- 
rected (splntht)  diameters.  Jf  that  of  the  sun  be  multiplied  by 
the  number  of  the  suns  revolutions  in  an  Age,  and  divided  by 
that  of  the  moon’s, 

3.  Or  if  it  bo  multiplied  by  the  moon’s  orbit  ( kaksha),  and 
divided  by  the  sun’s  orbit,  Liu1  result  will  be  its  diameter  upon 
the  moon’s  orbit:  all  these,  divided  by  fifteen  give  the  measures 
of  the  diameters  in  minutes. 

The  absolute  values  of  the  diameters  of  the  sun  and  moon  being 
stated  in  yojaiins,  it  is  required  to  liml  their  apparent  values,  in  minutes 
of  arc.  In  order  to  this,  they  are  projected  upon  the  mootfs  orbit,  or 
upon  a circle,  described  about  Hie  earth  at  the  moon's  mean  distance,  of 
which  circle — since  324,000-7-21,600=15 — one  miuute  is  equivalent 
to  fifteen  yojanas. 


128 


Sdrya-Siddhdnta , [iv.  3- 

The  method  of  the  process  will  be  made  dear  by  the  annexed  figure 
(Fig.  19).  Let  E be  the  earth’s  place,  E M or  E m the  mean  distance  of 

Fig.  10. 


the  moon,  and  E S the  mean  distance  of  the  sun.  Let  T U oqual  the 
sun's  diameter,  65007.  1 >ut  now  let.  the  sun  lie  at  the  greater  distance 

ES;:  the  part  of  his  mean  orbit  which  his  disk  will  cover  will  no  longer 
he  TU,  but  a less  quantity,  t ir,  and  tu  will  be  to  T IJ,  or  T'  LT/,  as  E»S 
to  ES'.  -But  the  text  is  not  willing  to  acknowledge  here,  any  more 
than  in  the  second  chapter,  an  acftial  inequality  in  the  distance  of  the 
sun  from  the  earth  at  different  times,  even  though  that  inequality  be 
most  unequivocally  implied  in  the  processes  it  prescribes : so,  instead  of 
calculating  ES'  as  well  ns  ES,  which  the  method  of  epicycles  afford* 
full  facilities  for  doing,  it  substitutes,  for  the  ratio  of  ES  to  ES#,  the 
inverse  ratio  of  the  daily  mot  ion  at  the  mean  distance  ES  to  that  at  the 
true  distance  ES'.  The  ratios,  however,  are  not  precisely  equal.  The 
arc  am  (Fig.  4,  p.  67)  of  the  eccentric  circle  is  supposed  to  be  trav- 
ersed by  the  sun  or  moon  with  a uniform  velocity.  If,  then,  the  motion 
at  any  given  point,  as  wi,  were  perpendicular  to  K m,  the  apparent  mo- 
tion would  be  inversely  as  the  distance.  But.  the  motion  at  m is  per- 
pendicular to  tm  instead  of  Em.  The  resulting  error,  it  is  true,  aiul 
especially  in  the  case  of  the  sun,  is  not  very  great.  It  may  be  added 
that  the  eccentric  circle  w hich  best  represents  the  apparent  motions  of 
the  sun  and  moon  in  their  elliptic  orbits,  gives  much  more  imperfectly 
the  distances  and  apparent  diameters  of  those  bodies.  The  value  of  fir, 
however,  being  thus  at  least  approximately  determined,  /'ir',  the  arc  of 
the  moon’s  mean  orbit  subtended  by  it,  is  then  found  by  the  proportion 
ES : Em  (or  KM) : : tu : Vu' — excepting  that  here,  again,  for  the  ratio 
of  the  distances,  ES  and  EM,  is  substituted  either  that  of  the  whole 
circumferences  of  which  they  arc  respectively  the  radii,  or  the  inverse 
ratio  of  the  number  of  revolutions  in  a given  time  of  the  two  planets, 
which,  as  shown  in  the  note  to  the  preceding  passage,  is  the  same 
thing.  Having  thus  ascertained  the  value  of  Vu*  in  vojanas,  division 
by  15  gives  us  the  number  of  minutes  in  the  are.  V or  in  the  angle 
t'Eu'. 

In  like  manner,  if  the  moon  ho.  at  less  than  her  mean  distance  from 
the  earth,  as  E M',  she  will  subtend  an  are.  of  her  mean  orbit  no,  greater 
than  X 0,  her  true  diameter;  the  value,  of  no,  in  yojanas  and  in  minutes, 
is  found  by  a method  precisely  similar  to  that  already  described. 

There  is'  hardly  in  the  whole  treatise  a more  curious  instance  than 
this  of  the  mingling  together  of  true  theory  and  false  assumption  in  the 
same  process,  and  of  the  concealment  of  the  real  character  of  a process 
‘by  substituting  other  and  equivalent  data  for  its  true  dements. 


Translation  and  Notes. 


1*9 


iv.fi.] 

We  meet  for  the  first  time,  in  this  passage,  the  term  employed  in  the 
treatise  to  designate  a planetary  orbit,  namely  kakshd , literally 11  border, 
girdle,  periphery.”  The  value  finally  obtained  for  the  apparent  diame- 
ter of  the  sun  or  moon,  as  later  of  the  shadow,  is  styled  its  mdnaf 
“ measure.” 

In  order  to  furnish  a practical  illustration  of  the  processes  taught  in 
this  chapter,  we  have  calculated  in  full,  by  the  methods  and  elements  of 
the  S&rya-Siddh&nta,  the  lunar  eclipse  of  Feb.  (3th,  1800.  Rather,  how- 
ever, than  present  the  calculation  piecemeal,  and  with  its  different  pro- 
cesses severed  from  their  natural  connection,  and  arranged  under  the 
passages  to  which  they  severally  belong,  we  have  preferred  to  give  it 
entire  in  the  Appendix,  whither  the  reader  is  referred  for  it. 

4.  Multiply  the  curtli’a  diameter  by  the  true  daily  motion  of 
the  moon,  and  divide  by  her  mean  motion : the  result  is  the  t 
earth’s  corrected  diameter  (sfici).  The  difference  between  tlie 
earth’s  diameter  and  the  corrected  diameter  of  the  sun 

5.  Is  to  be  rnultiplmdjdpy  tin1  moon’s  mean  diameter,  and  divi- 
ded by  the  sun’s  moHpiameter : subtract  the  result  from  the 
earth’s  corrected  diarMer  (sfici),  and  the  remainder  is  the  diam- 
eter ol'  the  shadow ; which  is  reduced  to  minutes  as  before. 

The  method  employed  in  thin  process  for  finding  the  diameter  of  tlie 
earth's  shadow  upon  the  inonn^  mean  orbit  may  be  explained  by  tlie 
aid  of  the  following  figure  (Fig.  ‘.Mi). 

As  in  the  last  figure,  let  K represent  the  earth's  place,  S and  M points 
in  the  mean  orbits  of  the  sun  and  moon,  and  Al#  the  moon's  actual 
place.  Let  tu  be  the  sun's  corrected  diameter,  or  the  part  of  his  mean 
orbit  wliicb  his  disk  at  its  actual  distance  covers,  ascertained  as  directed 
hi  the  preceding  passage,  and  let  F G l»c  the  earth'*  diameter.  Through 


Fi;;.  ‘JO. 


F and  G draw  t*  F/and  wiig  parallel  to  S M,  and  also  tV h and  u Gt : 
then  hk  will  be  the  diameter  of  the  shadow'  wh.re  the  moon  actually 
enters  it.  The.  value  of  hk  evidently  equals  fg  (or  FG)  -Of  *+?*); 
and  the  value  of  fh-\-gk  may  be  found  by  the  proportion 

F e (or  E S) : t v+w  u (or  t u—  FG) : : F/(or  E M1)  :/J+^ k 

But  the  Hindu  system  provides  no  method  of  measuring  the  angular 
value  of  quantities  at  the  distance  E M',  nor  does  it  ascertain  the  value 
of  E M itself : and  as,  in  tlie  hut  process,  the  di^jjwter  of  the  moon.; 


ISO  Sftrya-Siddh&nta , [iv.  5- 

was  reduced,  for  measurement,  to  its  yalue  at  tlie  distance  EM',  so,  to 
be  made  commensurate  with  it,  all  the  data  of  this  process  must  be 
similarly  modified.  That  is  to  say,  the  proportion 

EM':  EM  ::fg:fg' 

— substituting,  as  before,  the  ratio  of  the  1110011*8  mean  to  her  true 
motion  tor  that  of  EM' to  EM — gives  which  the  text  calls  the 

suci : the  word  means  literally  “ needle,  pyramid  ; we  do  not  sec  pre- 
cisely how  it  comes  to  be  employed  to  designate  the  quantity  fg%  and 
have  translated  it,  for  lack  of  a bettor  term,  and  in  analogy  with  the 
language  of  the  text  respecting  the  diameters  of  the  sun  and  moon, 
“corrected  diameter  of  the  earth.”  It  is  also  evident  that 

E SI' : fh+g  k : : K M :/  h'+g'  V 

lienee,  substituting  the  latter  of  these  ratios  for  the  former  in  our  first 
proportion,  and  inverting  the  middle  terms,  we  have 

ES  : EM  : : tu-VC,  :fh'+g'k' 

Once,  more,  now,  we  hate  a substitution  otjatios,  ES:  KM  being  re- 
placed by  the  ratio  of  the.  sun's  mean  disi^|nr  to  that  of  the  moon. 
In  this  there  is  a slight  inaccuracy.  The  sun(pition  proceeds  upon  the 
assumption  that  the  mean  apparent  values  of  the  diameters  of  the  sun 
and  moon  are  precisely  equal,  in  which  ease,  of  course,  their  absolute 
diameters  would  be  as  their  di>tances;  but  wc  have  seen,  in  the  note  to 
the  first  \ersc  of  this  chapter,  that  tin*  urn oil's  mean  angular  diameter  is 
made  a little  less  than  the  sun's,  I lie  former  being  :j 2',  the  latter  32'  24".H. 
The  error  i&  evidently  neglected  as  being  too  small  to  impair  sensibly  the 
correctness  of  the  result  obtained  : it  is  not  easy  to  see.  however,  why  we 
do  not  have  the  ratio  of  the  mean  distances  represented  here,  as  in  verses 
2 and  3,  by  that  of  the  orbits,  or  by  that  of  the  revolutions  in  an  Age 
taken  inversely.  The  substitution  being  made,  we  have  the  final  propor- 
tion on  which  the  rule  in  the  text  is  based,  \iz.f  the  sun's  mean  diameter 
is  to  the  moon's  mean  diameter  as  tin.  excess  of  the  sun's  corrected 
diameter  over  the  actual  diameter  of  the  earth  is  to  a quantity'  which, 
being  subtracted  from  the  suet,  or  correc  ted  diameter  U the  earth,  leaves 
as  a remainder  the  diameter  of  the  shadow  os  projected  upon  the  moon's 
mean  orbit:  it  is  expressed  in  vojauas,  but  is  ro.duc.cd  to  miiiulcs,  as 
before,  by  dividing  by  fifteen.  The  earth's  penumbra  is  not  taken  into 
account  in  the  Hindu  process  of  calculation  of  an  ellipse. 

The  lines  fg^fg\  etc.,  arc  treated  here  as  if  they  were  straight  lines, 
instead  of  arcs  of  the  moon's  orbit:  but  the  inaccuracy  never  comes  to 
be  of  any  account  practically,  since  the  value  of  these  lines  always  falls 
inside  of  the  limits  within  which  the  Hindu  methods  of  calculation 
recognize  no  difference  between  an  arc  and  its  sine. 

6.  The  earth’s  shadow  is  distant  half  the  signs  from  the  sun : 
when  the  longitude  of  the  moon’s  node  is  the  same  with  that  of 
the  shadow*,  or  with  that  of  the  sun,  or  when  it  is  a few  degrees 
greater  or  less,  there  will  be  an  eclipse. 

To  the  specifications  of  this  verse  we  need  to  add,  of  course,  “at  the 
time  of  conjunction  or  of  opposition.” 


^translation  and  Notes . 


iv.  8.] 


131" 


It  will  be  noticed  that  no  attempt  is  made  here  to  define  the  lunar 
and  solar  ecliptic  limits,  or  the  distances  from  the  moon's  node  within 
which  eclipses  arc  possible.  Those  limits  arc,  for  the  moon,  nearly  12° ; 
for  the  sun,  more  than  17°. 

The  word  used  to  designate  “eclipse,”  grahana , means  literally 
“seizure” : it,  with  other  kindred  terms,  to  be  noticed  later,  exhibits  the 
influence  of  the  primitive  theory  of  eclipses,  as  seizures  of  the  heavenly 
bodies  by  the  monster  luiliu.  In  versos  1 7 and  10,  below,  instead  of 
gral&na  we  have,  graha*  another  derivative,  from  the  same  root  grah  or 
grabh , “ grasp,  seize.”  likiwhcre  grahn  never  occurs  except  as  signifying 
“planet,”  and  it  is  the  only  word  which  the  Surva-Siddlianta  employs 
with  that  signification:  as  so  m*ed,  it  is  an  active  instead  of  a passive 
derivative,  meaning  “seize.r,”  and  its  application  to  the  planets  is  due 
to  the  astrological  conception  of  them,  as  powers  which  “lay  hold  upon” 
the  fates  of  men  with  their  .supernatural  influences. 

7.  The  longitudes  of  the  sun  and  moon,  at  the  moment  of 
the  end  of  the  day  of  new  moon  (aitvh'tbytt).  are  equal,  in  signs, 
etc. ; at.  the  end  of  the  day  of  lull  moon  (jiavrtianwsi)  they  are 
equal  in  degree's,  etc.,  at  a distance*  of  half  the  signs. 

8.  When  diminished  or  increased  by  the  proper  equation  of 
motion  for  (lie  tim*-.  past  or  p>  come,  of  opposition  or  conjunc- 
tion, they  are  made  t*>  atrree.  to  minutes:  tin*,  place  of  the  node 
at  the  same  time  is  treated  in  the  omtrary  manner. 

The  \ory  general  direction*  ami  explanations  contained  in  verses  fi.  7, 
and  !)  seem  of  place  hero  in  the  middle  «.f  the  chapter,  and  would 
have  more  properk  continued  iN  introduction.  The  process  prescribed 
in  verse  S,  al.su,  which  has  li»r  ii-*  fhiei-i  the  iletcrmiuatioii  of  the  longi- 
tudes of  tin1  Min.  iin Min.  ami  nun  in's  node,  ai  the  moment-  of  opposition 
or  conjunction,  might  im  le>N  ii  wnuld  appear.  l«»  precede  the  nseortoin- 
ment  of  the  true  im*iiou>,  and  *»f  ll»e.  niea-mv<  of  the  di^k^  and  shadow, 
already  explained.  Yer**e  S,  indeed,  by  the  lack  of  cunnectnm  in  which 
it  slamls,  and  by  the  obscurity  of  its  language,  furnishes  a striking  in- 
stance of  the  want  of  precision  am!  imeHiuiliility  so  often  characteristic 
of  the  treatise.  The  subject  of  the  verse,  which  requires  to  he  supplied, 
is,  “the  longitudes  of  the  sun  and  moon  at  ihe  instant  of  midnight  next 
preceding  or  following  the  given  opposition  or  conjunction":  that  being 
ihe  lime  for  which  the  true  longitudes  ami  motions  are  first  calculated, 
in  order  to  test  tin;  question  of  the  probability  of  an  eclipse.  If  there 
appears  to  be  such  a probability,  the  next  step  is  to  ascertain  the  inter- 
val between  midnight  and  the  moment  of  opposition  tf>r  conjunction, 
past  or  to  come  : this  U done  by  the  method  taught  u ii.  66,  or  by  some 
other  analogous  process:  the  instant  of  the  occurrence  of  opposition  or 
conjunction,  in  local  time,  counted  from  sunrise  of  the  place  of  observa- 
tion, must  also  be.  determined,  In  ascertaining  Ihe  interval  between  mean 
and  apparent,  midnight  (ii.  16),  the.  length  of  the  complete  day  (ii.  59), 
and  of  its  parts  (ii.  fiO-Cfi),  etc. ; the  whole  process  is  sufficiently  illus- 
trated by  the  two  examples  of  the  calculation  of  eclipses  given*  in  the 
Appendix.  When  we  have  thus  found  the  interval  between  midnight 


182 


S&rya-Siddli&nta.  * [iv. 

and  the  moment  of  opposition  or  conjunction,  verse  8 teaches  us  how  to 
ascertain  the  t-ruo  longitudes  for  that  moment:  it  is  by  calculating — in 
the  manner  taught  in  i.  AT,  but  with  the  true  daily  motions — the 
^amount  of  mol  ion  of  the  sun,  moon,  and  node  during  the  interval,  and 
applying  it.  as  a corrective  equation  to  the  longitude  of  each  ut  mid- 
night, subtracting  in  the  ease  of  the  sun  and  moon,  and  adding  in  the 
case  of  the  node,  if  the  moment  was  them  already  past ; and  the  con- 
trary, if  it  was  still  to  come.  Then,  if  the  process  has  been  correctly 
performed,  the  longitudes  of  the  sun  and  moon  will  be  found  to  cosres- 
pond,  i»i  the  manner  required  by  verse  7. 

For  the  days  of  new  and  full  moon,  and  t.lieir  appellations,  see  the 
note  to  ii.  f»fi,  above.  The  teehuienl  expression  employed  here,  aa  in 
one  or  two  other  pa^aires  to  designate  ihe  “miuneiit  of  opposition  or 
conjunction'1  is  pur  van  at  l gas r.  “uadis  of  the  jn/nutn"  or  Ct time  of  the 
parvan  in  midis,  cte. pnrran  means  literally  ‘‘knob,  joint/’  and  is  fre- 

auently  applied,  as  in  thi*  term,  to  denote  a eon juncture,  the  moment 
_ lat  distinguishes  and  separates  two  intervals,  and  especially  otic  that  is 
of  prominence  and  importance. 

9.  The  moon  is  tlm  oclipscv  i>f  the  sun,  coining  to  stand  under- 
neath it,  like  a cloud:  the  mrnm,  moving  eastward,  enters  the 
earth’s  shadow,  and  the  hitter  becomes  iLs  eclipser. 

The  names  given  to  the  eclipsed  and  eclipsing  bodies  arc  either  ckadija 
and,  as  here,  chadaha , “the  body  to  be  obscured"  and  “the  obscurer,” 
or  gr&hya  and  grahaka , “the  body  to  bn  seized”  and  “the  scizcr.” 
The  latter  terms  are  akin  with  - grahana  and  grttha,  spoken  of  above 
(note  to  v.  0),  and  represent  the  ancient  theory  of  the  phenomena,  while 
the  others  are  derived  from  their  modern  and  .scientific  explanation,  as 
given  in  this  verse. 

10.  Subtract  the  moon’s  latitude  sit  the  time  of  opposition  or 
conjunction  lrom  half  the  sum  of  the  measures  of  Llio  eclipsed 
and  eclipsing  bodies:  whatever  the  remainder  is,  that  is  said  to 
be  the  amount  obscured. 

11.  When  that  remainder  is  greater  than  the  eclipsed  body, 
the  eclipse  is  total;  when  the  contrary,  it  is  partial;  when  the 
latitude  is  greater  than  the  half  sum,  there  takes  place  no  obscu- 
ration (gram). 

It  is  sufficiently  evident  Hint  when,  at  tin1  moment  of  opposition,  the 
moon's  latitude — which  is  the  distance  of  her  centre  from  the  ecliptic, 
where  is  the  centre  of  the  shadow — is  equal  to  the  sum  of  the  radii  of 
her  disk  and  of  the  shadow,  Ihe  disk  arid  the  shadow  will  just  touch  one 
another;  and  that,  on  the  other  hand,  the  moon  will,  at  the  moment  of 
opposition,  be  so  far  immersed  in  the  shadow  as  her  latitude  is  less  than 
the  sum  of  the  radii : and  so  in  like  manner  for  the  sun,  with  due  allow- 
ance for  parallax.  The  Hindu  mode  of  reckoning  the  amount  eclipsed 
is  not  by  digits,  or  twelfths  of  - the  diameter  of  the  eclipsed  body,  which 
method  we  nave  inherited  from  the  Greeks,  but  by  minutes. 


Translation  and  Notes. 


183 


Wi  13.] 

The  word  pr&sa , used  in  verse  11  for  obscuration  or  eclipse,  means 
literally  “ eating,  devouring,”  and  so  speaks  more  distinctly  than  any 
other  term  we  have  had  of  the  old  theory  of  the  physical  cause  of 
eclipses. 

12.  Divide  by  two  the  sum  and  difference  respectively  of  the 
eclipsed  and  eclipsing  bodies:  from  the  square  of  each  of  the 
resulting  quantities  subtract  the  square  of  the  latitude,  and  take 
the- square  roots  of  the  two  remainders. 

13.  These,  multiplied  by  sixty  am}  divided  by  the  difference 
of  the  daily  motions  of  the  sun  nrul  moon,  give,  in  naclis,  etc., 
half  the  duration  (sthiti)  of  the  eclipse,  and  half  the  time  of  total 
obscuration. 

These  rules  for  finding  the  intervals  of.  time  between  the  moment 
of  opposition  nr  conjunction  in  longitude,  which  is  regarded  ns  the 
middle  of  the  eel  ipse,  and  the  moments  of  first  ami  hist  contact,  and,  in 
a total  eclipse,  «»f  the  beginning  and  end  of  total  obscuration,  may  be 
illustrated  by  help  of  tin*  annexed  figure  (Fig.  'Jl). 

Let  15 L L represent  the  ecliptic,  tile  point  C being  the  centre  of  the 
shadow,  and  let  ('  D be  the  moon's  latitude  at  the  moment  of  opposi- 


SI. 


lion ; which,  for  the  present,  we  will  suppose  to  remain  unchanged 
through  the  whole  continuance  of  the  eclipse.  ft  is  evident  that  the 
first  contact,  of  the  moon  with  the  shadow  will  t.ik^-  place  when,  in  the 
triangle  C A M,  At!  cquaL  the  iu<»nn'< 'distance-  in  longitude  from  the 
centre  of  the  shadow,  A M her  latitmle.  and  FM  the  Mini  of  her  radius 
and  that  of  the  shadow.  In  like  manner,  the  moon  will  disappear  en- 
tirely within  the  shadow  when  RC  equals  her  distance  in  longitude  from 
the  centre  of  the  shadow,  R X her  latitude,  ami  C N the  difference  of 
the  two  radii.  Upon  subtracting,  then,  thr.  square  of  A M or®  X from 
those  of  C M mid  (.!  N respectively,  and  taking  the  square  roots  of  the 
remainders,  we  shall  have  the  values  of  A C and  ]>C  in  minutes.  These 
may  be  reduced  to  time  by  the  following  proportion  : as  the  excess  at 
18* 


184 


S&rya-Siddhdnta, 


[iv.  13- 


the  given  time  of  the  moon’s  true  motion  in  a day  over  that  of  the  sun 
is  to  a day,  or  sixty  nftdis,  so  are  A 0 and  It  C,  the  amounts  which  the 
moon.has  to  train  in  longitude  upon  the  sun  between  the  moments  of 
contact  and  immersion  respectively  ami  the  moment  of  opposition,  to 
the  corresponding  intervals  of  time. 

But  the  proee-s.  as  thus  conducted,  involves  a serious  error:  the 
moonY  latitude,  instead  of  remaining  constant  during  the  eclipse,  is  con- 
stantly  and  sensibly  changing.  Thu*,  in  the  figure  above,  of  which  tho 
conditions  are  those  found  by  tho  Hindu  processes  lor  the  eclipse  of  Feb. 
6th,  ltfUO,  the  moon's  path,  instead  of  being  upon  the  line  11 K,  parallel 
to  the  ecliptic,  is  real!\  uj.nu  It.  The  object  of  the  process  next 
taught  is  to  get  rid  of  this  error. 

14.  Multiply  tlio  daily  niotinns  l»y  tlio  half-duration,  in  uadis, 
and  divide  by  sixty : tin1  •result,  in  niiuuU-s,  subtract  for  the  time 
of  contact  i pray  rain  t\  and  add  I’nr  that  of  separation  (■ molcshd ), 
respectively ; 

15.  By  tin*  latitude?  thfinv.  derived,  the  half-duration,  and 
likewise  the  luiU-tiinc  of  total  * obscuration,  are  to  be  calculated 
anew,  and  the  pnuvss  repented.  In  the  case  of  the  node,  the 
proper  correction,  in  minutes  cU\,  is  to  be  applied  in  the  con- 
trary’ manner. 

This  method  of  eliminating:  the*  l•lT»lr  inv«d\ed  in  the  supposition  of 
a constant  lalitude.  and  of  .»l.taiiiing  anofhrr  and  more  accurate  dote r- 
lniuation  of  the  interval**  between  1 1n-  moment  of  opposition  and  those 
of  first,  and  la>1  emiiart.  and  of  inmierdmi  and  emergence,  is  by  a scries 
of  succcssixe  approximatum*.  I'nr  ii^tuin'c  : AC,  as  already  determined, 
being  resumed  as  tin*  interval  between  opposition  and  first,  contact,  a 
new  calculation  of  tin  moon's  longitude  is  made  for  the  moment  A,  and, 
with  this  ami  the  sun  of  tin-  radii,  a new  value  is  found  foi  AC.  But 
now,  as  the  position  of  A is  ehiimn-d.  the  former  determination  of  its 
latitude  is  vitiated  and  must  l>r  made  anew,  and  made  to  furnish  anew 
a corrected  \aluc  of  AC:  and  on,  until  llm  position  of  A is  fixed 
with  the  degree  of  accuracy  iv.piiivd.  The  pron-ss  iinist  Im  eondneted 
separately,  of  emnsc,  f,»r  «-si«-li  of  tin-  four  tpiaMities  affected ; since,  where 
latitude  is  inr renting.  i\<  in  the  c;m-  illuMralul,  the  true  values  of  AC 
and  BC  will  be  i-ivutcr  than  their  mean  values,  while  (SO  and  FC,  the 
true  intervals  in  the  after  part  of  the  eelipso,  will  be  less  than  AC  and  L\ 
liC:  arid  the  contrary  wiimi  lalilmh.  is  deereasing. 

Wrc  have  illustrated  these  processes  by  reference  only  to  a lunar 
eclipse : tlicir  application  to  the  conditions  of  a solar  eclipse  requires 
the  introduction  of  another  eieincut,  that  of  the  parallax,  and  will  be 
explained  in  the  notc<  up*)n  the  next  ehapter. 

The  first  contact  of  the  eclipsed  and  eclipsing  bodies  is  styled  in  this 
passage  pragrahn , ‘•seizing  upon,  laying  hold  of;”  elsewhere  it  is  also 
called  11  devouring,"  and  aptirfu^  “touching:”  the  last  contact,  or 
separation,  is  named  nwksha , “ release,  letting  go.”  The  whole  duration 
. of  the  eclipse,  from  contact  to  separation,  is  the  sthiti,  “ stay,  continu- 
ance;” total  obscuration  is  vimaraa,  “crushing  out,  entire  destruction.”  « 


Translation  and  Notes. 


135 


iv.  Cl.] 

16.  The  middle  of  the  eclipse  is  to  be  regarded  as  occurring 
at  the  true  close  of  the  lunar  clay : if  from  that  time  the  time  of 
half-duration  be  subtracted,  the  moment  of  contact  ( grdsa ) is 
found;  if  the  same  be  added,  the  moment  of  separation. 

17.  In  like  manner  also,  if  from  and  to  it  there  be  subtracted 
and  added,  in  the  cruse  of  a total  eclipse,  the  half-time  of  total 
obscuration,  tbe  results  will  be  the  moments  called  those  of  im- 
mersion and  emergence. 

The  instant  of  true  opposition,  or  of  apparent  conjunction  (see  below, 
under  cli.  v.  9),  in  longitude,  of  the  sun  and  moon,  is  to  he  taken  as  the 
middle  of  the  eclipse,  even  though,  owing  to  the  motion  of  the  moon  in 
latitude,  and  also,  in  a solar  eclipse,  to  parallax,  that,  instant  is  nut  mid- 
way between  those  of  contact,  and  separation,  or  of  immersion  ami 
emergence.  To  ascertain  tin1  moment  of  local  time  of  each  of  these 
phases  of  the  eclipse,  we  subtract  and  add,  from  and  to  ihe  local  time 
of  opposition  or  conjunction,  the  true  interval-'  found  by  the  processes 
described  in  verses  1 X1  to  IT). 

The  total  disappearance  of  the  eclipsed  body  within,  or  behind,  the 
eclipsing  body,  is  culled  nl  mi  laud,  literally  the  “elosiire  of  the  eyelids, 
as  ill  winking:”  its  first  eoiiiuicin'i  iiiciit.  of  reappi-ar.-mce  is  shied  ittimi- 
lana,  11  parting  of  the  eyelid-,  p«rping”  We  trui-hm*  the  terms  by 
"immersion”  and  “ emergen. ■e"  lv-puetivi-Iy. 

18.  If  from  half  I lit*  duration  of  ilic  eclipse  any  given  interval 
be  subtracted,  and  the  remainder  multiplied  by  iln-  difference  of 
the  daily  motions  of  the  sun  and  momi.  and  divided  l>y  sixty,  the 
result  will  be  the  perpendicular  </.•■.//)  in  minutes. 

19.  In  the  ease  of  an  eclipse  [•/rufui)  of  the  sun,  the  perpen- 
dicular in  minute's  is  to  be  multiplied  by  the.  mea  t half-duration, 
and  divided  by  the  true  (*phn (•/)  hall-duration,  to  give  the  true 
perpendicular  in  minutes. 

20.  The  latitude  is  the  base  t Uwjn):  the  square  root  of  the 
sum  of  their  squares  is  the  hypotlienuso  ('mr«r,r):  subtract  this 
from  half  the  sum  nf  the  measures,  and  the  remainder  is  the 
amount  of  obscuration  igntm)  at  the  given  time. 

21.  If  that  time  be  after  the  middle  of  the  eclipse,  subtract 
the  interval  from  the  half  duration  on  the  side  of  separation,  and 
treat  the  remainder  as  before : the.  result  is  the  amount  remaining 
obscured  on  tbc  side  of  separation. 

The  object  of  the  process  taught  in  this  passage  i lo  determine  tho 
amount  of  obscuration  of  the.  eclipsed  body  at.  any  givui  mome.nl  during 
the  continuance  of  the  .eclipse.  It,  as  well  as  that,  prescribed  in  the 
fallowing  passage,  i*  a variation  of  that  which  forms  the  subject  of  verses 
12  and  13  above,  being  founded,  like  the  latter,  upon  a consideration  of 
tho  right-angled  triangle  formed  by  the  line  joining  the  eon t res  of  the 
eclipsed  and  eclipsing  bodies  as  liypolhenuse,  tins  difference  of  their 
longitudes  as  perpendicular,  and  the  moon’s  latitude  as  base.  And 
whereas,  in  the  former  problem,  wc  had  the  base  and  hypothemisc  given 


1S6 


[iv.  21- 


S&rya-Siddhdnla, 

to  findthc  perpendicular,  here  we  have  the  base  and  peipendicular  given 
, to  find  the  liypotliennse.  The  perpendicular  is  furnished  us  in  time, 
and  the  rule  supposes  it  to  be  stated  in  the  form  of  the  interval  between 
the  given  moment  and  that  of  contact  or  of  separation : a form  to 
which,  of  course,  it  may  readily  he  reduced  from  any  other  mode  of 
statement.  The  interval  of  time  is  reduced  to  its  equivalent  as  differ- 
ence of  longitude  by  a proportion  the  reverse  of  that  given  in  verse  lft, 
by  which  difference  of  longitude  was  converted  into  time;  the  moon's 
latitude  then  calculated ; froui_  the  two  the  hypothenusu  is  deduced ; 
and  the  comparison  of  this  with  the  sum  of  the  radii  gives  the  measure 
of  the  amount  of  obscuration. 

Verse  *21  seems  altogether  superfluous  : it  merely  states  the  method  of 
proceeding  in  ease  the  lime  given  falls  anywhere  between  the  middle  and 
the  end  ol‘ the  eclipse,  as  if  the  specifications  of  the  preceding  verses  ap- 
plied only  to  a time  occurring  before  the  middle  : whereas  they  are  gen- 
eral in  their  character,  and  include  the  former  case  no  less  than  the  latter. 

When  the  eclipse  is  one  of  the  >un,  allowance  needs  to  be  made  for 
the  variation  of  parallax  during  its  continuance;  this  is  done  by  the 
process  described  in  ut*c  1!»,  of  which  tin1  explanation  will  l»e  given  ill 
the  notes  to  the  next  chapter  (v\.  N-l  7). 

In  verse  20,  for  tin*  lirst  and  mil v time,  we  hn\o  latitude  called  kshej/ft, 
instead  of  vikshrpn . as  ckewbriv.  In  the  same  \ci>c,  the  term  employed 
for  “ hypothciiuse"  is  rraru.  "•hearing,  organ  of  hearing;"  this,  as  well 
as  the  kindred  cramnw,  which  i*  also  i.nre  or  twice  employed,  is  a syno- 
nym of  the  ordinary  term  which  means  literally  “car."  It,  is 

difficult  to  see  upon  wlmt  conception  their  employment  in  this  significa- 
tion is  founded. 

* 22.  From  lialf  the  sum  of  the  c-clipsi -»l  and  eclipsing  bodies 
subtract  any  given  amount  of  obscuration,  in  minutes;  from  the 
square  of  the  remainder . subtract  the  N|iiaiis«if  the  latitude  at 
toe  time,  and  take  the  square  root  of  tlu-ir  difference. 

>28.  ?The  result  is  the.  perpendicular  (/■•//)  in  minutes — which, 
iti  an  eclipse  of  the  sun,  is  to  he  mulliplie'l  by  the  true,  and 
divided  by  the  mean,  half-duration — and  this,  converted  into 
by  the  same  manner  as  when  tinning  the  duration  of  the 
ecnipie,  gives  the  time  of  the  given  amount  of  obscuration  (grasa). 

The  conditions  of  this  problem  nr.*  pivcUr.U  the  sum:  with  those  of 
the  problem  stated  above,  .in  \er-vs  I i!--l  excepting  that  here,  instead 
of  requiring  the  instant  of  time  w hen  nlKciirntion  commences,  or  becomes 
total/  wc  desire  to  know  when  it  will  be  of  a certain  given  amount. 
The  solution  must  be,  as  before,  by  a succession  of  approximative  steps, 
since,  the  time  not  being  fixed,  the  corresponding  latitude  of  the  moon 
cannot  be  otherwise  determined.  • 

24.  Multiply  the  sine  of  the  hour-angle  ( nata ) by  the  sine  of 
ttlie  latitude  (aA^Ao),  and  divide  by  radius:  the  arc  correspond* 
ing  to  the  result  is  the  degrees  of  deflection  (valandnyU),  which 
are  Qgrth  and  south  in  the  eastern  and  western  hemispheres 
iJcapcua)  respectively. 


Translation  and  Notes. 


137 


iv.  25.] 

25.  From  the  position  of  the  eclipsed  body  increased  by  three 
signs  calculate  the  degrees  of  declination : add  them  to  the  de- 
rees  of  deflection,  if  of  like  direction ; take  their  difference,  if  of 
iltercfit  direction:  the  corresponding  sine  is  the  deflection  (va- 
lana) — in  digits,  when  divided  by  seventy. 

This  process  requires  to  be  performed  only  when  it  is  desired  to  pro- 
ject an  eclipse.  In  making  a projection  according  to  the  Hindu  method, 
as  nvill  be  seen  in  connection  with  tin*  sixth  chapter,  the  eclipsed  body 
is  represented  as  fixed  in  the  centre  of  the  figure,  with  a north  and 
south  line,  and  an  east  mid  west  line,  drawn  through  it.  The  absolute 
position  of  these  lines  upon  the  disk  of  the  eclipsed  body  is,  of  course, 
all  the.  time  changing:  but  the  change  is,  in  the  ease  of  the  sun,  not 
observable,  and  in  the  ca*u  of  the  muon  it  is  disregarded  : the  Shrya- 
Siddhanta  takes  no  notice  of  the  figure  \isibh-  in  the  mooli's  face  as 
determining  any  fixed  mid  natural  diiv»-li.m>  upon  her  disk.  It  is  de- 
sired to  represent  to  the  eye,  by  the  figure  drawn,  where,  with  reference 
to  the  north,  south,  east,  and  west  points  of  the  moment,  the  contact,  im- 
mersion, emergence,  separation,  nr  other  phases  of  the  eclipse,  will  take- 
place.  In  order  1o  this,  it  is  necessity  lo  know  what  is,  at  each  given 
moment,  the  direction  of  the  ecliptic,  in  which  the  motions  of  both 
eclipsed  and  eclipsing  bodies  are  made.  The  ea*t  and  west  direction  is 
represented  by  a small  circle  drawn  through  the  e-  li]^cd  body,  parallel 
to  the  prime  vertical;  the  north  ami  *«.utli  direction,  by  a great  circle 
passing  through  the  hod\  and  through  the.  north  and  south  points  of 
the  horizon:  and  the  direction  of  the  ecliptic  is  determined  hy  uscer- 
certaining  the.  angular 
amount  of  its  deflection 
from  the  small  and 
west  circle  at  the  point 
occupied  by  the  eclipsed 
body.  Thus,  in  the  an- 
nexed figure  (Fig.  *J2), 
if  M he  the  place  of 
the  celipsed  body  upon 
the  ecliptic,  C L and  if 
KAY  he  the  small  cast 
and  west  circle  drawn 
through  M parallel  with 
K'Z,  the  prime  vertical,  then  the  deflection  will  *»c  the  angle  made  at  M 
by  CM  and  KM,  which  is  nqual  to  lv  M X,  the  angle  made  by  perpen- 
diculars to  the  two  circle*  drawn  from  their  respective  poles.  In  order 
to  find  the  value,  of  this  angle,  a double  process  is  adopted:  first,  the 
angle  made  at.  M by  the  two  small  circles  K M and  OM,  which  is  equiv- 
alent to  V M N,  is  approximately  determined : a*  this  dopend*  for  it* 
amount  upon  the  observer's  latitude,  being  nothing  in  a right  sphere,  it 
is  caller!  by  the  commentary  akslui  ralamt , “the  deflect  iois  due  to  lati- 
tude:” the  text  calls  it  simply  sahniuuffa,  “degrees  of  deflection,”  since 
it  docs  not,  like  the  net  result  of  the  whole  operation,  require  to  be  ex- 
pressed in  terms  of  its  sine.  Next,  tfje  angle  made  at  M hv  the  ecliptic, 


133 


8&rya-Siddhdnta}  [iv.  25. 

C L,  and  tlie  circle  of  daily  revolution,  D R,  which  angle  is  equal  to 
PlI  P#,'  is  also  measured  : this  the  commentary  calls  Ayana  valana f “the 
deflection  due  to  tlie  deviation  of  the  ecliptic  from  the  equator  ;,v  the 
text  has  no  special  name  for  it.  The  sum  of  these  two  results,  or  their 
difference,  as  the  casu  may  be,  is  the  valana,  or  the  deflection  of  the 
ecliptic  from.the  small  cast  and  west  circle  at  M,  or  the  angle  P'  M N. 

In  explaining  the  method  and  value  of  these  processes,  we  will  com- 
mence with  the  sccoud  one,  or  with  that  bv  which  PM  P',  the  Ayana 
valana,  is  found.  In  tin;  following  figure  (Fig.  23),  let  OQ  be  tho 
equator,  and  ML  the  ecliptic,  P and  I"  being  their  respective  poles. 
Let  M be  the  point-  at  which  the  amount  of  deflection  of  M L from  the 
circle  of  diurnal  revolution,  I)  K,  is  sought.  Lot  ML  equal  a quadrant; 
draw  P'L,  cutting  the  equator  at  Q; 
as  also  P L,  cutting  it  at  1> ; then  draw  23« 

PM  and  QM.  .Now  P'  M L is  a tri- 
quadrantal  triangle,  and  hence  M Q is 
a quadrant ; and  therefore  Q is  a pole 
of  the  circle  POM,  ami  Q<>  is  also  a 
quadrant,  and  QMO  is  a right  angle. 

But  DR  also  makes  right  angles  at  M 
with  PM;  hence  Q M and  DU  are 
tangents  to  one  another  at  M,  ami  the 
spherical  angle  QM  L is  equal  In  that 
which  the  ecliptic  makes  at  .M  with  tho. 
circle  of  declination,  or  to  P M l,# : ami 
QML  is  measured  hv  (2  L.  Tno  rule 
given  in  the  text  produces  a result  w hich 
is  a near  approach  to  thi**,  although  not 
entirely  accordant  with  it  excepting  at  tho.  solstice  ami  equinox,  the 
points  where  the  deflection  is  greatest  and  where  it  is  nothing.  We 
are  directed  to  reckon  forward  a quadrant  from  the  position  of  tlio 
eclipsed  body — that  is,  from  M to  Lt  in  the  figmc — and  then  to  calcu- 
late the  declination  at  that  point,  which  will  he  the  amount  of  deflection. 
Btftfthc  declination  at  L is  J»  L,  and  since  LIlQ  is  a right-angled 
triangle,  having  a right  angle  at  l»,  and  since  Lt*  mid  L l\  are  always 
loss  than  quadrants,  L B must  be  less  than  LQ.  The  difference  between 
them*  however,  can  never  he  of  more  than  Hiding  amount;  for,  as  the 
angle  QLH  increases,  QL  diminishes;  and  the  contrary. 

In  order  to  show  how  the  Hindus  li.-ue  arrived  at  a determination  of 
this  part  of  the  deflection  so  nearly  correct,  and  yet  not  quite  correct, 
we  will  cite  the  commentators  explanation  of  the  process.  He.  says: 
“The  ‘east’  ( pract ) of  the  equator  [i.c.,  apparently,  the  point  of  the 
equator  eastward  toward  which  the  small  circle  must  he  considered  as 
pointing  at  MJ  in  a point  00°  distant  from  that  where  a circle  drawn 
from  the  pole,  (dhruva)  through  the  planet  cuts  the  equator:”  that  is  to 
nay,  it  is  the  point  Q (Fig.  2-1),  a quadrant  from  O : “and  the  interval 
by  which  this  is  separated  from  the  ‘ cast’  of  the  ecliptic  at  90°  from  the 
pallet,  that  is  the  Ayana  valana''  Thin  is  entirely  correct,  and  would 
gtvfe  us  QL,  the  true  measure  of  the  deflection.  But  the  commentator 
goes  on  farther  to  say  that  since  thfc  interval,  when  the  planet  is  at  tho 


r 


4- 


- - \ i 

H 


Translation  and  Notes. 


139 


iv.  25.] 

solstice,  .is  nothing,  and  when  at  the  equinox  is  equal  to  the  greatest 
declination,  it  is  therefore  always  equal  to  the  declination  at  a quadrant’s 
distance  from  the  planet.  Tins  is,  as  wc  have  seen,  a false  conclusion, 
and  leads  to  an  erroneous  result : whether  they  who  made  the  rule  were 
aware  of  this,  but  deemed  the  process  a convenient  one,  and  its  result  a 
sufficiently  near  approximation  to  the  truth,  we  will  not  venture  to  say. 

The  other  part  of  the  operation,  to  determine  the  amount  of  deflec- 
tion of  the  circle,  of  declination  from  the  east  and  west  small  circle,  is 
considerably  more  difficult,  and  the  Hindu  process  correspondingly 
defective.  Wc  will  lir*t  present  the  explanation  of  it  which  the 
mentator  gives.  He  state*  the  problem  tlm* : 14  by  whatever  interval  ; 
the  directions  of  the  equator  an*  deflected  from  directions  correspond- 
ing to  those  of  the  prime  vertical,  northward  or  southward,  that  is  the 
deflection  due  to  latitude  (iikska  veil  ana).  Now  then:  if  a movable 
circle  be  drawn  through  the  pole  *»f  the  prime  vertical  (stuma)  and.  the 
point  occupied  by  the  planet  |i.  «*.,  the  circle  N M K,  Fig.  then' tlie 
interval  of  the  4 easts,’  at  the  distance  of  a quadrant  upon  each  of  tlie 
two  circles,  the  equator  and  the  prim**  vertical,  from  tlie  points  where 
they  are  respectively  cut  by  that  circle  |i.  c.,  from  T ami  V]  will  be  the 
deflection.  . . . Now’  when  the  plain  ! is  at  the  horizon  [a>  at  J >,  referred 
l-o  JE'],  then  that  interval  is  equal  t»  the  latitude  |Z(/] ; when -the  planet 
is  upon  the  meridian  ( v&myattanirrtta , “south  and  north  circle")  [i.  c., 
wlienitisat.lt,  referred  to  and  Z|,  then*  i-  no  mien al  [as  at  E'l. 
Hence,  by  the  following  proportion  — with  a due  of  the  hour-angle 
which  is  equal  to  radius  tin1  sine  of  dclh-.thui  for  latitude  is  equal  to 
the  sine  of  latitude ; then  with  any  gi\cn  sim-  of  the  hour-angle  what 
is  it? — a sine  of  latitude,  is  found,  of  whh-li  the  an*  U the  required  de- 
flection for  latitude."  This  is,  in  the  llimiu  form  of  statement,  this 
proportion  represented  by  the  rule,  in  \«tm*  '1 1,  \iz.  11 : sill  hit. : : sin 
nour-angle. : sin  deflection. 

It  seems  to  us  very  questionable,  at  least,  whetlnr  the.  Hindus  had 
any  more,  rigorous  dniiun^lratiou  than  this  of  the  process  they  adopted, 
or  knew  wherein  lay  tlie  niuccimirie*  of  the  latter.  These  wc  will  now 
proceed  to  point,  out.  In  the  liiM  place,  instead  of  measuring  the  £Qgle 
made  at  the  point  in  question,  .M,  by  tin1  two  small  circles,  the  east  and 
west  circle  ami  tliai  of  daily  mnltifion — which  would  be  the.  angle 
P M N — they  refer  the  body  to  the  equator  hv  a eirelo-  passing  through 
the' north  and  south  points  of  the  horizon,  and  measure  the  deflection 
of  tlie  equator  from  a small  east  ami  west  circle  at  its  intersection  with 
that  circle — which  is  the  angle  FT \.  Or,  if  we  suppose  that,  in  the 
process  formerly  explained,  no  regard  was  liad  to  the  circle  of  daily 
revolution,  D R,  the.  intention  being  to  measure  the  difference  in  direc- 
tion of  the  elliptic,  at.  M and  the  equator  at  O,  then  the.  twp  parts  of 
the  process  are  inconsistent  in  this,  that-  the  one  ta.  es  as  its  equatorial 
point  of  measurement  O,  and  the  other  T,  at  which  two  points  the 
direction  of  the  equator  is  ditferent.  But  neither  is  the  value  of  PT  X 
correctly  found.  For,  in  the  spherical  triangle  PNT,  to  find  the  jgtglc 
ut  T,  wo  should  make  the  proportion  * 

sin  PT  (or  K) : sin  P N : : sin  PNT : sin  PTN 
.But-,  as  the  third  term  in  this  proportion,  the  Hindus  introduce  the  sine- 


Sarya-Sifldhdn  to. 


[iv.  25- 


wo 

of  the  hour-angle,  Z V M or  MVN,  although  witli  a certain  modifica- 
tion Which  tlu*  commentary  prescribes,  and  which  makes  of  it  some- 
thing very  near  l lie  angle  T V X.  The  text  says  simply  natajya , “the 
sine  of  the  hour-angle M (for  nafa,  see  notes  to  iii.  34- .'JO,  and  14-10), 
but  the  commentary  specifies  that-,  to  find  the  desired  angle  in  degrees, 
we  must  multiply  tin*  hour-angle  in  time  by  1)0,  and  divide  by  the  half- 
day of  tin*  planet.  This  is  equivalent  to  making  a quadrant  of  that 
part  of  the  rirelc  of  diurnal  revolution  which  is  between  the  horizon 
and  the  meridian,  or  to  measuring  distanees  upon  DR  as  if  they  were 
•'jMQportional  parts  of  K'(J.  To  make  the  Hindu  proeess  correct,  the 
"product  of  this  modification  should  l»e  the  angle  I*  XT,  with  which, 
however,  it  only  coincides  at  the  horizon,  where  Imtli  T1*X  and  TN  1* 
become  right -singles,  and  at  the  meridian,  where  hutli  are  reduced  to 
nullity.  The  error  i>  closely  analogous  to  that  involved  in  the  former 
process,  and  is  of  slight  acrnuiit  when  latitude  is  small,  as  b also  the 
error  in  substituting  T for  <>  or  M when  neither  the  latitude  nor  the 
declination  is  great. 

The  direction  of  the  ecliptic  dcllcctiou  (iti/ana  vnlana)  is  the  same, 
evidently,  with  that  of  the  declination  a quadrant  eastward  from  the 
point  in  question  ; thus,  in  the  ease  illustrated  by  the  figure,  it  is  south. 
The  direetiun  of  the  equatorial  deflection  (itkshu  vulani i)  depends  upon 
the  position  of  the  point  enn.-ddrml  with  reference  to  the  meridian, 
being — in  northern  latitude**,  w alone  the  Hindu  >\<lcni  contem- 
plates— north  when  thal  point  b eu-t  of  the  meridian,  and  south  when 
west  of  it,  as  specifii.il  in  vcr<e  'l  \ : since,  for  iiMnncc,  H'  being  the 
east  point  .of  the  horizon.  the  equator  at  any  puiut  between  K'  and  ii 
points,  eastward,  toward  a point  north  of  tin-  prime  wrt'wal.  Iii  tin* 
casfe  fill1  whicjl  ihe  figure  is  dlnwu,  thru,  tin-  difi'ereiii'e  of  the  two  would 
bclhc  finally  resulting  deilcrtioii.  Sir.ce,  in  making  the  projection  of 
the  eclipse,  it  is  lahLpff  .is  a straight  line  (mi  ihe  illustration  gr\en  in 
connection  with  elnffller  \i),  it  ni'i-l  lie  ,-i-«  1 n«-i-«l  to  its  \ .ilm-  as  a sine; 
and  moreover,  siiuy  it.  is  laid  down  in  ;i  riivle  of  which  the  radius  is 
40  digits  (sec  below,  \i.  -J),  m-  in  which  one  dbil  equals  To' — for 
tt48(f"7-40  = 70',  nearly — that  mho  i-  reduced  i . it**  \ahic  in  digits  by 
dividing  it  by  To. 

Till:  general  subject  of  thb  pa^agi*.  Hi-  determination  of  directions 
during  an  eclipse,  fur  the  purpose  of  r-M.ihlbuiiig  the  portion-,  upon  the 
disk  of  the  eclipsed  body,  of  1 in-  points  of  miilarf,  immersion,  eiocrg- 
enee,  and  separation,  also  engaged  the  attention  of  the  H recks;  Ptolemy 
devotes  to  it  thn  eleventh  and  iwelfth  chapters  of  tin*  sixth  hook  of  his 
Svntaxis : hb  representation  of  direct  ions,  however,  ami  fon.-equeuth. 
his  method  of  calculation  a bn,  an*  different  from  those  here  exposed. 

26.  To  the  altitude  in  time  (unnnfa)  arid  a day  and  a half,  and 
divide  by  a half-day;  by  tho  quotient  divide  the  latitudes  and 
the  disks;  the  results  are  the  measures  of  those  quantities  in 
digits  (angulo), 

;By  this  process  due  amount  is  taken,  in  Hie  projection  of  mi  eclipse, 
of  the  apparent,  increase  in  magnitude  of  the  heavenly  bodies  when 
near  the  horizon,  'flic  theory  lying  at  the  foundation  of  the  rule  is  this  ; 


Translation  and  Notes.' 


v.  1.] 


14^ 


that  three  minutes  of  are  at  flic  horizon,  and  four  at  the  zenith,  are 
equal  to  a digit,  the  diftereure  between  the  two,  or  the  excess' above 
three  minutes  of  the  equivalent,  of  a digit  at  the  zenith,  being  one 
minute.  To  ascertain,  then,  what  will  bo,  at  any  given  altitude,  the 
exdcss  above  three  ininuli-s  of  the  equivalent,  of  a digit,  we  ought  prop* 
erly,  according  to  the  mniinonturv,  l<>  make  the  proportion 
11:1'::  hii  altitude  : rnrresp.  excess 
Since,  however,  il  would  be  a lung  and  tedious  proems  to  (ind  the 
tilde  and  its  sine,  another  and  npproximulixe  pmpnrtinu  is  siibatitmHU 
for  this  “by  the  blessed  Sim,"  as  the  eoiniiientarv  phrases  it,  “throtigllQ| 
compassion  for  mankind,  and  out  of  regard  to  tin-  very  slight  difference1, 
between  the  two/’  It  is  assumed  that  the  (,f  fnui*  minutes  to  the  ■: 

digit-  will  be  always  the  true  «»n«-  at  the  iinun  *»f  the  planet  in  question^ 
or  whenever  it  crosses  the  meridian,  all li« mirli  not  at  tin-  zenith;  aridtSO.. 
likewise,  that  the  relation  of  the  aliiludi  to  ‘Jm-  mux  be  umasured^by 
that  of  the  time  since  lining  »»r  until  M-Uing  \ unnut  a — sec  above,  iii. 
37-30)  to  a half-day.  lienee  the  proportion  hi.*-:<.»nies 

half-day  : 1 ' : : altitude  in  time  : corrc&p.  excess 


and  tlie  excess  of  the  digital  equivalent  above  3'  equals 

Adding,  now.  the  three  minuter  and  bringing  tlicnii  into  the  fractional 
expression,  we  have 


equiv.  of  digit  iu  minute*  at  given  time 


si  It . in  time  4 3 luilf-davs 
half  day 


Tlie  title  of  the  fou rr  1 1 < li:ipli-r  U cfnoh'fvj^thifyuhikviru,  11  chapter  of 
lunar  eclipses/"  u*  that  tin*  !iit!i  U > irijniir'ihvnn*ltiihim,  ■■  •■haptor  ©f 
solar  eclipse*."'  In  truth,  hmi.o.-r  \\u>  pr.fc-sM'v  and  explanations  of 
this  chapter  applx  n«»t  I**'-*  t.»  *nhr  than  io  lunar  eclipses,  while  the  next 
treats  only  of  parallax,  a.-  eiit-MTiig  into  tlu*  raleulation  of  a solar  eclipse. 
Wo  have  taken  tin-  liberti.  ilfnT'iiv,  ..f  modifying  neennlinglv  the 
headings  which  we  haxe  pivti\»*d  l.»  tin-  ••hapter*. 


r II  A 1*  T K U V. 


or  P \ KAliliAX  l\  A SOL  Alt  KHJIVE. 

Contents:— 1,  when  there  is  no  parallax  in  longitude.  « ■ no  parallax  in  latitude ; 
2,  causes  of  parallax;  S,  to  find  ilie  orient-sine  ; ■]-.>,  the  i icridian-Mue ; 5-7,  and 
the  sines  of  ecliptic  xei»i*li-dir  lance  and  altitude  ; 7-9,  to  ti..d  the  amount,  in  time, 
of  the  parallax  in  longitude ; \\  its  application  in  detern  inintr  the  moment  of 
apparent  conjunction;  10-11,  to  find  die  amount,  in  arc,  of  the  parallax  in.l|M- 
tude;  12-13,  it*  application  in  calculating  an  eclipse;  H-17,  application  o£pfc 
parallax  in  longitude  in  determining  the  momenta  of  contact,  of  reparation,  ctC^\ 

i.‘  When  the  sun’s  place  is  coincident  with  the  meridi 
ecliptic-point  ( madhi/ahgna\  there  takes  place  no  parallax  | 


142 


S&rya-Siddh&nta. 


[y.  Id 


longitude  (harija) : farther,  when  terrestrial  latitude  (aksha)  and 
north  declination  of  tho  meridian  ecliptic-point  (madliyabha)  are 
the  same,  there  takes  place  no  parallax  in  latitude  (avanati). 

r Tlie  latter  of  these  specifications  is  entirely  accurate : when  the  north 
declination  of  that  point,  of  the  ecliptic  which  is  at  the  moment  upon 
the  meridian  ( madhi/atapna  ; see  iii.  -19)  is  equal  to  the  observer’s  lati- 
tude— regarded  by  the  Hindus  as  always  north — the  ecliptic  itself 
.posses  through  tin1  zenith,  and  becomes  a vertical  circle;  of  course,  then, 
®juie  effect  of  parallax  would  In:  only  to  depress  the  body  in  that  circle, 
not  to  throw  it  out  of  it.  The  other  is  less  exact : when  the  Run  is 
upon  the  meridian,  there  is,  indeed,  no  parallax  in  right,  ascension,  hut 
there  is  parallax  in  longitude,  uulcs<  the  ecliptic,  is  also  bisected  by  the 
meridian.  Hero,  as  below,  in  verses  8 and  9,  the  text  commits  the 
inaccuracy  of  substituting  the  meridian  ecliptic-point  (L  in  Fig.  20)  for 
the  central  or  highest  point  of  the  ecliptic  (1»  in  the  same  figure).  The 
latter  point,  although  we  arc  taught  below  (vv.  ,r>-7)  to  calculate  the  sine 
and  cosine  of  its  zenith-distance,  is  not  once  distinctly  mentioned  in  the 
text;  the  commentary  culls  it  Irib/iomilatpta , “the  orient  ccliptic-point 
( Ingna — see  above,  iii.  415--4N  : il  is  the  point  ('  in  Kig.  2G)  less  three 
signs.”  Tlie  commentary  points  mil  thi>  inaccuracy  oil  the  part  of  the  text. 

In  order  to  illustrate  the  Hindu  method  of  looking  at  the  subject  of 
parallax,  we  make  the  following  citation  from  the  general  exposition  of 
it  given  by  the  commentator  under  this  verse  : 14  At  the  end  of  the  day 
of  new  moon  (amdvusija)  the  »uu  and  moon  have  the  same  longitude; 
if.  now,  the  moon  has  no  latitude,  then  a line  drawn  from  tlie  earth's 

centre  [O  in  the  accompanying 
* 24,  figure]  to  the  sun’s  place  [»S]  just 

touches  the  inooit  [ M ] : hence, 
at  the  centre,  tlie  moon  becomes 
an  eclipsing,  and  the  sun  an 
eclipsed,  body  Since,  however, 
men  are  not  at  tin*  earth’s  centre, 
(fftirb/ta,  “ womh")  but  upon  tho 
cart  h\s  surface  ( prshfha . 14  back”), 
a ime  drawn  from  the  earth's 
surface  1 1 > | up  to  the  sun  docs 
not  just  touch  the  moon ; luit  it 
cuts  the  moon's  sphere  above  the 
point  occupied  by  the  moon  [at 
m],  and  when  the  moon  arrive* 
at  this  point,  then  is  she  at  the 
earth's  surface  the  edipsor  of 
the  sun.  Hut.  when  the  sun  is  at. 
tho  zenith  ( khamadhya , 44  mid- 
heaven”),  then  the  lines  drawn  up  to  the  sun  from  the  earth’s  centre 
and  aurfucfl,  being  one  and  the  same,  touch  the  moon,  and  so  the  moon 
becomes  an  eclipsing  body  at  the  end  of  the  day  of  new  moon.  Hence, 
tod;  the  interval  [\1  w]  of  the  lines  from  the  earth’s  centre  and  surface 
is  the  parallax  (fambrma)." 


Translation  and  Notes. 


148 


It  is  evident  from  this  explication  how  far  the  Hindu  view  of  parallax 
is  coincident  with  our  own.  The  principle  is  th^same,  hut  its  applica- 
tion is  somewhat  different.  Instead  of  taking  the  parallax  ataolutelv, 
determining  that  for  the  sun,  which  is  BK(.\  and  that  for  the  irioon, 
which  is  B M the  Hindus  look  at  the  subject  practically,  as  it  must  be 
taken  account  of  in  the  calculation  of  an  eclipse,  and  calculate  only  the 
difference  of  the  two  parallaxes,  which  is  m 1)  M,  nr,  what  is  virtually 
the  same  thing,  M C in.  The  Surya-Siildlianta,  however,  as  wo.  shall  see 
hereafter  more,  plainly,  takes  no  wemmt  of  any  case,  in  whieli  the  line 
CSS  would  not  pass  through  M,  that  is  to  say,  the  'noon's  latitude  iff. 
neglected,  and  her  parallax  calculated  as  if  she  wen;  in  the  eeliptie. 

\Vc  cite,  farther  from  the  coiiimculary,  in  illustration  of  the  resolution 
of  the  parallax  into  parallax  in  longitude  and  parallax  in  latitude. 

“Now  by  how  many  degrees,  measured  on  the  moon's  sphere  [gola\ 
the  line  drawn  from  the  earth's  surface  up  to  the.  sun  cuts  the  moon’s 
vertical  citric  (thyrri/n)  above  the  point  occupied  l»y  the  moon — this  is, 
when  the  vertical  circle  and  the  i*c!iptic  cniui-idc,  the  moon's  parallax  in 
longitude  (luinbanu).  But  when  the  eeliptie  deviates  from  a vertical 
circle,  then,  to  the  point  where  the  line  fimu  the.  earth's  suriiu-e  cuts  the 
mooir.s  sphere  on  the  moon's  vertical  circle  almvc  the  mnmi  |i.  e.v  to  m, 


1 

/. 

\ 

\ 

/ l 

X p\ 

j M : 

■ \ 

„ L _ 

\ \ N 

A 

< 1 

25  Tig.  ifo],  draw  through  the  pole 

of  the  ecliptic  (XW antbn)  a cir- 
cle | V'  in  //']  iiorih  ami  south  to 
iheeclijiiie  on  the  nmon's  sphere 
and  then  the  east  and 
w « interval  f M //'  | on  the  eclip- 
tic l.  twteii  the  point,  occupied 
l»y  the  moon  [_\|j  ami  the  point 

where  the  circle  as  drawn  cuts 
the  ecliptic  on  the  moon's  sphere 
[V]  is  the  moon's  true  (spAtrfa) 
parallax  in  longitude,  in  minutes,  nud  is  the  perpendicular  (io/£).  And 
since  the  moon  moves  along  w it h the  ecliptic,  the  north  and  south  inter- 
val, upon  the  circle  wo  have  drawn,  between  the  ecliptic  and  the  verbal 
circle  | j#i  n#|  is,  in  minutes,  rho  parallax  in  latitude  (nati);  wliich  is  the 
base  (b/mja).  The  interval,  in  minutes,  on  the  vertical  circle  [ZA]| 
between  the  lines  from  the  earth's  centre  and  surface  [w  M],  is  tlie  ver- 
tical parallax  (d nflarnbuna),  and  the  hvpotlienusc.'’ 

The  conception  here  presented,  it  will  he  noticed,  is  that  tho  moon’s 
path,  or  the  “ ecliptic  mi  the  moon’s  sphere,”  is  depressed  away  from 
CL,  which  might  he  called  ihc  “ ecliptic  on  tie*  sun's  sphere,”  tolsax 
amount  measured  as  latitude  hymn',  and  as  longitude  by  n'M.  To 
our  apprehension,  maAl,  rather  than  mn'M,  won  l be  the  triaogfc  cf 
resolution  : the  t0o  are  virtually  ec]iial. 

The  commentary  then  goes  on  thriller  to  explain  that  when  the  ver- 
tical citric  and  the.  secondary  to  the  ecliptic  coincide,  the  parallax 
longitude  disappears,  the  w hole  vertical  parallax  becoming 'parallax  in 
latitude : and  again,  when  the  vertical  circle  and  the  ecliptic  coincide, 


the  parallax  in  latitude  disappears,  the  whole  vertical  parallax  becoming 
parallax  in  longitude. 


144  S&rya-Siddhdnta , [v.  1- 

The  term  uniformly  employed  by  the  commentary,  ami  more  usually 
by  the  text*  to  express  parallax  in  longitude,  namely  lambana , is  from 
the  same  root  which  we  have  already  more  than  once  had  occasion  to 
notice  (see  above,  under  i.  25,  60),  and  means  literally  “hauging  down- 
ward/’ Iu  this  verse,  as  once  or  twice  later  (vv.  14,  1G),  the  text  uses 
harija,  which  the  commentary  explains  as  c()iiivalent  to  kshitija,  “pro- 
duced by  the  earth this  does  not  seem  very  plausible,  but  we  have 
nothing  better  to  suggest.  Fur  parallax  in  latitude  the  text  presents 
only  the  term  aranatf . “bending  downward,  depression/’  the  commen- 
tary always  substitutes  for  it  nuti,  which  lias  nearly  the  same  souse,  and 
is  the  ciisiomarv  modern  term. 

2.  Ilow  parallax  in  latitude  arises  by  reason  of  the  difference 
of  place  (*/*■*/!)  ami  time  (bilu),  and  also  parallax  in  longitude 
(Jambanu)  from  direction  (/lie)  eastward  or  the  contrary — that  is 
now  to  be  explained. 

This  distribution  «»f  the  throe  elements  of  direction,  place,  and  time, 
as  causes  respectively  parallax  in  longitude  and  in  latitude,  is  some- 
what arbitrary.  'Ihe  vr>e  is  to  be  taken,  however,  rather  as  a general 
introduction  In  tlio  subject  *4'  the  chapter,  than  as  a systematic  state- 
ment of  tin-  causes  of  parull-sx. 

3.  f'akuilatc.  by  tin*  equivalents  iu  oblique  ascension  {udaya- 
savas)  of  the  nbserverV  place,  the;  orient  ecliptic-point  {lw/nn)  for 
the  moment  of  eonjnuctiiiii  (purmrinaflyus):  multiply  the  sine 
of  its  longitude  by  ihe  mih:  uf  givntcsL  declination,  and  divide 
by  the  sine  of  co-hit  it  tide  (/#n#//.i#j:  the  result  is  the  quantity 
known  us  the.  orient-sine  ymfayt). 

The  object  uf  lliis  first,  *tep  in  tin*  rat  her  icilimis  operation  of  calcu- 
lating the  parallax  U in  liud  Ibr  a giwui  lnoment  — In-re  the  moment  of 
true  conjunction- -the  ^ine  of  amplitude  «»f  that  point  of  the  ecliptic, 
which  is  then  upon  the  cnsl'Th  hori/<in.  In  the  iii>l  place  the  longitude 
of  that  point  \hiym)  i<s  determined^  by  the  data  and  methods  taught 
above,  ill  iii.  -16-48,  and  which  are  sutliei'uitiy  explained  iu  the  note  to 
that  passage:  then  its  sine  of  amplitude  b,  found,  by  a process  which  is 
a combination  of  that  for  finding  the  decliu.'lion  from  the  longitude, 
and  that  for  finding  the.  amplitude  from  the  declination.  TIuw,  by  ii.  28, 
it : sin  gr.  •led. : : sin  long. : ^in  deck 
and,  by  iii.  22-2-?, 

sin  co-1  at. : R : : sin  dec],  : sin  ampl. 
lienee,  by  combining  terms,  wo  have. 

sin  co-lat. : sin  gr.  dec!. : : sin  long. : sin  (flbpl. 

This  sine  of  amplitude  receives  tin;  technical  name  of  udaya , or 
udayujyu  .^tho  lileral  meaning  of  udaya  is  simply  “rising/’ 

4.  Then,  by  means  of’  the  equivalents  in  right  ascension 
.(Lrnkodaydsavafs),  lind  the  ecliptic-point.  (lagna)  called  that  of  the 
meridian  {madhyd) : of  the  declination  of  that  point  and  the  lati- 


Y.  O.]  Translation  and  Notes . 146 

tudeof  the  observer  take  the  sum,  when  their  direction  is  the 
same;  otherwise,  take  their  difference. 

6.  The  result  is  the  meridian  zenith-distance,  in  degrees  (na/tf? i- 
fds):  its  sine  is  denominated  the  meridian-siue  ( madhyajya ).  . . . 

The  accompanying  figure  (Fig.  iiG)  will  assist  the  comprehension  of 
this  and  the  following  processes.  Let  X K S \Y  be  a horizontal  plane, 

X S the  projection  upon  it  of 
the  meridian,  and  £ W that 
of  the  prime,  vertical,  Z being 
the  zenith.  Let  0 LTbc  the 
oeliplir.  Then  C i^lhc  orient 
ecliptic-point  (luynt i),  and  C 
])  the  sine  of  its  amplitude 
(udat/tijya),  found  by  the  last 
process.  The  meridian  ecliptic 
point  (iiKtfUii/ulutpta)  is  L:  it 
is  ascertained  hy  the  method 
prescribed  in  iii.  40,  above. 
Its  dislanee  from  the  zenith 
is  found  from  its  ■declination 
and  the  latitude  of  the  place 
of  ohsenntioii.  as  taught  in 
iii.  L'O and  the  sine  of 
that  distance,  by  which,  in 
the  figure,  it  is  seen  projected, 
is  Z L : it  is  railed  hy  the  icrlmica]  name  A’/q/7/d,  which  wc  have 
translated  14  meridian-sine.'* 

f> Multiply  tlir  mcridian-sino  by  the  orient-sine,  and  divide 

by  radius:  square  the  result. 

(j.  And  subtract  it  l‘n»ni  tin*  square.  of  the  meridian-pine:  the 
square,  root  of  the  remainder  is  the  sine  of  ecliptic  zenith-distance 
(urkkshcjnt) ; the  square  root  of  the.  difference  of  the.  squares  of 
that  ami  radius  is  the  sine  of  ecliptic-altitude  ('hyjati). 

Hero,  wo  are  taught  how  to  line!  the  sines  of  the  zenith-distance  and 
altitude  respectively  of  that  point  of  the  ecliptic  w liii-li  has  greatest  alti- 
tude, or  is  nearest  to  the  zenith,  and  which  is  also  the  central  point 
of  the  portion  of  the  ecliptic  nU»\e  the  horizon:  it-  is  called  by  the 
commentary,  :i*  already  noticed  (>ce  note  to  v.  1),  tnhhonalayna.  Thus, 
in  the  last  figure,  if  QR  b » ihe  vertical  circle  passing  through  the  pole 
of  the  ecliptic,  l,#t  and  cutting  the  ecliptic,  C'i,  in  B,  R is  the  central 
ccliptic-point  {friUntmthiytin),  and  the  arcs  seen  projected  in  ZB  and 
H It  are  its  zcr.ith-distanee  and  altitude  respect ive.y.  In  order,  now,  to 
find  the  sine  of  ZB,  we  first  find  that  of  B L,  and  by  the  following  pro- 
cess. Cl>  is  the  orient-sine,  already  found.  Blit  since  OZ  and  CPf 
are  quadrants,  (’  is  a pole  of  the  vertical  circle  QR,  and  CR  is  a quad- 
rant. KS  is  also  a quadrant.:  take  away  their  common  part  CS,  and 
C IS  remains  equal  to  S R,  and  the  sine  of  the  latter,  S 0,  is  equal  to 
that-of  the  former,  <’  I.),  the  u oricnt-sine.M  Now,  then,  ZB  L is  treated 


146  Surya-Siddhdnta , [v.  8-  , 

as  if  it  were  a plane  horizontal  triangle,  ami  similar  to  Z 0 8,  and  tko 
proportion  is  made 

ZS:SO:ZL:BL 

Or  K : or. -si lie  : : mcr.-sine  : 11  L 

This  is  so  far  a correct  process,  that  it  gives  the  true  sine  of  the  arc 
BL:  for,  hy  spherical  trigonometry,  in  the  spherical  triangle  ZBL, 
right-angled  at  11, 

sin  Z 11 L : sin  l>  Z L : : sin  aiv  Z L : sin  arc  l>  L 
or  U : S O : : Z L : sin  II L 

But  the  third  side  of  u plane  right-angled  triangle  of  which  the  sines 
of  the  arcs  Z II  and  Z L are  hypothcnusc  and  porpendieular,  is  not  the 
sine  of  B L.  If  we  concern  i1  the  two  funner  sines  to  he  drawn  from  Z, 
meeting  in  b and  l respect i\  civ  the  lines  draw  ii  from  11  ami  L to  the 
centre,  then  the  line  joining  hi  will  he  the  third  side.  Iicing  plainly  less 
than  sin  l>  L Hein  e,  on  subtracting  sin3  11  L from  sinzZ  L,  and  taking 
the  si  pin  re  root  of  the  remainder,  we  obtain,  not  sin  Z II,  but  a less  ipian- 
tity,  wliieli  may  rendih  be  shown,  by  spherieal  trigonometry,  to  be 
sin  ZB  cos  ]1  L.  The  value,  then,  of  t he-  sine  of  ecliptic  zenith-distance 
( drkkshepa ) as  determined  by  this  process,  is  always  less  than  the  truth, 
and  as  the  corresponding  cosine  (dr'/gati)  is  found  hv  subtracting  the 
square  of  the  sine  from  that  of  radius,  and  taking  tin*  square  root  of  the 
remainder,  its  value  is  always  proportionally  greater  than  the  truth.  This 
inaccuracy  is  noticed  by  the  cniumciit.'itor,  who  points  out  correctly  its 
reason  and  nature : probably  if  was  also  known  to  those  who  framed  the 
rule,  but  disregarded,  as  not  sufficient  to  vitiate  the  general  character  of 
the  process:  and  it  may,  indeed,  well  enough  pass  unnoticed  among 
all  the  other  inaccuracies  involved  in  the  Hindu  calculations  of  the 
parallax. 

As  regards  the  terms  employed  to  express  the  sines  of  ecliptic  zenith- 
distance  and  altitude,  we  have  already  met  with  the  first  member  of  cadi 
compound,  drf,  literally  ‘‘sight.”  in  other  connected  uses:  as  in  dryjyd, 
“sine  of  zenith-distance"  (see  above,  iii.  :i.T),  dryrrttj,  “wriicnl-cirelo" 
(commentary  to  the  first  verse  of  this  chapter)  “ here  it.  is  combined 
with  Words  which  seem  to  he  rather  arbitrarily  chosen,  1o  form  techni- 
cal appellations  fur  quantities  used  only  ii.  this  process:  tlm  literal 
meaning  of  kihejia  i«  “throwing,  hurling;”  of  yati%  “gait,  motion.” 

7.  The  fiinc  and  cosine  of  meridian  zenith-distance  (natannut) 
are  the  approximate  (asphnfrz)  sines  of  ecliptic  zenith-distance 
and  altitude  (ilrkfcshcpa,  drygnti).  . . . 

This  is  intended  ns  an  allowable  simplification  of  the  above  process 
for  finding  the  sines  of  ecliptic  zenith-distance  and  altitude,  by  substi- 
tuting for  them  other  quantities  to  which  they  arc  nearly  equivalent, 
and  which  arc  easier  of  calculation.  These  are  the  sines  of  zenith- 
distance  and  altitude  of  the  meridian  ecliptic-point  (nuidhyalagna — L in 
Fig.  28)  tin!  former  of  which  has  already  been  made  an  clement  in  the 
other  process,  under  the  name  of  “ meridian-sine”  (madhyajyA).  It 
indeed,  from  the  terms  of  the  text,  be  doubtful  of  what  point  the 
altitude  and  zenith-distance  were  to  be  taken ; a passage  cited  by  the 


Translation  and  Notes. 


147 


v.  8.] 

commentator  from  Bhfakara’s  Siddh&nta-^iromani  (fennel  on  page  221 
of  the  published  edition  of  the  tianit&dhv&ya)  directs  the  sines  of  zenith- 
distance  and  altitude  of  B (tribhonnlarjna)  when  upon  the  meridian — 
that  is  to  say,  the  sine  und  casino  of  the  arc  Z F — to  he  substituted  for 
those  of  ZB  in  a hasty  process:  but  the  value  of  the  sine  would  iu 
this  ease  be  too  small,  as  in  the  other  it  was  too  great:  and  as  the  text 
nowhere  directly  recognizes  the  point  B,  and  as  directions  have  been 
given  in  verse  5 for  finding  the  meridian  zenith-distance  of  L#,  it  seems 
hardly  to  admit  of  a douht  that  the  latter  is  the  point  to  which  the  text 
here  intern  Is  to  refer.  * 

Probably  the  permission  to  make  this  substitution  is  only  meant  to 
apply  to  cases  where  Z L is  of  small  amount,  or  where  C has  but  little 
amplitude. 

• 

7.  . . . Divide  the  square  of  the  sine  of  one  sign  by  the  sine 
called  that  of  ecliptic-altitude  (# Irfjgalijh'd ) ; the  cpioticnt  is  the 
41  divisor”  (rhetla). 

8.  By  this  “divisor”  divide  the  sine,  of  the  interval  between 
the  meridian  ecliptic-point  ( madhyalwjna ) and  the  sun’s  place: 
the  quotient  is  to  be  regarded  as  the  parallax  in  longitude  (t am- 
buna)  of  the  sun  and  moon.  eastward  or  westward,  in  nadts,  etc. 

The  true  nature  of  the  prucos*  hv  which  lhi<  liual  rule  fur  finding  the 
parallax  in  longitude  n .Claim'd  U altogether  iiidilt-u  from  sight  under 
the  form  in  which  the  rule  is  stated.  Its  method  n a>  follows: 

We  have  seen,  in  connection  with  the  fir-t  \itm*  of  the  preceding 
chapter,  that  the  greatest,  parallaxes  of  the  Min  and  moon  are  quite, 
nearly  equivalent  to  thcBnnaau  motion  of  each  during  t nailis.  lienee, 
were  hotli  bodies  in  the  hoi'i/mi,  and  the-  ecliptic  a vertical  circle,  the 
moon  would  he  depressed  in  In t orbit  lu  i«»w  the  -mi  to  an  amount  equal 
to  her  excess  in  motion  during  -I  liadi".  This.  then,  i*  the  moon's 
greatest  horizontal  parallax  iu  hmgitnd**.  To  find  what  it  would  beat 
any  utlicr  ]»oinl  iu  the  ecliptic.  still  cm.-idered  a>  a vertical  circle,  we 
make  the  proportion 

U : i (hor.  par.) : : sin  zcn.-di-l. : vert,  parallax 

This  proportion  is  entirely  correct,  and  in  accordance  with  our  modem 
rule  that,  with  a given  distance,  the  parallax  of  a body  varies  as  the  sine 
of  its  /.euith-distaucc : whether  the  Hindus  had  made  a rigorous  de- 
monstration of  its  truth,  or  whether,  as  in  so  many  other  eases,  seeing 
that  the  parallax  was  greatest,  when  the  sine  of  zenith -distance  wan 
greatest,  and  nothing  when  this  was  nothing,  they  assumed  it  1o  vary 
in  the  interval  as  the.  sine  of  zenith-distance,  faying  M if,  with  a sine 
of  zenith-distance  which  is  equal  to  radius,  the  j irallax  is  four  u&dis, 
with  a given  sine  of  zenith-distance  what  is  it  i" — diis  we  will  not  ven- 
ture to  determine. 

But  now  is  to  be  considered  the  farther  case  in  whieli  the  celiptic  is 
not  h vertical  circle,  but  is  depressed  below'  the  zenith  a certain  distance, 
measured  by  the  sine  of  ecliptic  zenith-distance  (drifohepa),  already 
found,  Jlcre  again,  noting  that  tho  parallax  is  all  to  be  reckoned  ns 
parallax  in  longitude  when  the  ecliptic  is  a vertical  circle,  or  when  tho 


1 4&:  Sdrya'Siddk&nta^  [v.  8- 

aine  of  ecliptic-altitude  is  greatest,  ami  that  it  would  be  only  parallax 
in  latitude  when  the  ecliptic  should  he  a horizontal  circle,  or  wnen  the 
nine  of  ecliptic-altitude  should  be  reduced  to  nothing,  the  Hindus  assume 
it  to  vary  in  the  inton  al  as  that  sine,  and  accordingly  make  the  propor- 
tion: “if  with  a sine  of  ecliptic  altitude  that  is  equal  to  radius,  the  par- 
allax in  longitude  is  equal  to  the  vertical  parallax,  with  any  given  sine 
of  ecliptic-altitude  what  is  it?M — or,  inverting  the  middle  terms, 

II  : sin  rrl.-ah. : : vert.  paruUax  : parallax  in  long. 

But  we  lyul  before 

]»  : 4 : : sin  zen.-dist.  : vert,  parallax 

hence,  by  combining  terms, 

Ua  : 4 siu eel. -alt.: : sin  zen.-dist. : parallax  in  long. 

For  the  third  term  of  this  proportion,  now,  is  substituted  the  sine  of  the1 
distance  of  the  given  point  from  the  central  ecliptic-point:  that  is  to  say, 
Jim  (Fig.  26)  is  substituted  lur  Z in  ; the  two  are  in  fact  of  equal  value 
ouly  when  they  coincide,  or  else  at  the  horizon,  when  each  becomes  a 
quadrant;  but  the  error  invobed  in  tin*  substitution  is  greatly  lessened 
by  the  circumstance  that,  as  it  increases  in  proportional  amount,  the 
parallax  in  longitude  itself  decreases,  until  at  JJ  the  latter  is  reduced  to 
nullity,  as  is  the  vertical  parallax  at  Z.  The  text,  indeed,  as  in  verses 
1 and  6,  puls  madhtfn hnrnu.  L for  trihhonuhijna . 1$,  in  reckoning  this 
distance:  but  the  commentary,  without  ceremony  or  apology.  roads  the 
latter  fur  the  funner.  These  substitution'*  being  made,  and  the  propor- 
tion being  reduced  to  the  form  of  an  equation,  we  hate 

. , Kin  ili-t.X  4 mu  ecl.-ult. 

par.  in  lung.  = ^ , 

which  reduce*  to 

sin  (list.  sin 

- — - or 

■ It4  ~ >1  sill  rcl.-alt.  ] hm  cel.  all. 

and  siucc  4R2z=  (.jli)2,  and  .lit  — -in  :sn  , in-  haw*  finally 

. , sin  il.-t. 

nar.  ill  lnii".  . 

- in  - ..«» " -ill  eil.-.ill. 

which  is  the  rule  given  in  tin*  text.  Tu  t ii-  •iciiominnlor  of  the  fraction, 
in  its  final  form,  is  given  the  technical  name  of  chM*u  11  divisor,"  which 
word  we  have  find  before  similarly  iim-J,  tu  designate  oiu*  of  the  factors 
in  a complicated  operation  (see.  ubn'.c,  ii i.  :{•>,  USj. 

\Yc  will  now  examine  the  uuiTee.Lness  of  the  second  principal  propor- 
tion from  which  the  rule  is  deduced.  Jt  is,  in  terms  of  the  last  figure 
(Kig.  20), 

R : fin  Z I*  (=IS  Ji) : : m M : m » 

Assuming  the  equality  of  the  little  triangles  .M  m n and  M m and 
accordingly  that  of  the  angles  mMw  and  M m which  latter  equals 
ZmP1,  wc  have,  by  spherical  trigonometry,  as  a true  proportion, 
t sin  m vf  M : sin  M in  nf : : m M : m n7 
or  ft : sin  in  n 

J fence  the  former  proportion,  is  correct  only  when  sin  ZP'and  sin 
ZmP  are  equal ; that  is  to  say,  when  Z V'  measures  the  angle  ZmP; 


Translation  and  Notes. 


v.  10.] 


149" 


and  this  can  be  the  case  only  when  Zm,  an  well  as  P'm,  is  a quadrant, 
or  when  m is  on  the  horizon.  Here  again,  however,  precisely  as  in  the 
case  last  noticed,  the  importance  of  the  error  is  kept  within  very  narrow 
limits  by  the  fact  that,  as  its  relative  consequence  increases,  the  amount 
of  the  parallax  in  longitude  affected  hy  it  diminishes. 

9.  When  tlic  sun’s  longitude  is  greater  than  that  of  the  meri- 
dian ecliptic-point  ( inadlnjahigna ),  subtract  the  parallax  in  longi- 
tude from  the  end  of  the  lunar  day;  when  less,  add  the  same: 
repeat  the  process  until  all  is  fixed. 

The  text  so  pertinaciously  reads  l!  meridian  ccliptic-point”  (madhya- 
lagnu)  where  we  should  expect,  and  ought  to  have,  “ central  ccliptic- 
point”  ( tribhonalftt/na ),  that  we  arc  almost  ready  to  suspect,  it  of  mean- 
ing 1o  designate  the  latter  point  by  the  former  name.  It  i«  sufficiently 
clear  that,  whemwor  the  sun  and  moon  are  to  the  eastward  of  the  cen- 
tral ecliptic-point,  the  rllect  nf  the  parallax  in  longitude  w ill  bo  to  throw 
the  moon  forward  on  her  orbit  bcymid  the  sun,  and  so  to  range  the  time 
of  apparent  in  precede  that  of  real  conjunction;  and  the  contrary. 
Hence,  in  the  eastern  liciiiNplii.r<\  the  parallax,  in  time,  is  subtractive, 
while  in  the  western  it  is  additive.  Ih.it  a single  calculation- and  appli- 
cation of  the  correction  fur  parallax  is  nut  enough;  the  moment  of  ap- 
parent conjunction  imM  he  found  by  a scries  of  successive  approxima- 
tions : since  if,  lor  instance.  the  moment  of  true  conjunction  is  25n  2T, 
and  the  calculated  parallax  in  longitude  for  that  moment  is  2n21v.  the 
apparent  end  nf  the  lunar  day  will  nut  ho  at  27“  because  at  the 
latter  time  tin-  parallax  will  be  greater  than  2“  21v.  d -ferring  accordingly 
still  farther  the  time  nf  cuiijiinetiuii ; and  on.  The  commentary  ex- 
plain* the  Method  uf  procedure  iiimv  f.iily.  a*  follows ; for  the  moment 
of  true  conjunction  in  longitude  cah-ulate.  the  parallax  in  longitude,  and 
apply  it  to  that  moment : for  the  time  thus  found  calculate  the  parallax 
anew,  and  ajipK  it  t«»  ilic  moincni  nf  true  conjunction : again,  for  the 
time  found  a>  lie1  result  of  this  proco*.  calculate  the  parallax,  and  ap- 
ply it  as  before;  and  so  proceed,  until  a moment  is  armed  at,  at  which 
the  dillcrc.nec  in  actual  longitude,  according  to  tlus  motions  of  the  two 
planets,  will  just  equal  ami  counterbalance  the  parallax  in  longitude. 

The  accuracy  of  this  approximate  process  cannot  but  be  somewhat 
impaired  by  the  circumstance  that,  while  the  parallax  is  reckoned  in 
difference  of  mean  motions,  the  corrections  of  longitude  must  be  made 
in  true  motions.  Indeed,  the  reckoning  of  the  horizontal  parallax  in 
time  as  4 uadis,  whatever  be  the  rate  of  motion  of  the  sun  and  moon,  ia 
one  of  the  mu*t  palpable  among  the  many  errors  which  the  Hindu  pro- 
cess involves. 

To  ascertain  the  moment  of  apparent  conjunct!  n in  longitude,  only 
the  parallax  in  longitude  requires  to  be  known ; but  to  determine  the 
lime  of  occurrence  of  the  oLlicr  phases  of  the  eclipse,  it  is  necessary  to 
take  into  account  the  parallax  in  latitude,  the  ascertainment  qf  which  is 
accordingly  made  the  subject  of  the  next  rule. 

10.  If  the  Bine  of  ecliptic  zenith-distance  (drkkphepa)  be  multi- 
plied by  the  difference  of  the  mean  motions  of  the  sun  and 

SO 


150  Surya-Siddhdnta,  [v.  10-' 

71  i 

moon,  and  divided  by  fifteen  times  radius,  the  result  will  be  the 
parallax  in  latitude  (ncumti). 

As  the  sun's*  greatest  parallax  is  equal  to  the  fifteenth  part  of  his 
mean  daily  motion,  and  that  of  the  moon  to  the  fifteenth  part  of  hers 
(see  note  to  iv.  1,  above),  the  excess  of  the  moon's  parallax  over  that  of 
the  sun  is  equal,  when  greatest,  to  one  fifteenth  of  1 lie  difference  of 
their  respective  mean  daily  motions.  This  will  he  the  value  of  tho 
parallax  in  latitude  when  the  ecliptic  coincides  with  the  horizon,  or 
when  the  sine  of  ecliptic  /cidth-di.-tunce  heroines  equal  to  radius.  On 
the  other  hand,  the  parallax  in  latitude  disappears  when  this  same  sine 
is  reduced  to  nullitj.  Hence  it  is  to  he  n garded  as  varying  with  the 
sine  of  c-liptic  /cnith-di.-iance,  and,  in  order  to  find  its  value  at  any 
given  point,  we  say  11  if,  with  a sine  of  ecliptic  zenith-distance  which  is 
equal  to  radius,  the  parallax  in  latitude  is  one  fifteenth  of  the  difference 
of  mean  daily  motions,  with  a given  Mins  of  ecliptic  zenith-distance 
what  is  it or 

11 : did’,  of  mean  m.-f-l  ■’» : : ^in  c l.  zen.-di-t.  : parallax  in  hit. 

This  proportion,  it  is  e\id:  nl.  would  gin*  with  entire  correctness  the 
parallax  at  the  centra!  i clip  tic-  point  lit  in  fig,  :Mi|,  wlu-re  the  whole 
\ertical  parallax  i-  1«»  he  re*  honed  as  pa  ral  hr;  in  latitude,  lint  the  in  It 
given  in  I in  text  a 1m»  ihiiii*  ^ that,  with  a giwn  [MWiion  of  the  ecliptic, 
the  parallax  in  latitude  is  the*  --line  at  any  point  in  tin*  ecliptic.  Of  this 
the  cesnmei.r  : * othu  = i,«»  di  iuon't'-'-tiou,  hut  it  r—ciitially  true,  for, 
regarding  tin*  jutle.  irianglc  M ;//  n a pine  triangle.  right-angled,  at 
and  with  jis  j<  m M e*;.ial  t»i  I Si**  ■*.:  gSe  Z m II,  we  liau> 

!; : -hi  7.  !» : : .M  n*  : M // 

But,  in  the  spherical  triangle  Z tu  B,  right-angled  at  B. 

It  : -in  7tm  B : . -in  Z;/i  : sin  Z B 
nencc,  by  equality  of  ratios, 

‘sin  Z m : .-in  ZB::  M m : M n 


But,  as  before  shown, 

11 : .-in  Z iti : : gi . [•nr.-llux  : M m 
JIcnce,  by  combining  ti-nn-.. 

IL : -in  ZB::  gr.  painilnx  ■ M n 

That  is  to  «aj,  wliatewr  he,  th*  [i«»-;ti«.n  uf  //#,  tin;  point  for  which  the 
parallax  in  latitude  is  -ought.  ti.i>  will  In-  equal  to  the  product  of  the 
greatest  parallax  iut«^  the  jdise  of  ediplic  zenith-distance,  divided  by 
radius:  or,  a.-  the  greatest  parallax  equals  the  di  Here  nee  of  mean  mo- 
tions divided  by  fifteen, 


. , sin  erl. 3Liiii.-ili<t.xdiif-l>f m.m.-!-l5 
par.  in  Lt.  = - ur 


hiii  crl.acn.-di-t.XdifT.  of  m.  m. 
KX \r> 


The  next  verse  toadies  more  summary  methods  of  arriving  at  the 
Baine  quantity. 


11.  Or,  the  parallax  in  latitude  is  tlie  quotient  arising  from 
dividing  tlic  sine  of  ecliptic  zonith-distancc  (drkfahepa)  by  sev- 


v.  I3f]  Translation  and  Notes.  151 

Ok 

enty,  or,  from  multiplying  it  by  forty-nine,  and  dividing  it  by 
radius. 

In  the  expression  given  above  for  the  value  of  the  parallax  in  latitude, 
all  the  terms  arc  constant  excepting  the  sine  of  ecliptic  zenith-distance. 
The  difference  of  the  mean  dnilv  motions  is  7-11'iT",  and  fifteen  times 
radius  is  51,570'.  Now  731' 1,37  0'  equals  or  48.77—11; 
to  which  the.  expressions  given  in  the  text  are  sufficiently  near  approxi- 
mations. 

12.  The  parallax  in  latitude  is  to  be  regarded  as  south  or 
north  according  to  the  direction  of  the.  mcridian-Kiiic  ( mculhyajyd i). 
When  it  and  the.  moon’s  latitude  arc  of  like  direction,  take  their 
surn;  otherwise,  tlieir  difi'crnicc : 

13.  With  this  calculate  the  half-duration  (si/u'ti)}  half  total  ob- 
scuration (vrnvirrfu)'  ii]n«)uut  of  obscuration  (yrttstn.  etc.,  in  the 
manner  already  i aught;  likewise  the  scale  of  projection  (pra- 
rnana),  the  do  I lection  (ra/nuni  the  requirr  <1  amount  of  obscura- 
tion, etc.,  as  in  the  case  of  a lunar  r*clip.-c. 

In  nscevtainiii'g  the  I me  lime  of  occurrence  uf  the  various  phases  of 
a solar  eclipse,  sis  determined  by  tin-  parallax  of  the  'rheu  point  of  ob- 
servation, wc  arc  taught  fir.d  t< > main-  tin*  v.lmic  .Mrnvtiuii  for  parallax 
in  latitude,  ami  then  afterward  to  appb  that  !‘**i  parallax  in  longitude. 
The  fiinner  pari  of  the  jirn.vss  is  «r,^i  ii,.  ilv  tniird  m mtsc^  l’J  auu  13: 
the  rules  l’»r  tin*  •■thcr  !•  *!!-»%%  in  the  next  1 1:\ — igc.  The  language  of  the 
text,  its  u-ual.  i>  l»y  l.o  uii  ain  >n  clear  and  explicit  as  *-ui.!d  be  wished. 
Thus,  in  tli-*  itim*  lu-f.nv  1 1 ■*,  n,-  :ir ' ii< it  t -x - : * 1 v.h:  llicr,  a*  th**  first  step 
in  this  process  of  «ri •■■■I *.  >n,  wc  :.iv  to  :.it f i*.-  momi"*  parallax  in 
latitude  for  I lie  time  i.f  mu-  >nj ; i n«-i  inn  l /#/////«  o.  5/,  “cud  t»f  the  lunar 
day"),  or  fur  that  of  appaivnl  c.mji'in-ii'  M (##*'#»  7# //^/rcAf/wu,  “middle  of 
the.  celip>e  It  might  !"■  -.iippu'-cd  ih  u,  as  we  have  thus  far  only  had 
in  the  text  diivi'iioiis  f.n  lindii.g  l !. • .-dm-  aid  rodm-  of  ecliptic  zcuitli- 
dbtauce  at  the  moment  of  true  i-i.iijuni  lion,  tin*  fornmr  of  them  was  to 
lie  us'd  in  the  eah'iilaiioiiN  of  xi-r-^  1*»  ;li n { I I.  and  t !:«-  result  from  it, 
which  would  be  the  parallax  at  the  nmiiieiil  .if  true  coujimefiou,  applied 
hero  as  the  correction  le  edrd,  \<r.  m»  far  a-*  we  have  been  able  to 
discover,  does  the  eoiuinent.itor  expound  whnr  is  she  true  meaning  of 
the  text  upon  tliih  point.  It  i*  ^nllii-i«ant!\  c.  ident,  !■:•"»  »v or.  that  the 
moment  of  apparent  •‘oiijimdioii  is  I lie  time  required.  Ve  I save  found, 
by  si  process  of  siie-avsive  approximation,  at  what  llm  1 p'.v  l-'ig.  Jo),  the 
moon  (her  latitude  being  neglected)  being  at  m an  I t1*.:*  sun  at  a,  the 
parallax  in  longitude  ami  liie  dilicivnce  of  Ma>.  1 longitude  will  both  bo 
the  same  quantity,  m nm  and  so,  when  apparent  eonjuu,  ;iou  will  take 
place.  Now,  to  know  tin*  distance  of  the  two  c it  res  at  that  moment, 
wc  require  to  ascertain  the  parallax  in  latitude,  n V,  fur  the  moon  at  to, 
and  to  apply  it  to  the  moon's  latitude  when  in  tin-  same  position,  taking 
their  sum  w lien  their  direction  is  the  same,  and  their  ditlejcnee  when 
tlieir  direction  is  different,  as  prescribed  by  the  text;  the  net  result  will 
bo  the  distance  required.  '1  he  commentary,  it  may  be  remarked,  ex- 
pressly states  that  the  moon's  latitude  is  to  be  calculated  in  this  opera- 


152  S&rya-Siddhdnta,  [v.  13- 

f 

tion  for  the  time  of  apparent  conjunction  (madhyagraham).  The  dis- 
tance thus  found  will  determine  the  amount  of  greatest  obscuration,  and 
the  character  of  the  eclipse,  as  taught  in  verse  .10  of  the  preceding  chap- 
ter. It  is  then  farther  to  be  taken  ns  the  foundation  of  precisely  such  a 
process  as  that  described  in  verses  32-15  of  the  same  chapter,  in  order 
to  ascertain  the  half-time  of  duration,  or  of  total  obscuration  : tlmt  is  to 
say,  the  distance  in  latitude  ot  the  two  centres  being  first  assumed  ns 
invariable  through  the  whole  duration  of  the  eclipse,  the  half-time  of 
duration,  and  the  resulting  moments  of  contact  and  separation  are  to  bo 
oscertsiined  : for  these  moments  the  latitude  and  parallax  in  latitude  arc 
to  be  calculated  anew,  ami  by  them  a new  determination  of  the  times  of 
contaet  and  separation  U to  be  made,  and  so  on.  until  these  are  fixed 
with  the  degree  of  accuracy  required.  If  the  eclipse  be  total,  a similar 
operation  must  be  gone  through  with  to  ascertain  the  moments  of  im- 
mersion and  emergence.  No  account  is  made,  it  will  be  noticed,  of  the 
possible  occurrence  of  an  annular  e«  lipM*. 

The  intervals  thus  found,  after  correetinii  for  parallax  in  latiludc 
. only,  between  the  middle  of  the  eclipse  and  the  moments  of  contact  and 
separation  respectively,  are  tho>e  which  are  called  in  the  la.4  chapter 
(vv.  19,  2'l).  the  “mean  half-duration  ” ( madh gasth it  y a nlha ) . 

In  this  process  for  finding  the  net  result,  a>  apparent  latitude,  of  tlie 
actual  latitude  ami  the  paiallux  in  latitude,  is  hroiighi  out  with  dis- 
tinct ness  the  inaccuracy  already  alluded  to;  that,  whatever  he  the 
moon's  actual  latitude,  her  parallax  is  always  calculated  as  if  she  were 
in  the  ecliptic.  In  an  eclipse,  however,  to  wliirb  e.-ise  alone  the  Hindu 
processes  are.  intruded  to  be  applied,  the  moon’s  latitude  can  never  be 
of  any  considerable  amount. 

The  propriety  of  determining  the  direction  of  the  parallax  in  latitude 
by  means  of  that  of  tlie  meridian-sine  (Z  L in  Fig.  2<S).  of  which  the 
direction  is  established  as  south  or  north  by  the  process  of  its  calcula- 
tion, is  too  evident  to  call  for  remark. 

Iu  verse  Hi  is  given  a somewhat  confused  >preijl<  ation  of  matters 
which  arc,  indeed,  affected  by  the  parallax  in  latitude,  but  in  different 
modes  and  degrees.  The.  amount  of  greatest  obscuration,  ami  the 
(mean)  half-times  of  duration  and  total  uhsui ration,  arc  llic  ipuintiiics 
directly  dependent  upon  the  calculation  oi  that  parallax,  as  hero  pre- 
sented: to  find  the  amount  of  obscuralion  at  a given  moment — as  also 
the  time  corresponding  to  a given  amount  of  obscuration — we  require 
to  know  also  the  true  half-duration,  us  found  hy  the  rule-**  stated  in  the 
following  passage : while  the  scale  of  projection  and  the  deflection  are 
affected  by  parallax  only  so  far  as  this  alters  the  time  of  occurrence  of 
tlie  phases  of  the  eclipse. 

14.  For  the  end  of  the  lunar  day,  diminished  and  increased  by 
tlie  half-duration,  as  formerly,  calculate  again  the  parallax  in 
longitude  for  the  times  of  conuict  (grdsa)  and  of  separation  (mob 
«Ao),  ami  find  the  difference  between  these  and  the  parallax  in 
longitude  \harija)  for  the  middle  of  the  eclipse. 

15.  If,  in  the  eastern  hemisphere,  the  parallax  in  longitude 
for  the  contact  is  greater  than  that  for  the  middle!  and  that  for 


t.  IT.]  Translation  and  Notes.  15S 

the  separation  less ; and  if,  in  the  western  hemisphere,  the  con- 
trary is  the  case — 

10.  Then  the  difference  of  parallax  in  longitude  is  to  be  added 
to  the  half-duration  on  the  side  of  separation,  and  likewise  on 
that  of  contact  (pmgrafia§ja) ; when  llie  contrary  is  true,  it  is  to 
be  subtracted. 

17.  These  rules  arc;  given  for  cases  where  the  two  parallaxes 
are  in  the  same  hemisphere:  where  Lin  y arc  in  different  hemi- 
spheres, the  sum  of  the  parallaxes  in  longitude  is  to  be  added  to 
the  corresponding  hall-duration.  The  principles  here  stated  ap- 
ply also  to  the  lndf-tiino  of  total  ob.-curntion. 

We  are  suppos'd  In  liavc  ascertained,  by  l!i«^  preceding  process,  the 
true  .amount  of  apparent  latitude  at,  the  muunnN  »>f  first  atul  last,  con- 
tact of  the  eclipsed  and  i-f-Iij  *iug  bndie-,  :\\A  to  have  de- 

termined the?  dimcri'Iutis  « »i“  1 1,*1  triang!. — cnrir>p'»ndi:.g,  in  a solar 
eclipse,  to  Ctrl1,  Fig.  *-M,  i:i  a lunar  - made  up  «»f  tin*  iariiudc,  the  dis- 
tance in  longitude,  and  tin-  sur.i  uf  llie  i\\o  r:i.!i\  The  nu.Miuii  now  is 
how  the  duration  of  the  eelip>"  will  lie  a:i.'.-te-|  1 »\  the  paiv»!la\  in  longi- 
tude. If  this  parallax  iminincd  rnn^tiLiit  'luring  tl*"  enntinuuiwe  of  the 
eclipse,  it*  died  would  b»-.  nuihing : ainl,  ii:i\ isiig  ■»::.-«*  d«-tf-riiiiucil  hv  it 
the  time  uf  apparent  i-i >njiiin-; ims.  we  diouM  u-*l  i.i  ed  to  tak  - it  farther 
into  account.  I »nl  it  limn  limm  *i;t  {■*  !ii> and  the  effect  of 

its  variation  i * to  probing  die  duraiimi  «>i‘  * \«  i v juiri  of  a visible  eclipse. 
For,  to  the  c:ed  of  the  n-ntral  i-i,lipli*--poii.t.  il  llnows  tin*  iihnhiV  disk 
forward  upon  that  of  die  Min,  iln:^  ha-'eiil.ig  di«*  i..,curri,nee.  of  all  the 
phases  of  the  eel  ipse,  !.i-l  l.y  an  aujM.snt  w!:..*h  i>  all  tin*  time  decreasing, 
so  that  it  hasten*  the.  be  uiming  of  tin*  .••■iip.-e  limjv  than  the  middle, 
and  the  middle  iiuhv  tlian  the  ■-!« •.-«• : to  the  wcM  «*f  rliat  same  point,  ou 
the.  other  hand,  it  deprive*  tin1  iiiimu^  de-k  awuv  from  the  sun'*,  but  by 
ail  ainmuit  constantly  iiM'ieoing.  -o  il.af  ii  ivfanb  rln*  end  of  iho  eclipse 
more  than  it*  middle,  and  iis  middle  nmiv  than  i>  beginning.  The 
eifeel  of  the  parallax  in  longitndt,  then,  upon  ea-  h haiiMuratiou  of  the 
eclipse,  will  lie  nica*mvd  hv  the  diifi  ivnee  between  In  retarding  Mini  ac- 
celerating effects  upon  eontaet  :md  conjunction,  and  upon  conjunction 
and  separation,  respectively  : and  ihe  amounf.  of  tlii*  difference.  will 
always  bo  additive  to  tin*  lime  of  hul.'-diiration  as  oilicrwi.M*  determined. 
If,  however,  e* mtact  and  conjunction,  or  conjunction  and  separation, 
take  phiccupou  opposite  sides  of  the  point  of  no  parallax  in  longitude, 
then  the  sum  of  the  two  parallactic,  effects,  iiMead  of  their  difference, 
will  be  to  be  added  to  the  corresponding  lull duration  : since  the  one, 
on  the  oast,  will  hasten  the  occurrence  of  the  f inner  pi -Li.se,  while  tho 
other,  on  the  west,  will  defer  the  occurrence  of  he  latter  phase,  Tho 
amount  of  the  parallax  in  longitude  for  the  mid. lie  of  the  eclipse,  has 
already  been  found ; if,  now,  we  farther  determine  its  amount — reckoned, 
it  will  be  remembered,  always  in  time — for  tho  moments  of  contact  and 
separation,  and  add  the  difference  or  the  sum  uf  each  of  tlfesc  and  the 

Sarallax  for  the  moment  of  conjunction  to  the  corresponding  halt- 
uration  as  previously  determined,  we  shall  have  tho  true  times  of  hnlf- 
dnratiop.  In  order  to  find  the  parallax  for  contact  and  separation,  we 


151 


|y.  If- 


S&rya  Siddlt  dn  ta, 

repeat  the  same  process  (see  above,  v.  9)  by  which  that  for  conjunction 
^iras  found : as  we  then  started  from  the  moment  of  true  conjunction, 
and,  by  a seiies  of  successive  approximations,  ascertained  the  time  when 
the  difference  of  longitude  would  equal  the  parallax  in  longitude,  so  now 
urc  start  from  two  moment*  removed  from  that  of  true  conjiiULtion  by 
the  equivalents  in  time  of  the  two  « list ances  in  longitude  obtained  by  the 
last  profits,  ami,  by  a similar  series  of  successive  approximations,  ascer- 
tain the  times  when  the  differences  of  longitude,  together  with  the  par- 
allax, will  equal  those  di>tnm:cs  in  longitude. 

In  the  process  a*-  tlm>  conducted,  there  is  an  evident,  inaccuracy.  It 
is  not  enough  to  apply  the  whole  correct  ion  for  parallax  in  latitude,  and 
then  that  for  parallax  in  longitude,  since,  by  rca-oii  of  the  change  effected 
by  the  latter  in  the  time*  of  louiuct  ami  separation,  a new  calculation  of 
the  former  becomes  necessary,  and  then  again  a new  calculation  of  the 
latter,  ami  so  on,  until,  by  a scries  (if  doubly  compounded  approxima- 
tions, the  true  value  of  each  is  determined.  This  wa*  doubtless  known 
to  the  framers  of  the  system,  but  pa-sol  «ncr  l»y  them,  on  account  of 
the  excessively  laborious  character  of  the  complete  calculation,  and  be- 
cause the  accuracy  of  sucli  iv-ull-  as  they  could  obtain  was  not  sensibly 
affected  by  its  neglect. 

The  quest  inn  naturally  r.ri-es  why  tin-  sper -ill.  alioiis  of  verso  1:>  are 
made  hypothetical  instead  «>f  positin',  and  why.  in  the  latter  half  of 
verse  10,  a case  is  supposed  which  m-wr  ari-i-s.  Tin-  commentator  an- 
ticipates this  objection,  ami  lake*  much  paiii*  to  lvnmvc  it  : it  is  nut 
worth  while  to  follow  his  dilf*  rent  ]-■«■:!-,  w lti-a!i  amouiil  to  no  real  expla- 
nation, saxing  to  imii.-e  his  la-l  -liggc-tion.  that.  in  case  an  eclipse  begins 
before  sunrise,  the  parallax  fur  it-  earlier  pha-c  or  phases.  a-  calculated 
according  to  the  distance  in  lime  from  tin*  lower  meridian,  mav  be  less 
than  for  its  later  pha-1.^ — ami  ilic  rmitrary,  when  the  eclipse  ends  after 
smnset.  Tin-  may  | •« * — ibiy  be  l li«*  true  explanation,  although  we  are 
justly  surprised  at  limiing  a ease  i,f  little  practical  consequence,  and 
to  which  no  alludou  lias  been  • in  ihe  piwi.«u<  pruc (■-*".<,  here 
taken  into  account. 

The  text,  it  may  be  remarked,  bv  it-  inc  of  the  tenns  “eastern  and 
western  hemispheres ” {fatin'* /#/.  li'. Tally  “nq»,  w— cl").  repeats  once  more 
its  substitution  of  liie  meridian  ivliptic-i-.  int  (utmUnjnluttwt)  fur  the 
central  ecliptic-point  [tr if.fajwtluynt*),  a-  tiiat  uf  mi  parallax  in  longitude ; 
the  meridian  funning  the  only  proper  and  recognized  division  of  tho 
heavens  into  an  eastern  and  a western  hemisphere. 

\Yc  arc.  now  prepared  to  see  ihe  reason  of  ihe  special  directions  given 
inverses  19  and  ‘J.'J  of  ihe  la-1  cliaptcr,  respecting  the  reduction,  in  a 
solar  eclipse,  of  distance  in  time  from  the  middle  of  the  eclipse  to  dis- 
tance in  longitude  of  the  t«vu  centre-.  The  “mean  hall-duration" 
{miulh ya&thityardhn)  of  the  eclipse.  i>  the  time  during  which  the  true  dis- 
tance of  the  centres  at  1 lie  moments  uf  contact  or  separation,  as  found 
by  the  process  prescribed  in  wises  J‘J  ami  Itf  of  this  chapter,  would  be 
gained  by  the  moon  with  lmr  actual  excess  of  motion,  leaving  out-  of  ac- 
count the  variation  of  parallax  in  longitude:  the  “true  hall-duration" 
( sphutaalhityardha ) is  the  iuurcusc-d  time  in  which,  owing  to  that  varia- 
tion, the  same  distance  in  longitude  is  actually  gained  by  the  moon ; 


Translation  and  Notes . 


155 


vi.  1.] 

the  effect  of  the  parallax  being  equivalent  cither  to  a diminution  of  the 
moon’s  excess  of  motion,  or  to  a protraction  of  the  distance  of  the  two 
centers — both  of  them  in  tin*  ratio  of  this  true  to  the  mean  half-duration. 
If  then,  for  instance,  it  be  required  to  lciimv  wlial  will  he  the  amount  of 
obscuration  of  the  sun  half  an  hour  after  the  first  eouract,  wo  shall  first 
subtract  this  interval  from  the  true  half-duration  before  conjunction ; the 
remainder  will  be  the  actual  interval  to  the  middle  of  the  eclipse:  this 
interval,  then,  we  shall  reduce  to  its  value  n<  diMnnec  in  longitude  by 
diminishing  it,  either  before  or  after  its  reduction  to  minutes  of  arc,  in 
the  ratio  of  the  true  to  t lit-  mean  half-duration.  The  rest  of  the  process 
will  be  performed  pivriM-ly  a*  in  the  case  of  an  eclipse  of  the.  moon. 

Notwithstanding  the  ingenuity  and  approximate  correctness  of  many 
of  the.  rules  ami  methods  of  calculation  taught  in  ilii*  chapter,  the  whole 
process  for  the  a-rertuinincnt  of  parallax  cuntum*  so  muuv  elements  of 
error  that  it  liurdh  deserve*  to  he  called  otln-rwiM:  than  cumbrous  and 
bungling.  The  false1  e.-timaii*  of  tin*,  diil  ere  lire  between  the  sun's  and 
moon’s  horizontal  parallax — the  neglcr,  in  tiTUiiniug  it,  of  the  varia- 
tion of  llic  inoonV.  distance — llie  e^iimati>>u  of  its  value,  in  thru*  made 
always  according  to  mean  motions.  wliuu-v  it  in*  the  true  motions  of  the 
planets  at  ihe  moment— tin-  neglect,  in  calculating  1 lie  amount  of  par- 
allax, of  the  moon's  latitude — tln>«\  with  all  tin  other  inaccuracies  of 
the  processes  of  calculation  wliiih  Imu*  been  t» -inS'-tl  out  in  the  notes, 
vender  it  impossible  th.it  the  iv-ulis  obtaiueil  >in»uld  ever  be  more  tliau 
a rude  approximation  to  the  tru! li. 

In  farther  illi;.-l r;il l.in  of  the  subject  ■if  sniar  eclipses,  as  exposed  in 
this  and  the  prenslii.g  « liapter.-,  we  pivj-.'i.*,  in  the  Appendix,  n full  cal- 
culation'of  the  eclipse  uf  May  |>:>|,  mainly  as  made  for  the  trans- 

Jator,  during  hi*  rc»idcuce  in  India,  b\  a native  a-trunomer. 


c ir  a i'T  i in  v i. 

OP  T1IK  PUn.IF.rnON  OF  i CLIPSKS. 

Contents  : — 1 , value  of  u projection;  2— 1,  general  directions;  5-<»t  hoxv  to  layoff 
the  deflection  and  latitude  fur  the  beginning  and  end  nf  the  eelijM?;  7,  to  exhibit 
the  points  of  contact  and  >eparation;  8-1 1».  hu\v  to  lav  oil'  the  deflection  and  lati- 
tude for  the  middle  of  the  •*cli|?>o;  11,  to  «Ji«»ur  ilu:  unoiaU  of  greatest  obscura- 
tion; 12,  rever.-al  of  din*eti<uis  in  the  western  heiui»|ihere ; 1:1  least  amount  of 
obscuration  uWrvsible ; 1 1-10,  to  draw  the  path  of  tin  eclipsing  body;  17-10,  to 
show  the  iinnnuit  of  nl  neural  inn  at  a iriven  linn- ; 2U-22  In  exhibit  the  points  of 
immersion  and  cmeigenco  in  a total  eclipse;  23.  colot  of  the  part  of  the  moon 
obscured;  21,  caution  as  to  communicating  a knowledge  of  these  matters. 

• 

1.  Since,  without  u projection  (chahjukd),  the  precise  (sphuia) 
differences  of  the  two  eclipses  arc  not  understood,  1 shall  proceed 
to  c^plain  tho  exalted  doctrine  of  the  projection. 


l»u 


Siirya-Siddh&nta , 


[v.l- 


The  term  chedyaka  is  from  the  root  chid,  u split,  divide,  Minder,”  and 
indicates,  na  here  applied,  the  instrumentality  hy  which  distinctive  dif- 
ferences arc  rendered  evident.  The  name  of  the  chapter,  parilekhAdhu 
not  taken  from  this  word,  hut  from  parilekha,  “delineation, 
vjutoh  occurs  once  below,  in  the  eighth  verse.  . \ 

IfeMf , ft (jeeft,  ttpon  a well  prepared  surface,  a point,  tie- 
! m tlfe  nrst  place^  with  a radius  of  forty -mne  digits 

V*)*  a cffrbta  Ibr'tho  deflection  (volana) : 

Phfeq  a second  circle,  with  a radius  equal  to  half  the  sum  of 
thd^JJi!^,i{j^dl‘$j^4  .eclipsing  bodies ; this  is  called  the  aggregate- 
then  a third,  with  a radius  equal  to  half  the 

determination  of  the  directions,  north,  south,  east,  and 
we^ybjcis ^formerly.  In  a lunar  eclipse,  contact  (grahana)  takes 
pl«|o^fhe  east,  and  separation  (mofaha)  on  the  west ; in  a so- 
the  contrary. 

^burger  circle,  drawn  witli  a radius  of  about  three  feet,  is  used  solgty 
rag  off  the  deflection  ( caiann ) of  the  ecliptic  from  an  east  afid 
?iirao.  Wc  have  seeu  above  (iv.  24,  25)  that  the  sine  of  this  dc- 
UetftfOi  was  reduced  to  its  value  in  a circle  of  forty-nine  digits’  radius, 
by  Eroding  by  seventy  its  value  in  minutes.  The  second  circle  is  em- 
piuifud  (see  below,  vv.  6,  7)  in  determining  the  points  of  contact  and 
separation. ' Tlio  third  represents  the  eclipsed  body  itself,  always  main- 
tiu^g  a fixed  position  in  the  centre  of  the  figure,  even  though,  in  a 
hu^&plipsc,  it  is  the  body  which  itself  moves,  relatively  to  the  eclipsing 
sh^Pp£[  Fur  the  scale  r>y  which  the  measures  of  the  eclipsed  and 
eeln^^  bodies,  the  latitudes,  etc.,  arc  determined,  see  above,  iv.  26. 

Xfj&'ibethnd  of  laying  down  the  cardinal  directions  is  the  same  with 
tli£$;iiscd  in  constructing  a dial;  il  is  described  in  the  first  passage  of 
tlur third  chapter  (iii.  1-4). 

the  specifications  of  tin*  hitler 
body,  designating  upon  whirl 
terminate. 

5.  In  a lunar  ccii]»«r>,  the  ch  lhv-tic.i  (mlniw)  for  the  contact  is 
to  be  laid  off  in  its  own  jnop'jr  direction,  but  tlmt  for  the  separa- 
tion in  reverse;  in  an  eclipse  of  the  sun,  the  contrary  is  the  case. 

The  accompanying  figure  (tig.  27)  will  ilhi^rati*  the  Hindu  method 
of  exhibiting,  by  a pn»ji-r:ii»n,  the  \:irinus  phases  of  an  eclipse.  Its 
condition*  arc  those  of  tin*  lunar  eclipse  of  Fell,  filli,  1HG0,  as  deter* 
mined  bv  the  did  a ami  method*-  of  this  treatise:  for  the  calculation  tfce 
the  Appendix.  Let  M be  the  centre  of  the  figure  and  the.  place  of  the 
moon,  and  lot  X S and  1£\Y  be  the  circles  of  direction  drawn  through 
the  moon's  c.en fro;  the  former  representing  (see  above,  under  iv.  24,  25) 
a great  circle  drawn  through  the.  north  and  south  points  of  the  horizon, 
the  laltcr  a small  circle  parallel  to  the  prime  vertical.  In  explanation 
of  the  manner  in  which  these  directions  aie  presented  by  the  figjj^jre 
would  remark  that  we  have  adapted  it  to  a supposed  positifSBflto 


half  of  verse  -I  apply  In  the  eclipsed 
!•■  of  it  nhM'iindi'Ui  will  commence  and 


vi.  *.]  Trai&iation  and  Notes.  157 

- observer  on  die  north  side  of  hiTprojection,  as  at  N,  and  looting  ooutli* 
ward — a position  which,  in  our  latitude,  ho  would  naturally  assumi1,  for 

Fig.  27. 


the  purpose  ol  comparing  tin*  actual  pha^e*  of  t!i»*  (•■■lipse.  as  thev  oc- 
curi’i:  1 with  hi*  delineation  r,f  th-m.  Tin*  hiv&vii-r  rin-i  \ l i\  i/that 
drawn  with  the  sum  of  tin'  scmi-ili.imetcns  ur  the  aggregate-circle 
while  the  outer  one,  NES  \Y,  is  that  tor  the  drfli'ctiun. ' This,  in  order 
to  reduce  the  size  of  the  whole  figure,  v. have  drawn  upon  a s.’ale  very 
much  smaller  than  that  proscribed;  its  relative  dimensions  being1  a mat- 
ter of  no  cunseipieiiee  whatever,  pruviileu  the  sine  of  the  deflection  be 
made  commensurate  with  its  radius.  In  our  own,  or  the  Greek,  method 
of  laying  off  an  are,  l»y  its  angular  value,  the  rams  of  the  circle  of  de- 
flection would  also  l»e  a matter  «>f  indifference : he  Hindus,  ignoring 
angular  measurements,  adopt  the  more  awkward  a.ul  bungling  method 
of  laying  off  the  arc  by  means  of  its  sine.  Let  r w equal  the  deflection, 
calculated  for  the  moment  of  contact,  expressed  as  a sine,  and  in  terms 
of  a circle  in  which  E M is  radius.  Now,  as  the  moon's  contact  with 
the  shadow  takes  place  upon  her  eastern  limb,  the  deflection  fi>T  the 
contact  must  be  laid  ofT  from  the  east  point  of  the  circle ; and,  an  tho 
cal^Sliltftdfldircction  of  the  deflection  indicates  in  what  way  tho  ecliptic 
‘‘ptwardlv,  it  must  be  laid  off  from  E in  its  own  proper  di- 
al 


168 


Sdrya-Siddhdf^j 


[vi.  5- 


rection.  In  the  case  illustrated,  the  detection  for  the  contact'is  north : 
hence  we  lay  it  off  northward  from  E;  and  then  the  line  drawn  from  M 
to  v,  its  extremity — which  line  represents  the  direction  of  the  ecliptic 
at  the  moment — points  northward.  Again,  upon  the  side  of  separation 
r — which,  for  the  moon,  is  the  western  side — wc  lay  off  the  deflection  for 
the  moment  of  separation:  but  wo  lay  it  off  from  IV  in  the  reverse  of 
its  true  direction,  iu  order  that  the  line  from  its  extremity  to  the  centre 
may  truly  represent  the  direction  of  the  ecliptic.  Thus,'  in  the  eclipse 
figured,  the  deflection  tor  separation  is  south  ; we  lay  it  off  northward 
from  W,  and  then  the  line  v1  M points,  toward  M,  southward.  In  a solar 
eclipse,  in  which,  since  the  sun’s  western  limb  is  tlic  first  eclipsed,  the 
deflection  for  contact  imn-t  bo  laid  off  from  \V,  arid  that  for  separation 
from  K,  the  direction  of  the  former  requires  to  be  reversed,  ami  that  of 
the  latter  to  be  maintained  as  calculated. 


0.  From  the  extremity  of  either  deflection  draw’  a line  to  tlio 
centre:  from  the  point  where  that  cuts  ilie  aggregate-circle* 
(mnuisa)  arc  to  be  laid  oil*  the  latitudes  of  contact  and  of  separa- 
tion. 

7.  From  the  extremity  • »l*  the  latitude,  again,  draw  a lino  to 
iho  central  point:  when*  that,  in  cither  case,  louche*  the  eclipsed 
body,  there  point  out  the  contact  and  separation. 

8.  Always,  in  a solar  eclipse,  the  latitudes  arc  to  be  drawn  in 
the  figure  (purihlr/ta)  in  their  proper  direction;  in  a lunar 
eclipse^  in  the  opposite  direction.  . . . 

The  linos  >•  M and  i,f  M,  drawn  from  r and  »■',  the  extremities  of  the 
bines  or  w.mi  which  lnca-mv  the  deflection,  to  the  •■outre  of  the  figure, 
represent,  a*  a Ire  a ly  noticed,  the  direction  of  the  ecliptic  with  reference 
to  an  east  and  vcht  line  at  the  moments  uf  contact  and  separation. 
From  them,  accordingly,  and  at  light,  angles  to  them,  ar«  to  bn  laid  off 
the  values  of  tin*  moon's  iatitud.-  at  thosi*  iMBicnK  Owing,  however, 
to  tlic  principle  adopted  in  the  prnii-ctioniY  regarding  the  eclipsed 
body  as  fixed  in  the  centre  of  tin?  ligarc,  and  the  eclipsing  body  as  pass- 
ingiover  it,  the  lines  »•  M ami  v'  M do  not,  in  the  case  of  a lunar  eclipse, 
represent  the  ecliptic  il«Hli  in  which  il«e  centre  of  the  shadow',  but  the 
small  circle  of  latitude,  in  which  is  the  moon's  centre:  hence,  in  laying 
off  the  moon's  latitude  lo  di-tmnine  the  •■'■wire  of  the  shadow,  wc  re- 
verse its  direction.  Thus,  in  liie  ca-n*  illuMi-ab-d,  tin:  moon's  latitude  is 
always  south:  wu  l.-.\  n'l,  then,  llu:  iim*<  k!  aud  k ' l\  representing  its 
value  at  the  moments  uf  < u!ii.,n  t un  i M-oarat ion,  northward  : they  t.- re, 
like  the  deflection,  drawn  a*  nines  and  In  sucii  manner  that,  their  ex 
tromitics,  l and  arc  in  the  agerregate-cin-ic. : then,  since  l M and 
are  each  equal  to  the  sum  of  the  two  semi -diameters.  and  Ik  and  V k* 
to  the  latitudes,  JfcM  and  k 9 M will  represent  the  distances  of  the  centres 
in  longitude,  and  l and  V the  places  of  the  centre  of  the  shadow,  at  con- 
tact and  Reparation  : and  upon  describing  circles  from  l and  V,  with  radii 
equal  to  the  semi-diameter  of  the  shadow',  the  points  c and  sf  where 
these  tonch  the  disk  of  the  moon,  will  be  the  points  of  first  and,  last  con- 
tact: c and  a being  also,  as  stated  in  the  text,  the  points  whore  l M and 
/'M  meet  the  circumference  of  the  disk  of  the  eclipsed  body.  ;s 


▼i.  11.]  Translation  and  Notes.  159 

8.  In.  accordance  with  this,  then,  for  the  middle- of  the 

eclipse,  — 

9.  ' The  deflection  is  to  be  laid  off— eastward,  when  it' and  the 
latitude  arc  of  the  same  direction:  when  they  are  of  different 
directions,  it  is  to  be  laid  off  westward:  this  is  for  a lhnar 
eclipse : in  a soiar,  tlic  contrary  is  the  case. 

10.  From  the  end  of  the  deflection,  again,  draw  a line  to  the 
central  point.,  and  upon  this  lino  of  the  middle  lay  off  the  lati- 
tude, in  the  direction  of  the  deflection. 

11.  From  the  extremity  of  lk;  latitude  describe  a circle  with 
a radius  equal  to  half  the  measure  of  the  eclipsing  body:  what- 
ever of  the  dish  of  flic  eclipsed  body  is  enclosed  within  that 
circle,  so  much  is  swallowed  up  by  the  darkness  (luma#). 


The  phraseology  of  the  \v\:  in  Hu**  pii-«:i\ro  i-  smut1  what  intricate  nnd 
obscure;  it  i-  IbPy  i*\jf;:iiiu*d  l».  the  ms-.ry.  as  null'd,  its  mcan- 

injr  is  al>o  * 1 r- • 1 u . * i i > l ■ with  <;ui : i ; • 1 1 1.  •■lenrr.i--  ir«»m  *ln‘  •'unditioiis  of  the 
problem  t » hi-  : niv  1.  »T  i-  r»-*iuii-d  *.«»  represent  the  deflection 

of  tin-  ei'liplii*  I rum  on  ;*rd  v--  *'s  line  at  tin-  iii-.-jiiont*  «ff  greatest 
ohsi-nratkn,  siinl  io  i'i\  t!.  i-- i,  m *,ii  ■ *■  -mr.-  -f  tho  edipung  body 
at  that  ln-'in-ii1..  Tin*  • 5.  I« »i:  U i.r.^  t’..  . ■ i ■ i—  determined  b}r  a 
sccuiukin  io  t J:.?  -ti* . ds-.i.-  n n • » i.-a.*  : ii-.*  iso.-i n or  south  point  of 
tin- figure.  Tin-  lir-i.  ijii.'-iMii  i-.  i'.misi  w nf  two  points  shall 
the  deflection  I 'i*  u'f.  •i’  -I  *.,n-  .im*  t-»  h-  -!*mv  •!.,a\vu.  Vow  since, 

according  to  ' • i i".  I'n-  Ini':  ■ ■ it  .-•■!:*  • : .-.-isnrcd  upon  the  litio  - 

of  duflet-i.i«Mi%  the  la'.i.T  iv\.a  ilrr.-.n  uwnrd  or  northward  accord- 
ing to  the  in  \vhi*-h  the  l-i* ;.t »iil**  i- m If  Hid  off.  And  this  is 

the  meaning  of  tin:  i el  p..r*  ;»:  u _•  **  ; -in  :«.*e  »r«iaiu,*\"  namely,  with 
the  dirt-cl ion  in  uhi«-h,  :i  ■ i--  ■ ;-ie\ »«.rs  parr  of  the  ver>i\  th* 

latitude  U to  In-  -ii.iv.  u.  iJv  i ■ whu-h  direction  from  the  north 

or  south  p-iisu.  ;»■»  1 ii:i^  '•hail  ;1,.-  li.-u  ■ •lion  he  measured? 

This  it) list,  of  ■•ours:,  he  «!--•  i»r  nin-d  h\  ij.e  dire*  i i«*n  uf  the  deflection 
itself:  if  sonlh,  il  msir-t  omiicedv  f-  ■ m "i-inv.1  !i-«»tn  liie  north  point 
and  west  from  the  south  p/iini : if  »!■■:••  ii.  tin*  contrary.  The  rules  of 
the  text  are  in  ne-ordaiser  whli  tins  :d!hoi»«di  t <!«'t-?iaiiiiuii:g  circuin- 
tiiaticu  is  made  !<»  h-1  tie.*  r.-^oviteutt  or  nor.-aj.wmor.s  in  respect  to 
direction,  of  the  deik  ti.kn  with  the  moons  la',  .tilde-—  I lie  latter  being 
this  time  nv'.o".-.  * .1  in  ii--  «v.t  a «■]»  t d rc"«u>.!.  and  not,  in  a lunar 
eclipse,  vo\ei->ed.  Thus,  in  t!»  * ease  for  which  the  figure  is  drawn,  Us 
the  moon'*  huitude  i>  MMih,  an  i inn  l bo  hii«i  off  northward  from  M, 
the  dcilci:l'.o:i,  il!v\  n iiuusiin.-d  from  the  in  nil  point ; as  deflection  • 
and  latitude  are.  hm'i  sua:ilu  it  is  measured  ts « m N.  In  an  eclipse 
of  the  sun.  on  the  other  hand,  the  moons  labia1.-  would,  if  north,  be 
luid  off  northward,  as  in  the  figure,  and  lioneo  also,  tiie  detleetion  would 
be  measured  from  the  north  point:  but  it  would  be  measured, eastward, 
if  its  own  direction  were  south,  oi  disagreed  with  that  of  the  latitude. 

The  line  of  deflection,  which  is  M v*  in  the  figure,  being  drawn,  and 
having  the  direction  of  a perpendicular  U>  tlio  ecliptic  at  the  moment  uf 
moon's  latitude  for  that  moment,  M l"}  is  laid  off  directly 


160  Surya-Siddhdnta,  [vi.  11-  . 

upon  it.  The  point  l"  is,  accordingly,  the  position  of  the  centre  of  the 
shadow  at  the  middle  of  the  eclipse,  and  if  from  that  centre,  with  a . 
radius  equal  to  the  semi-diameter  of  the  eclipsing  body,  a circle  be  drawn, 
it  will  include  so  much  of  the  disk  of  the  eclipsed  body  as  i*  covered 
when  the  obscuration  is  greatest..  In  the  ligurc  the  eclipse  is  shown  as 
total,  the  Hindu  calculations  making  it  so,  although,  in  fuel,  it  is  only  a 
partial  eclipse. 

12.  By  the  wise  man  who  draws  the  projection  { ’rhedyakd ), 
upon  the  ground  or  upon  a board,  a reversal  of  directions  is  to 
be  made  in  the  eastern  and  wesn-rn  hemispheres. 

This  verse  is  inserted  here  in  order  to  remove  the  objection  that,  in 
the  eastern  hemisphere,  indeed,  all  take**  nlace  a*  Mated,  but,  if  the 
eclipse  occurs  west  of  the.  meridian,  lln*  stated  directions  require  to  bo 
all  of  them  reversed.  In  order  l«»  understand  ih'c-  ol  ject ion.  wo  must 
take  notice  of  the  origin  aid  literal  meaning  uf  the  Sanskrit  words 
which  doignatc  the  cardinal  direct  ions.  Tim  fan*  of  the  observer  is 
supposed  always  to  be  eastward  : then  4*  o.;M"  i>  pn)ir\  " furwan!,  toward 
the  front";  “vest"  pn'-rtit.  “backward,  toward  tin-  icar”:  4'm»uIIi"  is 
dak»hinnm  lfc  on  the  right";  14  north"  is  vNorn,  11  upward"  (i.  c.,  jirnliably, 
toward  the  mountain^  nr  up  tin1  c.i.ir-e  i »f  the  river-:  in  nnrth-wcstum 
India).  Thc?c  wonls  apph.  then,  in  i-tymnlogical  ^riefrev.,  only  when 
ono  is  looking  eaMward — :rml  n»,  in  lln:  prcM'ist  i-a-**,  only  when  the 
eclipse  is  taking  place  in  tnc  v:i>l'aru  limn^plierc,  and  tin*  pri'jcccor  is 

■ watching  it  from  the  west  side  if  liis  i* .n,  with  th-  latter  l»cf.»ro 

him:  if,  on  tlic  other  hand,  he  ivnmv'  * t«»  K,  turning  his  fu'T  weMwiinl, 
and  comparing  the  phenomena  i in-y  occur  in  tin*  wcM-  rn  hemisphere 
with  his  delineation  of  iheui,  then  “forward"  (/u-»ii#r)  is  u<>  longer  eas!, 
but  west ; “right.1'  (dakuhinn)  i*  n<»  longe.r  -outh,  but  north,  etc. 

It  is  unnecessary  to  point  nut  ihal  lid-  nlijcrlimi  i<  oic  of  the  most 
frivolous  and  hail  -splitting  chancier,  ami  it>  rummal  by  the  text  a waste 
of  trouble  : the  terms  in  ipicM'ion  have  fully  a>  .prred  in  the  language  an 
absolute  meaning,  as  indicating  •hroelieiis  in  fimch,  with* uu regard  lo  the 
position  of  the  observer. 

13.  Owing  to  her  clcarncrs,  even  the  Hvdfili  part  of  ihc  moon, 
when  eclipsed  (gmsta^  is  observable  ; but,  owing  to  his  piercing 

* brilliancy,  even  three  minutes  of  the  sun,  when  eclipsed,  are  not 

observable. 

The  commentator  regards  the  negative  which  is  expressed  in  the  lat- 

■ ter  half  of  this  verse,  as  also  implied  in  the  former,  the  meaning  being 
that  an  obscuration  of  the  moon's  did*  extending  over  only  the  twelfth 
part  of  it  does  not  make  itself  apparent.  Wc  have  preferred  the  inter- 
pretation given  above,  as  being  belter  accordant  both  with  the  plain  and 
simple  construction  of  the  text  and  with  fact. 

14.  At  the  extremities  of  the  latitudes  make  three  points,  of 
corresponding  names;  then,  between  that  of  the  contact  and 


vi.  22.]  . Translation  and  Notes.  16l 

that  of  the  middle,  and  likewise  between  that  of  the  separation* 
and  that  of  the  middle, 

16.  Describe  two  fish-figures  ( malsyd ):  from  the  middle  of 
these  having  drawn  out  two  lines  projecting  through  the  mouth 
and  tail,  wherever  their  intersection  takes  place, 

16.  There,  with  a line  touching  the  three  points,  describe  an 
are  : that  is  culled  the  path  of  the  eclipsing  uody,  upon  which 
the  latter  will  move  forward. 


Tho  deflection  and  the  latitude  of  three  points  in  the  continuance  of 
the  eclipse  having  been  determined  and  laid  down  upon  the  projection, 
it  is  deemed  unnecessary  to  take  tin*  sain-'  trouble  with  regard  to  any 
other  points,  i1k*w»  tlnvo  being  «uljiri<‘iit  t«»  d'-tcnninc  the  path  of  the 
eclipsing  body  : accordingly,  an  arc-  of  a ciivl«:  i**  drawn  through  them, 
and  is  regarded  as  represent  in*;  that  path.  'flu;  method  of  describing 
the  arc  is  the  wmio  well  that  which  h:i->  iiliwlv  been  more  than  once 
employed  (sec  above,  iii.  I-*,  1 I -1*JI : it  i>  explained  hero  with  some- 
what more  iwllm-s-  than  l»**!biv.  Thu*.  in  tin*  lig'irc,  f,  / *,  anil  /*'  are  the 
three  extreinilies  «*f  l!*i*  r.im  n's  'i-li*,  at  the  moment*  of  contact, 
opposition,  :m«l  s-'*iim,:i.i"n,  ri^;i*>«a(.i\**'y : v.  <■  jnisi  , and  upon 

these  lines  iIcm'hIm'  ii>h-ii*jrur*  < (-cv  n«»n'  id.  i their  two  extremi- 
ties (“mouth”  ac«l  - tail”)  sir»-  hniicati-il  by  th»*  inlrwctinjr  dotted  lines 
in  the  llgmv:  then,  at  : Ii.-  ;i"iut,  not  in«-i'i****  i i'i  In*.*  figure,  where  thqg 
lines  drawn  through  ih.-m  nuet  one  i*i  r,  L the  centre  of  a circle' 

passing  through  L :».•■*!  /#. 

1 


17.  from  half  the  rum  n't  be  er*!ip?od  and  eclipsing  bodies 
subtract  the  amount  of  nlwi-nuioii.  us  calculated  for  any  given  * 
time:  take  a link  nick  e«pul  to  the  remainder,  in  digits,  and, 
from  tho  ventral  poin., 

18.  Lay  it  oil'  toward  th*1  path  upon  either  side — when  the 
time  is  before  that  ol*  greatest  ohsouraliou.  toward  the  side  of 
contact-;  when  the  obscuration  is  decreasing,  in  the  direction  of 
separation — ami  where  the  slick  am l the  path  of  the  eclipsing 
body 

li).  Sleet  one  another,  from  that  point  describe  a circle  with  a 
radius  orpin  I to  hal  i‘  the  eclipsing  body : whatever  of  the  eplmsed.  " 
body  is  included  within  it,  that  point  out  as  swallowed  ^fby  ; 
the  darkness  (hunas).  " 

20.  Take  a little  stick  equal  to  lisiK  tiie  difference  of  tile 
measures  (mdno),  and  lay  it  off  in  the  direction  of  ontact,  calling 
it  the  slick  of  imincision  (nimihunt):  who  o it  touches  the  patl^. 

■ 21.  From  that  point,  with  a radius  equal  to  half  the  eclipsing 
body,  draw  a circle,  as  in  tho  former  ease:  where  this  meets  the 
circle  of  tho  eclipsed  body,  there  immersion  takes  pljice. 

22.  So  also  for  the  .emergence  ( unmilana ),  lav  it  off  in  the 
direction  of  separation,  and  describe  a circle,  as  before : it  will 
show  the  point  of  emergence  in  the  manner  explained. 


162 


S&nja-Slddhdnta,  [vi.  22- 

■ The  method  of  these  processes  is  so  clear  as  to  call  for  no  detailed 
explanation.  The  centre  of  the  eclipsing  body  being  supposed  to  be 
always  in  the  are  //•'/',  drawn  as  di reeled  in  the  last  passage,  wo  havo 
only  to  ii\  a point  in  this  are  which  shall  be  at  a distance  from  M cor- 
responding to  iho  calculated  distance  of  the.  centres  at.  tin?  given  time, 
and  from  lhal  point  t»»  describe  s circle  of  ihe  dimensions  nf  tlie  eclipsed 
body,  and  the  result  will  be  a represent al ion  of  the  then  phase-  of  the 
-eclipse.  If  the  point  thus  fixed  l>e  distant  from  M by  the  difference  of 
the  two  scnii-dianielers.  a>  M I . Yi  t'm  the  ci ivies  described  will  touch  the 
disk  of  the  eclipsed  Innlj  at  the  points  of  immersion  and  emergence, 
i and  r. 

28.  The  jmrt  obscured,  when  less  than  half,  will  he  dusky 
(sadhtimra):  when  more  than  half,  it  will  bo  hlaek  ; when  emerg- 
ing, it  is  dark  copper-color  ^rduju^hurt) : when  the  obscuration 
is  total,  it.  i.s  tawny  (h/filu). 

The  commentary  adds  the  imp  irient  eireunistauee.  nmil’i'd  in  tlir- 
text,  that  the  monu  alom*  is  lnue  Mmken  of;  no  .spccilh-aiiou  being 
added  with  rclbiviu-p  in  tlie  -nil,  Uvnu-v,  in  a solar  irlipsc,  the  pari 
obscured  U alba's  blrn-k. 

A more  suitable  pi;.  migSit  hn\o  been  fi.imd  for  liiU  \erse  in  tin- 
fourth  chapL-T,  as  ii  lia>  n»«limig  t-»  «ln  wiih  ihe  pioj.-.-ii-in  of  an  cHipse. 

24.  This  mysicry  of  tin1  -jwU  is  imt  !•»  be  im|»nrb*d  indiscrim- 
inately : it  i.s  to  he  made  known  1o  the.  w<  li-lricd  pupil,  who 
remains  a year  under  iustruclion. 

The  commuinai  v uinler^tamls  h\  1 hi<  mxslery,  whi.-li  is  to  be  kept 
with  so  jealous  i-uv,  i!ic  kimw  i.-.ljv  r ■»  ili«-  subji-et  nf  this  eliapicr.  tho 
delineation  of  an  -i-lip-e,  as.*l  i."i  ihe  g'-in-ral  -uhj.-.-t  of  I'dip^s  a- 
treated  in  the  pu.M  iIipm*  eliap:i  r*.  h m-i-ihv  ;i  lit i !.•  curnM!.-  tn  find  a 
matter  of  so  suhnniinati*  r-«in— -iji,i-in-<-  In  r:ddi-d  <•  ■ p'oiip-msly  in  tho 
first  verso  of  the  chapter,  and  guarded  mi  eaiiliiiu^K  at  i1  ^ clo-i*. 


c ii  a vt  h it  v 1 1. 

OF  V U\ X KT-t  It  V ( It ) N.T  F XfTTON  H. 

Contexts 1 p general  clas"ifieit ion  of  planetary  ronj auctions;  2- k tjictliofi  of  de- 
termining at  what  point  nn  the  ecliptic,  fuel  tit  what,  time,  two  planets  will  come 
to  have  the  same  longitude.;  7-10,  how  to  find  the  point  on  the.  ecliptic  to  which 
B planet,  having  latitude,  will  be  refeired  by  a circle  passing  through  tho  north 
and  south  points  of  the  horizon  ; 11,  when  a planet  must  be  so  referred;  12,  how 
to  ascertain  the  interval  between  two  planets,  when  in  conjunction  upon  such  a 
north  and  south  line;  13-14,  dimensions  of  the  lesser  planets;  15-18,  modes  of 
exhibiting  the  coincidence  between  the  calculated  and  actual  places  of  the  planets ; 
18-20,  definition  of  different  kinds  of  conjunction ; 20-21,  when  a planet,  in  con- 


Translation  and  Notes . 


168 


vii.  6.] 

junction,  is'  vanquished  or  victor;  22,  farther  definition  of  different  kinds  of  con- 
junction; 23,  usual  prevalence  of  Venus  in  a conjunction;  23,  planetary  conjunc- 
tions with  the  moon;  24,  conjunctions  apparent  only;  why  calculated. 

1.  Of  the  star-planets  there  take  place,  with  one  another,  r 
encounter  ( yutklha ) and  conjunction  (sarnd.yama) ; with  the  moon, 
conjunction  (sarndyamu) ; with  the  sun,  heliacal  setting  (aslamana). 

The  “star-planets”  ( turugraha ) arc,  of  course,  the  five  lesser  planets, 
exclusive  of  the  sun  and  moun.  Their  conjunctions  with  one  another 
and  with  the  moon,  with  the  nstcrisin*  {luikshatra),  and  with  the  sun, 
arc  the  subjvcK  « if  this  and  the  two  fnl  lowing  chapters. 

For  the  general  idea  of  “conjunction"  various  terms  are  indifferently 
employed  in  llii-*  chapter,  as  sanutyama,  ••  coming  1 oifdl ier",  samyoga, 

“ conjunction,"  yogaH  ••  junction"  (in  viii.  I t,  aUo,  iuvluka,  “fc  meeting”)  : 
the  word  ynti,  fci  union,"  which  i-  rmi-Tantly  use* l in  the  same  sense  by 
the  commentary,  and  which  ■'Ut«>i>  into  tin1  title  of  the  chiiptpr,f/r<i/ia- 
yntyad hik’d rtt,  does  not  occur  anywhere  in  the  text.  Thu  word  which 
we  translate  “ riici muter,”  ymhlhtt%  iu<  sin-  literally  ■•  war,  conflict" 
Verses  18-20,  ami  w*r»e  l»2,  below,  give  di-tiin-tivo  dcliniliuin  of  some 
of  ihe  dillmnL  kinds  of  cnc.Minler  and  conjunction. 

2.  When  the  Inngitudr  of  the  swilVinoving  planet  is  greater 
tluui  that  of  the  slow  one,  the  conjunction  "vya)  is  jurist:  oth- 
erviise,  it  is  to  conn1:  this  i>  the  ease  when  tin?  two  are  moviug 
eastward;  ttfehowevt-r,  they  arc  retrograding  (cab-in),  the  con- 
trary is  tru®F 

3.  When  the  longitude  of  the  one  moving  eastward  is  greater, 
the  conjunction  {mnidgama)  is  past;  hut  when  that  of  the  one 
that  is  retrograding  is  greater,  it  is  to  conic.  Multiply  tho  dis- 
tance in  longitude  of  the  planets,  iu  minutes,  by  the  minutes  of 
daily  motion  of  each, 

4.  And  divide  the  products  by  the  difference  of  daily  motions, 
if  both  arc  moving  with  direct.,  or  both  with  retrograde,  motion: 
if  one  is  retrograding,  divide  by  the  sum  of  daily  motions. 

5.  The  quotient,  in  minutes,  etc.,  is  to  be  subtracted  when  the 
conjunction  is  past,  and  added  when  it  is  to  come : if  the  two  are 
retrograding,  the  contrary : if  one  is  retrograding,  the  quotients 
are  additive  and  subtractive  respectively. 

6.  Thus  the  two  planets,  situated  in  the  zodiac,  are  made  to  be 
of  equal  longitude,  to  minutes.  Divide  in  like  manner  the  dis- 
tance in  longitude,  and  a quotient  is  obtained  whLIi  is  the  time, 
in  days,  etc. 

The  object  of  this  process  is  to  determine  where  and  when  the  two 
planets  of  which  it  is  desired  to  calculate  the  conjunction  will  have  the 
same  longitude.  The  directions  given  in  Ihe  text  are  in*the  main  so 
clear  as  hardly  to  require  explication.  The  longitude  and  the  rate  of 
motion  of  the  two  planets  in  question  is  supposed  to  have  been  found  for 
some  time  not  far  removed  from  that  of  their  conjunction.  Then,  in 


164 


Sfaya-Suid/i&iita,  |vii.  0- 

determimug  whether  the  conjunction  is  past  or  to  come,  and  at  wluit  dfc* 
tance,  in  arc  ami  in  time,  three  separate  cases  require  to  be  taken  into 
qpconnt — when  both  are  advancing,  when  both  are  retrograding,  and 
when  one  is  advancing  and  the  other  retrograding.  In  the  two  former 
cases,  the  planets  are  approaching  or  receding  from  one  another  by  the 
difference  of  their  daily  motions;  in  the  latter,  by  the  slim  of  their  daily 
motions.  The  point  of  conjunction  will  be  found  by  the  following  pro- 
portion : as  the  daily  rate  ai  which  the  two  are  approaching  or  receding 
from  each  other  is  to  their  distance  in  longitude,  so  is  the  daily  motion 
of  each  one  to  the  distance  which  it  will  have  to  move  before,  or  which 
it  lias  moved  fince.  the  conjunction  in  longitude.  The  time,  again, 
elapsed  or  to  elapse  between  the  giwn  monieiil  and  that  of  the  eoiijnne- 
tion,  will  be  found  l>v  dividing  the  distance  in  longitude  by  the  same  divi- 
sor as  was  used  in  the  other  puit  of  the  procos,  namely  the  daily  rate 
of  approach  or  separation  of  the  two  planets. 

The  only  other  matter  whirli  seems  to  call  for  more  special  explana- 
tion than  is  to  be  found  in  tlie  te\r  i%  at  what  moment  the  process  uf 
calculation,  as  thu*  conducted,  shall  rummenee.  If  a time  be  lixed 
upon  which  is  too  far  removed — as,  l«»r  iiedanee,  by  an  iutenal  of  sev- 
eral days — from  the  moment  of  actual  conjunction.  the  vale  of  motion 
of  the  two  planets  will  be  liable  to  change  in  tin*  mean  time  so  much  a-* 
altogether  1o \itiale  the  eonvdness  «if  tlie  i,:dcul;<lioii.  h is  probable 
that,' as  in  tlie  calculation  of  an  eclipse  (soe  above,  note  to  iv.  7-*),  we  are 
supposed,  before  entering  upon  tin*  particular  process  which  is  the  sub- 
ject of  this  parage,  to  have  ascertained,  by  previous  ttfjbtive  calcula- 
tions, The  midnight  next  preceding  or  following  the  cnrgPjption.  and  i • » 
have  determined  tor  that  time  the  loic/it  tides  and  rates  of  moiimi  of  the 
two  planets  If  so,  the  oneralion  will  give,  without  farther  repetition, 
results  having  the  desired  degree  of  accuracy.  ’I  h * commentary,  it  may 
be  remarked,  give*  us  1,0  light  upon  this  pnim,  a-*  it  -rave  ns  ti.»ne  in  the 
case  of  the  eclipse. 

We  have  not,  howo\er,  tlin-*  nseerlaiimd  tin*  tins.-  end  place  of  | he 
conjunction.  This,  to  the.  Hindu  appivhcn-iim,  lakes  plai,e,  not  when 
the  two  planets  arc  upon  the  same  '•■enmlan  1 • * the  ecliptic,  hut  when 
they  are  upon  the  .-nine  >ocnnc)nr\  to  the  prime  vertical,  or  upon  the 
same  circle  passing  through  the  north  and  .-outli  point*  of  the  horizon. 
Upon  such  a circle  two  stars  rise  and  set  .simultaneously  ; upon  such  a 
one  they  together  pass  tlie  incridi:,-.i : such  a line,  then,  determines 
approximately  their  relative  height  above  tlie  horizon,  each  upon  its  own 
circle  of  daily  revolution.  We  have,  also  M-cn  above,  w hen  considering 
the  deflection  ( valana — sec  iv.  24-25),  that  a secondary  to  the  prime  ver- 
tical is  regarded  ps  determining  the  north  and  south  directions  upon  the 
starry  concave.  To  ascerjpin  what  will  he  the  place  of  each  planet  upon 
the  ecliptic  when  referred  to  it  by  such  a circle  is  the  object  of  the  fol- 
lowing processes. 

7.  Having  calculated  the  measure  of  the  clay  and  niglit>  and 
likewise  the  latitude  (- vileshepd ),  in  minutes  ; having  determined 
the  meridian-distance  (?i ata)  and  altitude  ( unnatd ),  in  time*  accord- 
ing-to  the  corresponding  orient  ecliptic-point  (i lagnd ) — 


Translation  and  Note, 


\iL13.] 


8.  Multiply  the  latitude  by  the  equinoctial  shadow,  and  divide 

by  twelve ; the  quotient  multiply  by  the  meridian-distance  in 
nadis,  and  divide  oy  the  corresponding  half-day:  ** 

9.  The  result,  when  latitude  is  north,  is  subtractive  in  the 
eastern  hemisphere,  and  additive  in  the  western ; when  latitude 

• is  south,  on  the  other  hand,  it  is  additive  in  the  eastern  hemi- 
sphere, and  likewise  subtractive  in  the  western. 

10.  Multiply  the  minutes  of  latitude  by  the  degrees  of  declin- 
ation of  the  position  of  the  planet  increased  by  three  signs:  the 
result,  in  seconds  (uikahi),  is  additive  or  subtractive,  according  aa 
declination  and  latitude  are  of  unlike  or  like  direction. 

11.  In  calculating  the  conjunction  (yoya)  of  a planet  and  an 
asterism  {liakshatni),  in  determining  the  setting  and  rising  of  a 
planet,  and  in  finding  the  elevation  of  the  moon’s  cusps,  this  ope- 
ration for  apparent  longitude  {rfrkkarmun)  is  first  prescribed. 

12.  Calculate  again  the  longitudes  of  the  two  planets  for  the 
determined  time,  and  from  these  their  latitudes:  when  the  latter 
are  of  the  same  direction,  take  their  diilerencu  ; otherwise,  their 
sum : the  result  is  the  interval  of  the  planets. 

The  whole  operation  for  determining  the  point  on  the  ecliptic  to 
which  a planet,  having  a given  latitude,  will  be  referred  by  a secondary 
to  the  prime  vortical,  is  •■ailed  it»  ilrkkarman.  Doth  pails  of  this  com- 
pound wc  have  had  befoiv — the  latter,  signifying  operation,  process  of 
calculation,”  in  ii.  ft  7,  42,  etc. — 6»r  t.lnk  former.  >ec  the  notes  to  iii.  28- 
34,  and  v.  5-0  : here  we  are  to  understand  it  as  signifying  the  i%  appar- 
ent longitude'1  of  a planet,  when  referred  to  the  eeiiptic  in  the  manner 
stated,  as  distinguished  from  il»  into  or  actual  longitude,  reckoned  in  the 
usual  way:  we  accordingly  translate  the  whole  term,  as  in  verse  11, 

14  operation  for  apparent  longitude.”  The  operation,  like  the  somewhat 
analogous  one  by  which  the  ccliptic-detlociion  (uulanu)  is  determined 
(see  above,  iv.  24-25),  consists  of  two  separate  processes,  which  receive 
in  the  commentary  distinct  names,  corresponding  with  those  applied  to 
the  two  parts  of  the.  process  for  calculating  the  deflection.  The  whole 
subject  may  be  illustrated  by  reference  to  the  next  figure  (Fig.  2S).  This 
represents  the  projection  of  a part  of  the  sphere  upon  a horizontal  plane, 
N and  E being  the  north  and  cast  points  of  the  horizon,  and  Z the 
zenith.  Let  C L be  the  position  of  the  ecliptic  at  the  moment  of  con- 
junction in  longitude,  C being  the  orient  ecliptic-point  {lofjna) ; and  let 
M be  the  point  at  which  the  conjunction  in  longitude  of  the  two  planets 
S and  V,  each  upon  its  parallel  of  celestial  latitude,  cl  aijd  c' i\  and  hav- 
ing latitude  equal  to  SM  and  YM  respectively,  wil  take  place.  Through 
V and  S draw  secondaries  to  the  prime  vertical,  Is  V and  N S,  meeting 
the  ecliptic  in  v and  s:  those  latter  arc  the  points  of  apparent  longitude 
of  the  two  planets,  which  are  still  removed  from  a true  conjunction  by 
the  dUtfuce  v s : in  order  to  the  ascertainment  of  the  time  of  that  true 
conjunotionv  it  is  desired  to  know  the  positions  of  v and  a,  or  their  re- 
spective distances  from  M.  From  F,  the  pole  of  the  equator,  draw  also 
circles  through  the  two  planets,  meeting  the  ecliptic  in  i'  and  v’ : then, 
23 


l&uryii  • Siddkdnta, 


in  order  to  find  M t,  wc  ascertain  the  values  of  # #'  and  M s' ; and,  in 
like  manner,  to  find  M v,  we' ascertain  the  values  of  v v'  and  Mr\  Now 

at  the  equator,  or  in  a right 
snlierc,  the  circles  N S au«i 
PS  would  coincide,  and 
the  distance  x **  disappear  : 
hence,  the  amount  of  * / 
being  dependent  upon  the 
latitude  (akxltft)  of  the  ob- 
server, N 1\  the  process  hpr 
which  it  is  calculated  is 
called  the  “ operation  for 
latitude”  ('tkshuih;kkarman} 
or  cl  c dks/ia  drkkarman). 
Again,  if  P and  V 9 were  the 
same  point,  or  if  the  eclip- 
tic and  equator  coincided, 
V S and  P'  S would  coin- 
cide. and  M s'  would  d ‘^ap- 
pear : hence  the  process  of 
calculation  of  M *'  is  called 
the  44  operation  for  ecliptic- 
deviation”  (ayunadrkkar- 
man.  or  dyana  drkkarman). 
The  latter  of  the  two  pro- 
cesses, although  statcil  after 
the  other  in  the  text,  is  the 
one  first  explained  by  the 
commentary  : wc  will  also, 
as  in  the  case  of  the  deflec- 
tion (note  to  iv.  24-25), 
give  to  it  our  first  attention. 
The  point  s\  to  which  the  planet  is  referred  by  a circle  passing  through 
the  pole  P,  is  styled  by  the  commentary  ayanay^aha,  11  the  planet's  lon- 
gitude to  corrected  for  cclipt'e-dcviation,"  and  the  distance  Mi',  which 
it  is  desired  to  ascertain,  is  called  ayanakiias , 44  the  correction,  in  min- 
utes, for  ecliptic-deviation.”  Instead,  however,  of  finding  Ms',  the  pro- 
cess taught  in  the  text  finds  M t,  the  corresponding  distance  on  the  cir- 
cle of  daily  revolution,  D U,  of  the  point  M — which  is  then  assumed 
equal  to  M s'.  The  proportion  upon  which  the  rule,  as  stated  in  verse 
10,  is  ultimately  founded,  is 

K : sin  M S f : : M S : M t 


the  triangle  MSf,  which  is  always  very  small,  being  treated  as  if  it 
were  a plane  triangle,  right-angled  at  t.  But  now  also,  as  the  latitude 
MS  is  always  a small  quantity,  the  angle  P S P'  may  be  treated  as  if 
equal  to  PmP'  (not  drawn  in  the  figure);  and  this  angle  is,  as  was 
qhown  in  connection  with  iv.  24-25,  the  deflection  of  the  ediptiq  from 
the  equator  {dyana  valana ) at  M,  which  is  regarded  as  equal  to  the 
<fe<$rtation of  the  point  00°  in  advance  of  M:  this  pointy  for  convfu- 
feqptfp  Mke,  we  will  call  M'.  Our  proportion  becomes,  then 


▼2.  l'$i]  Translation  and  Notes.  187  - 

R : sin  dccl.  M' ::MS:  M t . 

aU  the  quantities  which  it  contains  being  in  terms  of  minutes.  To  bring, 
this  proportion,  now,  to  the  form  in  which  it  appears  in  the  text,  it 
made  to  undergo  a most  fantastic  and  unscientific  serin*  ofsjtfc * 
The  greatest  declination  (ii.  98)  being  24#,  and  its  sine"  1 
nearly  fifty-eight  times  twenty-four — since  58  X &4±± 1 ' 
that  fifty-eight  times  the  number  of  degrees  in  any  given 
tion  will  be  equal  to  the  number  of  minutes  in  the  sine  5 or 
Again,  the  value  of  radius,  3438',  admits  of  being  roughly  £n3^Jn$b 
the  two  factors  fifty-eight  and  sixty — since  58  X 00=3480.  SubstltUt 
ing,  then,  these  values  in  the  proportion  as  stated,  we  have 

58X00  : 58Xdecl.  M'  in  degr. : : latitude  in  min.  :Uf  ^ 

Cancelling,  again,  the  common  factor  in  the  first  two  terms;*  and  ttajbe- 
ferring  the  factor  80  to  the  fourth  term,  we  obtain  finally 

1 : dccl.  M'  in  degr. : : latitude  in  min. : M tXOO 
that  is  to  sav,  if  the  latitude  of  the  planet,  in  minutes,  be  multiplied  by 
the  declination,  in  degrees,  of  a point  90°  in  advauce  of  the  planet,  the 
result  will  be  a quantity  which,  after  being  divided  by  sixty,  or  reduced 
from  seconds  to  minutes,  is  to  be  accepted  as  the  required ‘interval  on 
the  ecliptic  between  llic  real  place  of  the  planet  and  the  point  to  which 
il  is  referred  by  a secondary  to  the  equator.  i 

This  explanation  of  the  rule  is  the  one  given  by  the  coqweikmAi 
nor  are  wo  able  to  sec  that  it  admits  of  any  other.  The  rMUijfipii  Qf 
the  original  proportion  to  its  final  form  is  a process  to  which  w*  Kavfc 
heretofore  found  no  parallel,  and  which  appears  equally  absuri^  ahd 
uncalled  for.  That  M t is  taken  as  equivalent  to  M s' has,  as  will  appear 
from  a consideration  of  flic  next  process,  a certain  propriety. 

The  value  of  the  arc  M s’  being  thus  found,  the  question  arises,  in 
which  direction  it  shall  be  measured  from  M.  This  depends  upon  the 

tiositiou  of  M with  reference  to  the  solstitial  colurc.  At  the  colure,  the 
ines  PS  and  P'S  coincide,  so  that,  whatever  be  the  latitude  of  a planet, 
it  will,  by  a secondary  to  the  equator,  be  referred  to  the  ecliptic  at  its 
tnft  jpoint.  of  longitude.  From  tho  winter  solstice  onward  to  the  auinwer 
solstice,  or  when  the  point  M is  upon  the  suuh  uorthward  path  (uMarufe- 
yoiia),  a plauet  having  north  latitude  will  be  referred  backward  on  tb£ 
ecliptic  by  a circle  from  the  pole,  and  a planet  having  south  latitude, will 
be  referred  forward.  If'M,  on  tho  other  hand,  be  upon  tbo  sun’s  south* 
ward  path  (dakskiiuhjana),  a planet  having  north  latitude  at  that  point 
will  be  referred  forward,  and  one  having  south  latitude  backward : this 
is  the  case  illustrated  by  the  figure.  The  statement  of  the  text  virtually 
agrees  with  this,  it  being  evident  that,  when  M is  ou  tiie  northward 
path,  the  declination  of  the  point  00°  in  advauce  if  it  will  be  north,  and 
the  contrary. 

Wc  come  now  to  consider  the  other  part  of  the  operation,  or  ths 
d kska  drkkarman , which  forms  the  subject  of  verses  7-9.  '4*  the  first 
step,  we  arc  directed  to  ascertaiu  the  day  and  tho  night  respectively  of 
the  point  of  the  ecliptic  at  which  the  two  planets  are  iu  conjunction  in 
longitude,  for  the  purpose  of  determining  also  its  distance  in.  time  frdrii 
the  horizon  and  from  the  meridian.  This  is  accomplished  as  ' follows. 


168 


S&nja*Siddh&nta}  [vii.  12. 

Having  the  longitude  of  the  point  in  question  (M  in  the  last  figure), 
we  calculate  (by  ii.  28)  its  declination,  which  gives  us  (by  ii.  60)  the- 
^radius  of  its  diurnal  circle,  and  (by  ii.  Gl)  its  ascensional  difference; 

, ' whence,  again,  is  derived  (by  ii.  (32-63)  the  length  of  its  day  and  night. 
£g&in,  having  the  time  of  conjunction  at  Al,  we  easily  calculate  the 
^tin’s  longitude  at  the  moment,  and  this  ami  the  time  together  give  us 
(by  iii.  4G-4S)  the  longitude  of  C,  the  orient  ecliptic-point : then  (by 
* iii.  50)  we  ascertain  directly  the  difference  between  the  time  when  M rose 
and  that  when  0 rises,  which  is  the  altitude  in  time  ( unnuta ) of  M : the 
difference  between  this  and  the  hulf-duy  is  the  meridian-distance  in  time 
( nata ) of  the  same  point.  If  the  conjunction  takes  place  when  M is 
below  the  horizon,  or  during  its  night,  its  distance  from  the  horizon  and 
from  the  inferior  meridian  is  determined  in  like  manner. 

The  direct  object  of  this  part  of  the  general  process  being  to  find  the 
value  of  8 s',  we  note  first  that  that  distance  is  evidently  greatest  at  the 
horizon;  farther,  that  it  disappears  at  the  meridian,  where  the  lines  PS 
and  NS  coincide,  if,  then,  it  is  argued,  its  value  at  the  horizon  can  be 
ascertained,  we  may  assume  it  to  vary  as  tin*,  distance  from  the  meridian. 
The  accompanying  ligure  (l;ig.  l’U)  will  illustrate  the  method  by  which 
it  is  attempted’  to  calculate  n'  at  the  horizon.  Suppose  the  planet  S, 
Pi!r  eg,  being  removed  in  latitude  t«»  the  distance. 

■ M S from  M,  the  point  «»f  the  ecliptic 

which  determine*  its  longitude,  to  be  upon 
the  horizon,  ami  let  as  before,  be  the 
I lint  to  wliirh  il  i>  referred  by  a circle 
from  tin*  north  j»i«le:  it  is  desired  to  deter- 
mine 1 lie  value  of  s s'.  Let  ]>  It  be  the 
•divlr.  of  diurnal  levobuiou  of  the  point 
M,  meeting  S s'  in  /,  and  the  horizon  in  w : 
S tw  may  be  regarded  as  a plane  right-angled  triangle.,  having  its  angles 
at  S and  w respectively  equal  to  tin;  observer's  latitude  aiul  co-latitude. 
In  that  triangle,  to  tiud  the  value  of  t ir.  we  should  make  tin;  proportion 
cos  t S to  : ‘•in  t S w : : / S : t :o 

Now  the  first  of  these  ration,  that  of  the  co>ii:e  to  tlio  >iim  of  latitude, 
is  (see  above,  iii.  17)  the  same  with  that  of  the  gnomon  to  ihc  equinoc- 
tial shadow:  again,  ns  the.  differem-e  of  M i and  M s'  was  in  the  pre- 
ceding process  neglected,  so  here  the.  difference  of  SM  and  S t\  and 
finally,  l w,  the  true  result  of  the  process,  is  accepted  as  the  equivalent 
of  8*8,  the  distance  sought.  The  proportion  then  becomes 

gnom. : eq.  shad.  : ■ latitude : required  di-t.  at  horizon 
The  value  of  the  required  distance  at  the  horizon  having  been  thus 
ascertained,  its  value  at  any  given  alt iLml c is,  as  pointed  out  above,  deter- 
mined by  a proportion,  as  follows  : as  the  planet’s  distance  in  time  from 
the  meridian  when  upon  the  horizon  is  to  the  value  of  this  correction  at 
' the  horizon,  so  is  any  given  distance  from  the  meridian  (nata)  to  tlio 
value  at  tlut  distance ; or 

half-day : mcr.-dist.  in  time : : result  of  last  proportion  : required  distance 
The  direction  in  which  the  distance  thus  found  is  to  be  reckoned,  start- 
ing in  each  case  from  the  dyaua  graha , or  place  of  the  planet  on  the 


Translation  and  Notes. 


169 


vii.  12.] 


ecliptic  as  determined  by  u secondary  to  the  equator,  which  was  ascer- 
tained by  the  preceding  process,  is  evidently  as  the  text  states  it  in  verse 
0.  In  the  eastern  hemisphere,  which  is  the  case  illustrated  by  the  figure, 
s' 9 is  additive  to  the  longitude  of  a1,  while  v'v  is  subtractive  from  the 
longitude  of  v* : in  the  western  hemisphere,  the  contrary  would  be  the 
case.  The  final  result  thus  arrived  at  is  the  longitude  of  the  two  points 
s and  ?*,  to  which  S and  V are  referred  by  the  circles  NS  and  NV, 
drawn  through  them  from  the  north  and  south  points  of  the  horizon. 

The  many  inaccuracies  involved  in  these  calculations  are  too  palpable 
to  require  pointing  out  'in  detail.  The  whole  operation  is  a roughly 
approximative  one,  of  which  the  errors  are  kept  within  limits,  and  the 
result  rendered  sufficiently  correct,  only  by  the  general  minuteness  of 
the  quantity  entering  into  it  as  its  main  element — namely,  the  Latitude 
of  a planet — ami  by  the  absence  uf  any  severe  practical  tot  of  its  accu- 
racy. It  may  be  remarked  that  the  commentary  is  well  aware  of,  and 
points  out,  must  of  the  error-  of  the  processes,  excusing  them  by  its 
stereotyped  plea  of  their  insignificance,  and  t!ic  merciful  disposition  of 
the  divine  autimr  uf  the  treati.-e. 

Having  thus  nhl.'iincd  s nnd  t\  !lic  apparent  longitudes  of  the  two 
planets  at  the  time  when  their  true  longitude  is  M.  the  question  arises, 
how  we  shall  determine  llie  time  «»f  apparent  mu  junction.  Vpnn  this 
point  the  text  gives  u-  in*  light  at.  all : according  to  the.  coimnentarv,  we 
are  lo  repeal  tin-  proe*-s  pivM-rihr.l  in  \erscs  ^-1»  above,  determining, 
from  a consideration  of  tin*  rale  and  direction  of  motion  of  the  planets 
in  connection  with  their  new  place-,  w ln-tlior  the  conjunction  sought  for 
is  past  or  to  come,  and  lin  n :i->-ei-t:iiniu«r.  by  dividing  the  distance  vs 
bv  their  daily  rate  of  approach  i.r  recession,  thu  time  of  the  conjunction. 

It  is  evident,  linwexer,  that  one  uf  tin-  i-lcincnt- **f  the  process  of  correc- 
tion for  latitude  {aMi^h'kkurintin).  namely  the  meridian-distance,  is 
changing  so  npidlv,  a-  ■■■•niparcd  with  the  slow  motion  of  the  planets  in 
their  orbits,  that  -licli  a prove—  ci.nld  m*i  yield  results  at  all  approaching 
to  accuracy : it  also  appears  that  two  slow-moving  planets  might  liavo 
more  than  one.  and  even  several  apparent  conjunctions  on  successive 
days,  at.  difiereut  limes  in  the  day,  being  found  to  stand  together  upon 
the  same  secondary  to  the  prime  vertical  at  different  altitudes.  We, 
do  not  see.  how  this  difficulty  i-  met  by  anything  in  the  text  or  in^ 
the  commentary.  The  text,  a— liming  the  moment  of  apparent  conjunct 
tion  to  have  been,  by  whatever  method,  already  determined,  goes  on  to 
direct  us,  iu  verse  li,  to  calculate  anew,  for  that  moment,  the  latitudes 
of  the  two  planets,  in  order  to  obtain  their  d\*t;nice  from  one  another. 
Here,  again,  is  si  slight  inaccuracy  : the  intervr1.  between  the  two,  meas- 
ured upon  a secondary  »o  the  prime  vertical,  is  not  pr'  iselv  equal  to 
the  sum  or  difference  of  ilicir  latitudes,  which  are  neasured  upon  second- 
aries to  the.  ecliptic.  The  ascertainment  of  this  interval  is  necessary,  in 
order  to  determine  the  name  and  character  of  the  conjunction,  as  will 
appear  farther  on  (vv.  18-20,  -JJ). 

The  cases  mentioned  inverse  11,  in  which,  as  well  as  in  “calculating 
the  conjunctions  of  two  planels  with  one  another,  this  operation  for 
apparent  longitude  (drkltairman)  needs  lo  be  performed,  are  the  subject* 
of  the  three  following  chapters. 


170  ■ 


Sdrya-Siddlidn  lat  [vfi.  13- 

13.  The  diameters  upon  the  moon’s  orbit  of  Mars,  Saturn, 
Mercury,  and  Jupiter,  are  declared  to  be  thirty,  increased  suc- 
cessively by  half  the  half ; that  of  Venus  is  sixty. 

14.  These,  divided  by  the  sum  of  radius  and  the  fourth  liypotli- 
tinuse,  multiplied  by  two,  and  again  multiplied  by  radius,  arc  the 
respective  corrected  (sphut/i)  diameters:  divided  by  fifteen,  they 
are  the  measures  (jndna)  in  minutes. 

We  have  seen  above,  in  connection  with  the  calculation  of  eclipses 
(iv.  2-5),  that  the  diameters  of  the  snn,  moon,  and  shadow  had  to  be 
reduced,  for  measurement  in  minutes,  to  the  moon’s  mean  distance,  at 
which  fifteen  yojanas  make  a minute  of  arc.  Here  wc  find  the  dimen- 
sions of  the  five  lesser  planets,  when  at  their  mean  distances  from  the 
earth,  stated  only  in  the  form  of  the.  portion  of  the  moon’s  mean  orbit 
covered  by  them,  their  absolute  size  being  left  undetermined.  We  add 
them  below,  in  a tabular  form,  both  in  yojanas  and  as  reduced  to  min- 
utes, appending  also  the  corresponding  estimates  of  Tycho  Brahe  (which 
wc  take  from  Delauibrc),  and  the  true  apparent  diameters  of  the  plan- 
"ots,  as  seen  from  the  earth  at  their  greatest  and  least  distances. 

y Apparent  Diameters  of  the  Planets , according  to  the  Sun/a-Siddhuntn , 
V . to  Tycho  Brahe . and  to  Modern  Science. 


Planet. 

j Sui  v:i-Sid«llii'iil:i : 

j in  yoji.iwiR.  | in  arc. 

Tychu 

lir.Uie. 

J Moderns : 

IpbvI.  groatcat. 

Mars, 

j 3<j 

r 

4" 

a?" 

Saturn, 

3-4 

\ r 5o#i 

i5' 

>1'' 

Meicury. 

45 

* .. . 

! T 

?’  Id" 

1 -i" 

la" 

Jupiter, 

i 

• V ’)■>” 

s >’  A:i" 

3n" 

IQ" 

Venus. 

! r>o 

i .r 

i 3f  i:i" 

: v"  : 

; if 

— 

• . . — — 

1 

— 

— 

This  tabic  shows  bow  greatly  nxaggenited  are  wont  to  be  anv  deter- 
minations of  the  magnitude  of  the  planetary  orbs  made  by  tile  unas- 
sisted eye  alone.  This  effect  is  due  to  the  well-known  phenomenon  of 
. the  irradiation,  which  increase*  the  apparent  hizo  of  a brilliant  body 
when  seen  at  some  distance.  It.  will  lie  noticed  that  the  Hindu  esti- 
mates do  not  greatly  exceed  those  of  Tjelio,  the  most  noted  and  accu- 
rate of  astronomical  observers  prior  to  the  invention  of  the  telescope, 
fn  respect  to  order  of  magnitude  they  entirely  agree,  and  both  accord 
with  the  relative  apparent  hi/o  of  the  planets,  except  that  to  Mercury 
and  Venus,  who&c  proportional  brilliancy,  from  their  nearness  to  the 
sun,  is  greater,  is  assigned  too  high  a rank.  Tycho  also  established  a 
scale  of  apparent  diameters  for  the  fixed  stars,  varying  from  2',  for  the 
first  magnitude,  down  to  20",  for  the  sixth.  Wc  do  not  find  that 
Ptolemy  made  any  similar  estimates,  cither  for  planets  or  for  fixed  stars. 

The  Hindus,  however,  push  their  empiricism  one  step  farther,  gravely 
laying  dom  a rule  by  which,  from  these  mean  values,  the  true  values 
of  the  apparent  diameters  at  any  given  time  may  be  found.  The  funda- 
mental proportion  is,  of  course, 

true  dist. : mean  disk : : mcau  app.  diam. : true  app.  diam. 


Translation  and  Notes. 


171 


*w- 

The  second  lenn  of  this  proportion  is  represented  bjr  radius : for  the 
first-  we  have,  according  to  the  translation  given,  one  half  the  sum  of 
radius  and  the  fourth  hypothenusc,  by  which  is  meant,  the  11  variable 
liypothcnuse”  {cala  karna)  found  in  the  course  of  the  fourth,  or  last,  . 
process  for  finding  the  true  place  of  the  planet  (see  above,  ii.  43-4C&  ^ 
The  term,  however  (tricalv hkartiu),  which  is  translated 11  radius  and  Ityfjf,;. 
fourth  hypothenusc”  isimu-h  more  naturally  rendered  “third  and  fourtff 
liypotheimscs" ; and  the  latter  interpretation  is  also  mentioned  by  the  '* 
commentator  as  one  handed  down  by  tradition  (samprod&yika) : but, 
lie  adds,  owing  to  the  fact  that  the  length  of  the  hypnthonuse  is  not 
calculated  in  the  third  process,  that  lur  finding  filially  the  equation  of 
the  centre  (nuuuluknrwah),  ami  that  that  liyputhciiusc  cannot  therefore 
be  referred  to  here  as  known,  mu  drill  interpreters  understand  the  first 
member  of  the  compound  (in')  as  an  abbreviation  for  “ radius”  (trijyd), 
and  translate  it  accordingly.  We  must  confers  that  the  other  interpre- 
tation seems  to  us  r«»  be  powerfully  supported  by  both  the  letter  of  the 
text  and  the  reason  of  the  matter.  The  sub>titulioii  of  tri  for  Irijyb  in 
such  a connection  is  quite  too  \ioicnt  to  bo  borne.  iv>r  do  wo  see  why 
half  the  sum  of  radius  and  the  fourth  hypoilicnu<o  should  be  taken  as 
representing  the  planet's  true  diMance,  rather  than  the  fourth  hypothc- 
ti use  alone,  which  was  employed  (see  above,  ii.  oG-5S)in  calculating  the  .. 
latitude  of  the  planets.  On  the  other  hand,  there  is  reason  for  adopt-'- 
ing,  as  the  relative  value  of  a plain  tV  true  distance,  the  average,  or  half 
the  sum,  of  the  third  l»vpotliei»i>»',  or  the  planet’s  distance  as  affected 
by  the  eccentricity  of  it*  orbit,  and  the  fourth,  or  its  distance  as  affected 
by  the  motion  of  the  earth  in  her  orbit.  There  seems  to  us  good 
reason,  therefore,  to  suspect  that  verse  1 1— and  with  it,  probably,  also 
verse  13 — is  an  intrusion  into  the  Surya-Siddlianta  from  some  other  sys- 
tem, which  did  not  make  the  grossly  erroneous  assumption,  pointed  ont 
under  ii.  30,  of  the  equality  of  the  sine  of  anomaly  in  the  epicycle 
(hhujajyuphala)  with  the  sine  of  the  equation,  but  in  which  the  hypoth- 
e n use  and  the  sine  of  the  equation  were  duly  calculated  in  the  process 
for  finding  the  equation  of  the.  ap^is  (manrfak<irm«u),  as  well  as  in  tliafc 
for  finding  the  equation  of  the  conjunction  (ffnhrakarman). 

15.  Exhibit,  upon  the  shadow-ground,  the  planet  at  the  ex- 
tremity of  its  shadow  reversed : i:  is  viewed  at  the  apex  of  the.., 
gnomon  in  its  mirror. 

As  a practical  test  of  the  accuracy  of  his  calculations,  or  as  a con- 
vincing proof  to  the  pupil  or  other  person  of  hi*  knowledge  and  skill, 
the  teacher  is  here  directed  to  set  up  a gnomo  i upon  ground  properly 
prepared  for  exhibiting  the  shadow,  and  to  calculrte  and  Ly  off  from.-the 
base  of  the  gnomon,  but  in  the  opposite  to  the  ii  ic  direction,  the  shad- 
ow which  a planet  would  east  at  a given  time  ; upon  placing,  then,  a 
horizontal  mirror  at- the  extremity  of  the  shadow,  the  reflected  image  of 
the  planet's  disk  will  be  seen  in  it  at  the  given  time  by  an  eye  placed  at 
the  apex  of  the  gnomon.  The  principle  of  the  experiment  is  clearly 
correct,  and  the  rales  and  processes  taught  in  the  second  and  third  chap- 
ters afford  the  means  of  carrying  it  out,  since  from  them  the  shadow 
which  any  star  would  cast,  had  it  light  enough,  may  be  as  readily  deter- 


S&  i *ya  - Sit  hlh&nt'i, 


mined  as  that  which  the  sun  actually  casts.  As  no  case  of  precisely  this 
7 character  has  hitherto  been  presented,  we  will  briefly  indicate  the  course 
g$  the  calculation.  The  day  mid  night  of  the  planet,  and  its  distance 
jftjfi&xn  the  meridian,  or  its  hour-angle,  arc  found  in  the  same  manner  its  in 
.process  previously  explained  (p.  108,  above),  excepting  that  here  tlm1^? 
$jplanet's  latitude,  and  its  declination  as  affected  by  latitude,  must  be  cal-  ‘ 
eulated,  by  ii.  50-58 : and  then  the  hour-angle  and  the  ascensional  differ- 
ence, by  iii.  84-30,  give  the  length  of  the  shadow  at  the  given  time, 
together  with  that  of  its  hypotlicmisc.  The  question  would  next  be  in 
what  direction  to  lay  off  t lie  shadow  from  the.  base  of  the  gnomod. 
This  is  accomplished  by  means  of  the  base  ( bkvja ) of  the  shadow,  or  its 
value  when  projected  on  a north  ami  south  line.  From  the  declination 
is  found,  by  iii.  2 0-2  2,  the  length  of  the  noon-shadow  and  its  hypothe- 
nuse,  and  from  the  latter,  with  the  declination,  comes,  l>v  iii.  22-23,  the 
measure  of  amplitude  (uara)  of  the  given  shadow;  whence,  by  iii.  23- 
25,  is  derived  its  base.  Having  thus  both  its  length  and  the  distance 
of  its  extremity  from  an  east  and  wc*t  line  running  Till  rough  the  base  of 
the  gnomon,  we  lay  it  off  without  difficulty. 


16.  Take  two  gnomons,  live  mbits  (hcisla)  in  lu-ight,  stationed 
^according  to  the  variation  of  direction,  separated  by  the  inter- 
nal of  the  two  planets,  and  buried  at  the  base  one  cubit. 

17.  Then  fix  the  two  hyputhenuscs  of  the  shadow",  passing 
from  the  extremity  of  the  shadow  through  the  apex  of  each 
gnomon;  and,  to  a person  situated  at  the  point  of  union  of  the 
.^tremities  of  the  shadow  and  hypothcnusc,  exhibit 

! ; 18.  The  two  planets  in  the  sky.  situated  at  the  apex  cacb#of 

own  gnomon,  and  arrived  at  a coincidence  of  observed  place 
-.<%) — 


This  is  a proceeding  of  much  the  same  character  with  that  which 
forms  the  subject  of  the  preceding  passage.  In  order  to  make  nppre- 
4btosible,  by  observation,  the  conjunction  of  two  planets,  as  calculated  by 
the  methods  of  this  chapter,  two  gnomons,  of  rfoout  the  height  of  a 
quin,  arc  set  up.  At  what  distance  and  direction  from  one  another  they 
are  to  be  fixed  is  not  clearly  shown.  The  commentator  interprets  the 
expression  “interval  of  the.  two  planets ' (v.  Hi),  to  mean  their  distance  in 
minutes  on  the  secondary  to  the  prime  vertical,  as  ascertained  according 
to  verse  12,  above,  reduced  to  digits  by  the  method  taught  in  iv.  2&i 
while,  by  “ according  to  the  variation  of  direction,”  he  would  understimfc 
merely,  in  the  direction  from  the  observer  of  the  hemisphere  in  which 
plates  at  the  moment  of  conjunction  arc  situated.  The  latter  phrase, 
however,  as  thus  explained,  seems  utterly  nugatory ; nor  do  we  see  of 
what  use  it  would  be  to  make  the  north  and  south  interval  of  the  bases  of 
,the  gnomons,  in  digits,  correspond  with  that  of  the  planets  in  minutes. 
\Vc  do  not  think  it  would  be  difficult  to  understand  the  directions  given 
ip  the  tcxt‘as  meaning,  in  effect,  that  the  two  gnomons  should  be  so  sta-  . 
tfoned  as  to  cast  their  shadows  to  the  same  point;  it  frould  be  easy  to 
do  thjs,  since,  at  the  time  in  question,  the  extremities  of  two  shadows 
cast  from  one  gnomon  by  the  twro  stars  would  be  in  the  same  ngrth  and 


Translation  and  Notes. 


178 


vii.  M.j 

south  line,  and  it  would  only  be  necessary  to  set  the  second  gnomon  as 
far  south  of.the  first  as  the  end  of  the  shadow  cast  by  the  southern  star 
was  north  &f  that  cast  by  the  other.  Then,  if  a hole  were  sunk  in  the 
ground  at  the  point  of  intersection  of  the  two  shadows,  and  a person  c 
Enabled  to  place  his  eye  there,  he  would,  at  the  proper  moment,  see  both.' 

. the  planets  with  the  same  glance,  and  each  at  the  apex  of  its  own  gnomon. 

In  the  eighteenth  > erse  also  we  ha\c  ventured  to  disregard  the  author- 
ity of  the  commentator  : lie  translates  the  words  drktulyat&m  i ids 
“come  within  the  sphere  of  sight/’  while  we  understand  by  drktulyatA , 
as  in  other  cases  (ii.  14,  iii.  11 ),  the  coincidence  between  observed  and 
computed  position. 

Such  passage*  as  this  and  the  preceding  are  not  without  interest  and 
value,  as  exhibiting  the  rudeness  of  the  Hindu  methods  of  observation, 
and  also  as  showing  the.  unimportant  and  merely  illu>trati\c  part  which 
observation  was  meant  to  play  in  their  developed  *y>lem  of  astronomy. 

18.  . . . When  them  is  contact  of  the  stars,  it  is  styled  “de- 
piction” (nVckha) ; when  there  is  separation,  “division"  ( hheda ) ; 

19.  An  encounter  iyuddha)  is  eiil!«,«l  “ray -obi iteration”  (anqu- 

vimarda)  when  there  is  mutual  lihiiglmgof  rays:  when  the  inter- 
val is  less  than  a degree,  the  encounter  is  named  “dexter”  (apar 
savya) — if,  in  this  ease,  one  lie  faint  {ati").  */ 

20.  If  the  interval  he  more  than  a degi  *,  it  is  “conjunction” 
(samoyamd),  if  both  are  endued  with  powi  (Uda).  One  that  ia 
vanquished  (jiUt)  in  a dexter  encounter  ( viwvya  yuddha) ),  one 
that  is  covered,  faint  lutjv\  destitute  of  hi  liancv, 

21.  One  that  is  rough,  i-.dorlos,  struck  down  (cidhvasta),  situ- 
ated to  the  south,  is  uiierly  vanquished  (r  ).  One  situated  Jo 
the  north,  having  brilliancy,  large,  is  victor  (jayin) — andeveniil 
the  south,  if  powerful  (halin). 

22.  Even  when  closely  approached,  if  both  are  brilliant,  it  is 
“conjunction”  (« mmtgama) : if  the  two  arc  very  small,  and  struck 
down,  it  is  “front”  (kfif/t)  and  “conflict"  (riyraha),  respectively;* 

23.  Venus  is  generally  victor,  whether  situated  to  the  north  or 
to  the  south.  ... 

In  this  passage.  a.s  later  in  a whole,  chapter  (chap,  xi),  wo  quit  the 
proper  domain  of  astronomy,  and  trench  upon  that  of  astrology.  How- 
ever intimately  connected  the  two  sciences  may  be  in  practice,  they  are, 
■in  general,  kept  distinct  in  treatment — the  Siddh&ntas,  or  astronomical 
text-books,  furnishing,  as  in  the  present  instance,  only  the  scientific  basis*.- 
the  data  and  methods  of  calculation  of  the  positions  of  the  heavenly 
bodies,  their  eclipses,  conjunctions,  risings  and  settings,  and  the  like, 
while  the  Sanhitas,  Jfitakas,  TAjikas,  etc.,  the  ast . ologieal  treatises,  malm 
the  superstitious  applications  of  the  science  to  die  explanation  of  the 
planetary  influences,  and  their  determination  of  human  fates.  Thus  the* 
celebrated  astronomer,  Varaha-miliirn,  besides  liis  astronomies*  com- 
posed separate  astrological  works,  which  are  still  extant^  while  die  for- 
mer have  become,  lost.  It  is  by  no  means  impossible  that  these  verses 
may  bajuai  interpolation  iuto  the  original  text  of  the  Sftrya-Siddh&nta. 
They  foSf-only  a disconnected  fragment : it  is  not  to  be  mppposed  that 


174 


[viL  23- 


they  contain  a complete  statement  and  definition  of  all  the  different 
kinds  of  conjunction  recognized  and  distinguished  by  .technical  appella- 
tion*;- nor  do  they  fully  set  forth  the  circumstances  which  determine  Uio 
^result  of  a hostile  41  encounter 1 between  two  planets:  while  a detailed 
f explanation  of  sonic  of  the  distinctions  indicated — as,  for  instance,  when 
planet  is  “powerful”  or  the  contrary — could  not  be  given  without  enter- 
ing quite  deeply  into  the  subject  of  the  Hindu  astrology.  This  we  do 
- not  regard  ourselves  as  called  upon  to  do  here : indeed,  it  would  not  be 
possible  to  accomplish  it  satisfactorily  without  aid  from  original  sources 
which  arc  not  accessible  to  us.  We  shall  content  ourselves  with  follow- 


ing the  example  of  the  commentator,  who  explains  simply  the  sense  and 
connection  of  the  verses,  as  given  in  our  translation,  citing  one  or  tivp 
parallel  passages  from  works  of  kindred  subject.  We  would  only  point 
out  farther  that  il  has  been  shown  in  the  musi  satisfactory  manner  (as  by 
WliUh,  in  Trans.  Lit.  Soc.  Madras  1 K-JT ; Weber,  in  his  Indische  Studien, 
ii.  23(i  etc.)  that  the  older  lliiiflu  science  of  astrology,  as  represented  by 
Yar&ha-iniliira  and  other*,  reposes  entirely  upon  the  (ircek,  as  its  later 
forms  depend  also,  in  part,  upon  the  Arab:  the  latter  connection  being 
indicated  even  in  the  common  title  of  the  more  modern  treatises,  tftjikct , 
/which  comes  from  the  IVrsiun  Mr?,  “Arab."  Weber  gives  (Ind.  Stud, 
^ii.  277  etc.)  a translation  of  a passage  from  Varalm-mili  ira's  lesser  treat- 
■ -fee,  which  states  in  part  t li«-  circmn<tanees  determining  the  “power”  of  a 
planet  in  different  situation*,  absolute  or  relative:  partial  explanations 
upon  the  same  subject  furnished  to  the  translator  in  I/idiu  by  his  native 
^assistant,  agree  with  tliL.-e,  sun1  both  accord  closely  with  the  teachings 
’ pf  the  Tetrubihlos,  the  astrological  work  attributed  to  I’tolcniv. 


v . . . Perform  in  like  manner  ill*'  calculation  of  the  con- 

I'^QCtion  {aWiit/v'ja)  of  the  planets  with  the  moon, 
r ^iis  is  all  that  the  treatise  siys  respecting  the  conjunction  of  the 
* jjjpon  with  the  lesser  planets  : of  the*  ]iheiionienon,  sometimes  so  striking, 
" of  the  occultatiun  of  the  latter  by  the  former,  it  takes  no  especial  notice. 
The  commentator  cites  an  additional  hall-verse  as  sometimes  included  in 
the.  chapter,  to  the  effect,  that,  in  calculating  a conjunction,  the  moon’s 
latitude:  is  to  be  reckoned  a*  cmitccu-.I  by  her  parallax  in  latitude  (atwt- 
nati ),  but  rejects  it,  as  making  the  chapter  oi':r-full,  and  as  being  super- 
fluous, since  the  nature  of  the  ease  determines  the  application  nqra  of 
v the  general  rules  for  parallax  presented  in  the  fifth  chapter.  Of  any 

Iiarailax  of  the  planets  themselves  nothing  is  said : of  coprve,  to  calcul- 
ate the  moon's  parallax  by  the  methods  as  already  givtin  is,  in  effect,  to 
attribute  to  them  all  a horizontal  parallax  of  the  same  value  with  that 
assigned  to  the  sun,  or  about  4\  ■ : . 

The  final  verse  of  the  chapter  is  a caveat  against 
when  a “ conjunction”  of  two  planets  is  spoken 
meant  than  that  they  appear  to  approach  one  ; 

■ .^ess,  this  apparent  approach  requires  to  be 
' influence  upon  human  fates. 


24.  Unto  the  good  and  evil  fortune  of  sy*ittri  vet 

forth*:  the  planets  move  on  upon  thei^  Sws^^mfi;  approaching 
one  another  at  a distance. 


Translation  ami  Notes. 


vii'i.  i.J 


C II  A P T i:  It  VIII. 


or  THE  ASTERISKS.  1 ,> 

Contenti:— 1-9,  positions  of  the  nsterisms  ■.  10-12,  of  certain  fixed  stirs ; 12,  direct  * 
tinn  to  test  by  observation  the  accuracy  of  these  positions;  IP.,  splitting  of 
Uohini's  wain ; 14-16.  how  to  determine  the  conjunct  inn  «f  n planet  with  an  - 
asterism  ; 16-19,  which  is  the  junction -star  in  each  asterism  ; 20-21,  positions  of 
other  fixed  stars.  V 

1.  Now  arc  act  forth  the  positions  of  tlio  astcrisms  i bhn\  in 
minutes.  If  the  share  of  oacli  one,  then,  ho  multiplied  by  ten, 
and  increased, by  tlio  minutes  in  the  portions  (Utoya)  of  the  past 
astcrisms  (i ihishvya »,  the  result  will  bo  tin:  polar  longitudes 
(< d/truva ).  • 

The  proper  title  of  tlii<  chapter  is  n <ilm» li n t rtvjra hatjvhbfl L / ku r<t , “ fhap- 
tcr  of  the  conjunction  of  astcrisins  ami  planet*/1  hut  the  * abject  of  con- 
junction occupies  lint  si  small  space  in  it,  being  'limited  to  a direction 
(vv.  14-15)  to  apply,  wit  li  the  necessary  modification*,  the  methods/,, 
taught  in  the  preceding  chapter.  The  chapter  is  mainly  occupied  witfc 
such  a definition  of  the  positions  of  the  a*ti.T!sm — to  which  hre  addq$ 
also  those  of  a few  of  the  more  prominenl  among  the  fixed  star* — 
necessary  in  order  t*»  render  their  conjunction^  rapsihlc  of  l««-in«r  calculated!  A 
1 3clh  re  proceed  in*:  to  gi\e  tin*  parage  w hi  -li  states  tin*  positions  ofif! 
tlie  aslerisins,  we  will  explain  I he  manner  in  which  these  are  defined, 
the  accompanying  figure  (Fig.  ttUf.  let  K 1.  icpre-mt  the  equator,  aiiddS^! 

^ b the  ccjipiic.  I'niul  PM.oii.gtinnrresp^;.;: 

‘ ti\e  polo.  Let  S l,e  the  position  of  ifciiy 

given  sinr.  an. I through  it  draw  the  circle 
of  ileclinatiou  I1  Sri.  Then  a b the  point 
t»n  the  ecliptic  of  which  tin*  distance  frolU 
tin*  fiiM  of  Arie*  and  from  th&ftftr  respec- 
tively arc  here  gi\r»  as  il*  longitude  and 
latitude.  So  far  a*  the  latitude  i*  con- 
cerned, thi*  is  m»t  unnccordnut  with  the 
usage  of  the  treatise  hitherto.  Latitude 
[vikxhcpa,  4i  disject  ion")  is  the  amount  by 
which  any  body  is  removed  from  tlio 
declination  which  it  ought  to  have — that 
is,  from  tin:  point  of  the  ecliptic  which  it 
ought  to  occupy—  ileclinatiou  (lerdnii,  apa- 
lemma)  being  always,  according  to  tlu? 
Hindu  understanding  of  the  term,  in  tfife 
ecliptic,  itself.  In  the  ease  of  a planet, 
whose  propeft.  path  is  in  the  ecliptic,  the 
point  of  that  circle  which  it ought  to  occtt~> 
py  is  determined  by  its  calculated  longi- 
tude: in  the  case  of  a fixed  star,  whose  only  motion  is  about  the  pole  of 
the  heavdjftai  ife  point  of  declination  is  that  to  which  it  is  referred  by  a 


circle  through  that  pole.  ThuB,  in  the  figure,  the  declination  (kr&nti)  of 
8 would  be  c a , or  the  distance  of  a from  the  equator  at  o j its  latitude 
{ytkshepa)  is  a S,  or  its  distance  from  a.  We  have,  accordingly,  the 

pe  term  used  here  as  before.  To  designate  the  position  in  longitude 

A,  on  the  other  hand,  we  have  a new  term,  ilhruva , or,  as  below,  (vv. 

15),  dhruvaka.  This  comes  from  the  adjective  ilhruva , “fixed,  im- 
fpibvablc,"  by  which  the  poles  of  the  heaven  (see  below,  xii.  43)  arc  desig- 
^'Ihated ; and,  if  we  do  not  mistake  its  application,  it  indicates,  as  here 
" employed,  the  longitude  of  a star  ns  referred  to  the  ecliptic  by  a circle 
from  the  pole.  \Yc  venture,  then,  to  translate  it  by  “polar  longitude, ” 

•t  as  we  also  render  vikshepa,  in  this  connection,  by  “ polar  latitude, 17  it 
1 being  desirable  to  have  for  these  quantities  distinctive  names,  akin 
with  one  another.  < ‘olebrooke  employs  “ apparent  longitude  and  lati- 
tude,which  are  objectionable,  as  being  more  properly  applied  to  the 
results  of  the  process  taught  in  the  last  chapter  (w.  7-10). 

The  mode  of  statement  of  the  polar  longitudes  is  highly  artificial  and 
arbitrary  : a number  is  mentioned  uhich,  wlieu  multiplied  by  ten,  will 
give  the  position  of  each  asterism,  in  minutes,  in  its  own  “portion” 
(bhoga),  or  are  of  13°  “O'  in  the  ecliptic  (*oc  ii.  01). 

V This  passage  presents  a name  for  the  astcrisms,  dhiahnya , which  has 
'hot  occurred  before  ; it  is  found  mice  more  below,  in  \i.  *J l. 

:2.  Forty-eight,  fort}’,  sixty- live,  fifty -seven,  fi  fry-right,  four, 
fldventy-eiglit,  seventy-six.  fourteen, 

£ 3.  Fifty-four,  sixtv-four,  iitiv,  sixtv,  forty,  seventy-four.  sev-- 
(height,  sixty-four.  ‘ ‘ 

*.  Fourteen,  six,  four : L'ttara-Asliadhii,  (ctit\va)  is  at  the 
Httiddle  of  the  portion  {bhoga)  of  Purvu-Ashiidhu  {upya) ; Ablii- 
' jit,  likewise,  is  at  the  end  of  Purva-Asbudba;  Lite  position  of 
f;  §ravana  is  at  the  cud  of  I'ttara-Aslnidhii ; 

6.  (Jravishtlia,  on  the  other  hand,  is  at  the  point  of  connec- 
tion of  the  third  and  fourth  quarters  (jmfa)  of  Pravana:  then, 
in  their  own  portions,  eighty,  thirty -six,  twenty -two, 

0.  Seventy-nine.  Now  their  respeetivc  latitudes,  reckoned 
from  the  point  of  declination  (upuLratuaj  of  each  : ten,  twelve, 
live,  north ; south,  live,  ten,  nine ; 

7.  North,  six : nothing ; south,  seven : north,  nothing,  twelve, 
thirteen:  south,  eleven,  two:  then  thirty-seven,  north; 

8.  South,  one  and  a half,  three,  four,  nine,  live  and  a half,  five ; 
north,  also,  sixty,  thirty,  and  also  thirty-six ; 

9.  South,  half  a degree;  twenty-four,  north,  twenty-six  degrees; 
nothing — for  A^vinT  ( dasra ),  etc.,  in  succession. 

The  text  here  assumes  that  the  names  of  the  asterisms,  and  the  order 
of  their  succession,  arc  so  familiarly  known  as  to  render  it  unnecessary 
to  rehearse  them.  It  has  bejgp  already  noticed  (see  above,  i.  48-51,  55, 
Jiff-58,  etc.) | that' a similar  assumption  was  made  aa  regards  the  names 
and  succession  of  the  mouths,  signs'  of  the  zodiao,  yean  of  Jupiter’s 
oyde,  and  the  like.  Many  of  the  asteriams  have  more  than  one  appel- 
lation : wo  present  in  the  annexed  table  those  by  which  they  arc  more 


Translation  and  Notes , 


177 


viii.  9.] 

generally  mi,  familiarly  known;  the  others  will  be  stated  farther  on. 
Nearly  all  th^ce  titles  are  to  be  found  in  our  text,  occurring  here  and 
there;  a few  of  the  aster  isms,  however,  (the  5th,  6tli,  9th,  and  17th), 
are  mentioned  only  by  appellations  derived  from  the  names  of  the  dei-'  / 
ties  to  whom  they  arc  regarded  as  belonging,  and  oue  (the  25th)  chancfea.J 
not  to  be  once  distinctively  spoken  of.  We  append  to  the  names, 
tabular  form,  the  data  presented  in  this  passage ; namely,  the  positiw>;| 
of  each  asterism  ( nakskatra ) in  the  arc  of  the  ecliptic  to  which  it  givcjg^ . 
name,  and  which  is  styled  its  “portion"  (bhoga),  the  resulting  polar  lon- 
gitudes, and  the  polar  latitudes.  Ajfcd  since  it  is  probable  (see  note  to 
the  latter  half  of  v.  12,  below)  that  the  latter  welt;  actually  derived  by  ; 
calculation  from  true  declinations  and  right  ascensions,  ascertained  by  % 
observation,  we  have  endeavored  to  restore  tlmsi*  more  original  data  by" 
calculating  them  hack  again,  according  t.j  the  data  and  methods  of  this 
Siddhsintu—  the  declinations  l.y  ii.  2*,  the  right  aseeiisioiia  by  ili.  44-48 
— and  wc  insert  our  results  in  the  table,  rejecting  odd  minutes  less  than  ' 
ten. 

Positions  of  the  Junction- Stars  of  the  Asttrisms. 


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4o  ! 

224 

1 

0 : 

3 

i»  " 

721 

fin  | 

*9 

20 

(i  1 

5 

O i 

5 

O 

1 8 Jjycaktlift, 

2 

1 

20  . 

229 

i 

0 

1 

4 

11  11  ’ 

?'jf) 

5u 

21 

r)o 

I. 

12 

O 

12 

0 

19  iMiila, 

1 

O 

241 

1 

1 

9 

O “ 

238 

•0 

29 

5o 

Ii 

i3 

O 

id 

0 

20  P.-AslmdhA, 

0 

40 

3 54 

0] 

5 

3o  “ . 

252 

: > ■ 
1 

yS 

3o 

11  { 

6 

0 

6 3o 

ai  U.-Ash&dhA, 

. . 

. . 

2(Hl 

0 1 

5 

0 “ 

2 5 9 

20 

28 

4o 

6 

46 

7 

0 

3 a Abhijit, 

. . 

. . 

aGG 

4o| 

60 

1 

»X. 

2(H) 

20 
» 1 

36 

0 

N. 

i3 

20 

14 

3o 

23  ^rava^a, 

.. 

2H0 

0 . 

1 

3o 

1 

«-i 

28c) 

5o 

G 

30 

“ i 

i 10 

O 

1 10 

4o 

24  ^ravishtliA, 

.. 

> - 

290 

0 

30 

O " 

29I 

3n 

■3 

3o 

*■  i 

3o 

O 

3o  do 

a5  ^atftbhishaj, 

i3 

20 

320 

0 

0 

3o  i?.  '| 

322 

10 

i5 

4o  Bs 

e 

0 

6 

0 

26  P.-BhfidrapadA, 

6 

0 

3aG 

0 

34 

oN. 

32  b 

10 

10 

5o  N. 

a 

O 

10 

3o 

27  U.-BhAdrapadA, 

[ 3 4o 

337 

0 

26 

0“ 

338  4o 

16  5o 

11 

22 

5o 

21 

VO 

28  Rovati, 

i3 

10 

359  5o 

0 

0 

359  5o 

0 

0 

8 

to 

*7 

4o 

Translation  and  Notes. 


- I • B A "• 

Till.  9.J  . 


i7d 


Our  calculations,  it  should  be  remarked,  arc  founded  upon  the  as- 
sumption Ujftlb,  at  the  time  when  the  observations  were  made  of  which 
our  text!.^^prds  the  results,  the  vernal  equinox  coincided  with  the 
initial  point  of  the  Hindu  sidereal  sphere,  or  with  the  beginning  of 
the  portipn  of  the  ostcrism  Acvinl,  a point  10'  eastward  on  tlie  ecliptic 
from  the  star  £ Piscium  : this  was  actually  the.  case  (see  above,  under  i. 
27)  tfcbout  A.  D.  SCO.  The  question  how  fur  this  assumption  is  Biip-j;.' 
ported  by  evidence  contained  in  the  data  themselves  will  be  considered 
later.  To  fill  out  the  table,  we  have  also  added  the  intervals  in  right 
ascension  and  in  polar  longitude. 

The  stars  of  which  the  text  thus  accurately  defines  the  positions  do 
not,  in  most  cases,  by  themselves  alone,  constitute  the.  astcrisins  ( nnk - 
shatra) ; they  are  only  the  principal  members  of  the  several  groups  of 
stars — each,  in  the  calculation  of  conjunctions  [yoga)  between  the.  plan- 
ets and  the  asterisms  (see  below,  vv.  14- lii),  representing  its  group,  and 
therefore  called  (sec below,  vv.  10 -JO)  the  "junction-star”  (yogatarA)  of 
the  asterism. 

It  will  be  at  once  noticed  that,  while,  in  a former  passage  (ii.  64),  the 
ecliptic  was  divided  into  twenty-seven  equal  are**,  as  portions  for  the  aster- 
isms,  wo  have  here  presented  to  ti^i  twenty -eight  :t>ti*risins,  very  unequally 
distributed  along  the  eeliplie,  and  at  greatly  vaning  distances  from  it. 
And  it.  is  a point  of  so  much  eonscijuen.-c,  in  order  to  the  right  under- 
standing of  the  character  and  history  of  the  whole  system,  to  apprehend 
elearlv  the  relation  of  the  groups  of  stars  to  the  ares  allotted  to  them,.. 

’ that  wc  have  prepared  the  aecmiipatiting  diagram  (Fig.  31)  in  illustra- 
tion of  that  relation.  The  figure  represents  in  two  parts,  the  circle  of 
the  ecliptic  : along  the  central  lines  i->  market  I its  division  into  arcs  of 
ten  and  five  degree*  : up«ui  the  outride  of  these  linos  it  is  farther  divided 
into  equal  twenty-seventh*,  or  ares  of  133  'JO',  and  upon  the  inside  into 
equal  twenty-eighths  or  ares  of  1l>:#  ,M  J' : th.-<e  being  the  portion^ 
(i bhoga ) of  two  systems  of  a<iteri>ms,  twenty-seven  and  twenty-eight  in 
minibcr  respectively.  The  starred  lines  w hich  run  across  all  the  divisions 
mark  the  polar  longitudes,  n>  staled  in  llie  text,  of  the  junction-stars  of 
the  astcrisins.  The  names  of  lliu  hitler  are  set  over  against  them,  in  the 
inner  columns : the  names  of  the  portions  in  the  system  of  twenty-seven 
are  given  in  full  in  the  outer  commits,  and  th«»j>e  in  the  system  of  two nty- 
cight  arc  also'placcd  opposite  the  portions,  upon  the  inside,  in  an  abbre- 
viated form. 

The  text  nowhere  cxpresslystal.es  which  one  of  the  twenty-eight  aster- 
isms  which  it  recognizes  is,  in  its  division  of  the  ecliptic  into  only  twenty- 
seven  portions,  left  without  a portion.  That  Abhijit,  the  twenty-second 
of  the  scries,  is  the  one  thus  omitted,  how evn,  is  clearly  implied  in  the 
statements  of  the  fourth  and  fifth  verses.  Those  statements,  which  have 
caused  difficulty  to  more  than  one  expounder  n ’ the  passage,  -and  have 
been  variously  misinterpreted,  are  made  entirely  clear  by  supplying  the 
words  ‘fasterism”  and  portion”  throughout,  where  they  arc  to  be  under- 
stood, thus : 44  tho  asterism  Uttara-Asiiadhh  is  at  tliemiddle^of.thc  por- 
tion styled  Pftrva-Ash&dlm ; the  asterism  Abhijit,  likewise,^  atlblie  end 
of  the  portion  Pfirva- Ashftclha ; the  position  of  the  atf&rfom  Qr&vana  is 
at  the  0£)dof  the  portion  receiving  its  name  from  UitanhAwiftdh&  j while 


ml 


Sfirya-Siddh&nta} 


[vtfi.  0# ,/ 


the  astcrism  QravishtM  is  between  the  third  and  fourth  quarters  of  thft'.'s 
"portion  liAmed  for  Crnvan:i.”  After  this  interruption  to  the  regularity  of-  ' 
correspond ei ice  of  the  two  systems — the  astcrism  Abhijit  being  left  with- 
out a portion,  and  the  portion  </ravishtln\  containing  no  astcrism — 'they 

Son  again  harmoniously  together  to  the  close.  The  figure  illustrates 
sarly  this  condition  of  "things,  and  shows  that,  if  Abhijit  be  left  out  of 
accounl,  the  two  systems  agree  so  far  as  this — that  twenty-six  usterisms 
fall  within  the  limit*  of  portions  bearing  the  sumo  name,  wliilo  all  the 
discordances  are  confined  to  one  portion  of  the  ecliptic,  that  comprising 
the  20th  to  the  23d  portions.  If,  on  the  other  hand,  the  ecliptic  he  divi- 
ded into  twenty-eighths,  and  if  these  be  assigned  as  portions  to  the 
twenty-eight  astorisms.  it  i>  seen  from  tho  figure  that  the  discordances 
between  the  two  systems  will  he  very  great : that  only  in  twelve  instan- 
ces will  a portion  he  occupied  by  the  aslcrbin  hearing  its  own  name,  and 
by  that  alone;  that  in  sixteen  cases  «i.*tvi,i*ms  will  hr  found  to  fall  within 
the  limits  of  portion*  of  dill'erent  name;  that  four  portions  will  he  left 
without  any  uslerisiu  at  nil,  while  lbur  oilier-  will  contain  two  each. 

These  discordance*  are  enough  uf  them*elvej>  in  ,-rl  the  whole  sub- 
ject  of  the  asterism*  in  a new  light.  Whereas  it  might  ha\e  seemed, 
from  what  we  have  &een  of  it.  heretofore,  that  the  sy-teni  was  founded 
upon  a division  of  the  ecliptic  into  twnly—euni  equal  portions,  and  tho 
selection  of  a star  or  a constellation  to  mark  each  portion,  and  to  be,  as 
it  were,  its  ruler,  it  now  appears  that  tlu*  series  of  twenty-eight  aster- 
isms  may  be  something  independent  of,  and  anterior  to,  any  division  of 
the  ecliptic  into  equal  are*,  and  llmi  the  ..ue  ma\  Iuivi-  been  onh  arti- 
ficially brought  into  connoeiiuii  with  tin*  nth*-r.  complete  harmony 
Between  them  being  altogether  iiiip«->*ihlc.  And  this  view  is  fully  mis- 
, gained  bv  eviden.-i*  derivable  from  uiii*idia  the  Hindu  science  of  a<lron- 
^Omv,  and  beyond  the  bonier*  of  India.  Tim  I'ar-is.  the  Arab*,  ami  the 
Chinese,  are  found  also  to  be  in  |n » — - *>ii«n  of  a similar  *v*tein  of  divi- 
’sjjjp*.  of  the  heavens  into  twentv -eight  portions,  marked  or  separated  by 
.asiriany  single  stars  or  eo)is1i‘lhti.ioii*.  t M' the  I'an-i  *yst-m  little  or 
nothing  is  known  excepting  llm  numln-v  and  name*  of  the  divisions, 
which  arc  given  in  the  second  chapter  of  t Ins  Jhmdel.osh  (sec  Anquetii 
du  Perron’s  Zcndavesta.  rt«\,  ii.  3l!»).  The  Arab  divisions  arc  styled 
mantfML  al-kamur , ‘‘  lunar  mansions,  stations  of  i!m  moon/'  being  brought 
into  special  connection  with  the  moon's  revolution  : they  are  marked, 
like  the  Hindu  u portions,”  by  groups  of  star*.  Tin  first  extended  com- 
pnrison^f  the  'Hindu  asterNnis  and  the  Arab  mansions  was  made  by  Sir 
'WilliaUDt' Jones,  ill  the  second  volume  of  the  Asiatic.  Researches  for  1790 : 
it  was,  however,  only  a rude  and  imperfect  sketch,  and  led  its  author  to 
no  valuable,  or  trustworthy  conclusions.  The  same  comparison  was  taken 
up  later,  with  vastly  more  learning  ami  amtenes*,  by  (Jolcbrooke,  whose 
valuable  article,  published  also  in  the  Asiatic  Researches,  for  1807  (ix. 
323,  etc.;  Essays  ii.  321,  etc.),  has  ever  since  remained  the  chief  source 
of  knowledge  respecting  the  Hindu  usterisms  and  their  relation  to  the 
lunar  mansions  of  the.  Arabs,  To  Anquetil  (as  above.)  is  due  the  credit 
bftjjke  first  suggestion  of  a coincidence,  between  the  Parsi,  Hindu,  and*. 
Chinese  systems:  but  he  did  nothing  more  than  suggest  it:  the  oriflp 
— cie'r,  and  use  of  the  Chinese  divisions  were  first  established,  ? 


iir51 


Translation  and  Notes, 


viii.0.] 


181 


their  primitive  identity  with  the  Hindu  asfrrisnis  demonstrated,  by  Biot, 
in  a series  of  articles  published  in  the  Journal  dcs  Savants  fotll640:  and 
he  has  more  recently,  in  the  volume  of  the  same  Journal  for  1850,  re- 
viewed and  restated  his  former  exposition  and  conclusions.  These  we 
shall  present  more  fully  hereafter : at  present  it  will  he  enough  to  say 
that  the  Chinese  divisions  are  equatorial,  not  zodiacal ; that  they  are 
named  sicu,  “mansions”;  and  that  they  are  the  hit  reals  in  right  ascen- 
sion between  certain  single  star?,  wlii-li  an*  also  callril  xi?u,  and  have  the 
same  title  with  the  divisions  which  they  intrni!n«-i».  We  propose,  to  pro-, 
sent  here  a summary  cnmpari>nn  of  the  Hindu,  Arch,  ami  (Chinese  sys- 
tems, in  connection  with  an  identification  of  the  : * , s-v,  and  gropps^f 
stars  forming  the  Hindu  astcri.-iii.*,  and  with  ihu  stsit-'sursnt  of  such 
information  respecting  1 lie  latlor,  beyond  that  given  iri  i.ur  text,  as  will 
best  contribute  to  a full  understanding  of  their  /■e.jira.-ter. 

The.  identification  of  the  iisterhuns  fun,. led  upon  tl.o  po-itions  of 
tlieir  principal  or  juie-li  m-star-t,  ■-•■4  slated  in  the  t-.'xt-hooks, 

upon  the  relatin'  plse-s  «»f  llie-e  oars  in  th-  gmu..*  of  'v  h i**li  they  form 
a part,  and  upon  flu*  number  of  Mc.’n  r*.min-iiig  *.;**,h  group,  and  the 
jigur'e  by  which  their  :irmi'ir*'nii,i-1  i-  rc  i»r*— ■-!.* --«l  : in  :i  fciv  •■n sc*,  too, 
the.  names  IlicinscUcs  «.f  tin  si-i are  «ll-ri:ii-; i\ o.  and  assist  iden- 
tilication.  Tlic.  number  and  r*»uligiirc,.io!i  of  tin  Mar-  J':’Mning"tlio  groups 
arc  not  stated  in  our  tc\i  : \n-  derive  them  iiiainiy  fo-m  (Ad-brooke, 
although  o lira  lies  :i1m»  hating  had  aivc—  i-..  :.:.d  i-.uei  -.ivd,  m*-L  of  his 
authorities,  name)}  li  e (\»k::i\u-S-iulii:a.  the  Muliur;,--i 'intumani.  and 
tlic  Itnlunmuki  in-  i\\ed  !•■.  Joiic**.  A>.  Iu\-.,  ii.  Sir  William  Jones, 

it  may  be  remarked,  luriii-li--  i A-.  I Jo-.,  ii.  -J'J-'b  pk.ud  an  eugraicd  copy 
of  ^drawings  mmle  l.\  .i  i -i; iv  «*  aril.-1.  of  f !■■-  figure*  assigned  tn  the  aster- 
isms.  For  tin*  nun. her  of  ■ in  -■ i>  gii»ui»  wo  hi’.e  n:i  additional 
authority  in  al-Hiruni,  tie*  Aral*  ..f  ihc  e'  \cidh  c'Uuurv,  who 

travelled  in  India,  and  -indie.;  wiih  e-i.e.-ial  care  the  Hindu  astronomy. 
The  information  lurni-lied  by  him  w i ? 1 1 regard  t* » tin-  c-ieri-m-  wc  derive 
from  Biot,  in  the  Journal  ■ I.—  Saxant-  for  I ^ 4 (pp.  i’ I ) ; ii  professes 
to  be  founded  up«»n  T li« * Kliamla-Kataka*  « »f  I iralmi  igi; Al-Birfmi 
also  gives  an  idcnlitieation  of  the  a-tori.-m-,  -•»  far  a-  tlic  Hindu  n-trono- 
mers  of  his  da\  were  able  1-»  funii-ii  it  1 » ■ him,  which  was  onlv  in  pari : 
he  is  obliged  to  mark  -even  er  eight  of  the  series  as  unknown  or  doubt- 
ful. lie  speaks  x.*rv  .-liglitin-fly  nf  the  practical  acquaintance  with  the 
heavens  pu— .wd  |»\  the  Hindu-  *»f  his  time,  an • l they  certainly  hare, 
not' since  improved  in  ibis  rcr-pecl  ; the  modern  iuvestigatura  of  the 
same  subject,  as  Jones  and  (‘ulcbrouk*1,  .il<o  complain  of  the  impossi- 
bility of  obtaining  from  the  nali\e  a^livummcrs  of  India  satisfactory 
^identifications  of  the  astevisius  and  their  junction  stars.  Tlu*  translator, 
in  like  manner,  spent  inm  li  lime  and  eiiorl.  in  tl  c attempt  to  derive 
such  informal  in  n from  his  natiic  assistant,  but  wa  . able  to  arrive  at  no 
requite  which  could  constitute  any  valuable  addition  to  those  of  Cole- 
brooke.  It  is  evident  LlinL  for  centuries  past,  a*  at  present,  the  native 


* The  true,  form  of  tho  name  is  not  altogether  certain,  it  being  known  only 
ttaopgh  ite  Arabic  transcription : it  seems  to  designate  rather  a chapter  in  a treatise 
than  * complete  work  of  its  author. 

: ;'*r:  24 


tradition  has  been  of  no  decisive  authority  as  regards  the  position  and 
composition  of  the  groups  of  stars  constituting  the  astmsma : these 
must  be  determined  upon  the  evidence  of  the  more  ancient  data  handed 
down  in  the  astronomical  treatises. 

In  order  to  an  exact  comparison  of  the  positions  of  the  junction-stars 
' as  defined  by  the  Hindus  with  those  of  stars  contained  in  our  cata- 
logues, we  have  reduced  the  polar  longitudes  and  latitudes  to  true  longi- 
tudes and  latitudes,  by  the  following  formulas  (sec  Fig.  30) : 

(l-rcos  Aa)  rut  EbC  = tan  S ub 
sin  S<i b sin  Sn  = sin 
tan  S6  cut  Sfi6  = sin  ah 


A a being  the  polar  longitude  n<  dialed  in  the  Irxl  (=  180°),  Six 

the  polar  latitude,  H 1.  0 the  inclination  of  the  ecliptic,  S h the  true  lati- 
tude, and  aft  a quantity  to  l»o  added  to  or  subtracted  frbm  the  polar  lon- 
gitude to  give  the  true  longitude.  The  true  positions  of  the.  stars  com- 
pared we  take,  from  Flamsteed's  ('aialogus  liritt:micii>,  sulitracting  in 
each  ease  15°  42'  from  the  lough  tide*  Mure  gi\m,  in  order  to  reduce 
them  to  distances  from  the  vernal  equinox  of  A.  1 >.  jif*o,  assumed  to 
coiueide  with  the  initial  point  of  the  Hindu  sphere.  There  is  some 
discordance  among  the  different  Hindu  uutlmrilirs  n>  regards  the  stated 
positions  of  the  juii'-tion— lars  of  the  asli  rMii^.  The  ^ukalya-Sauhita. 
indeed,  agrees  in  every  puini  piwjai'lv  with  the  Surva-Siddhimta.  But 
the  SiddhAnta-^irum.uii  o!1«mj  ^iu^  a souiew  lia!  iliiiereut  value,  to  the 
polar  longitude  or  latitude,  or  K»lh.  With  ii,  s«»  far  :i*  tin*  longitude  is 
concerned,  exactly  a»v»rd  the  I »r:iliiiia-Si«ltlli;. nf :i,  as  n-]u«rtr:>.l  l»y  t'olft- 
fcfooke,  and  the  Khaiida-Kataka,  ;i*  reported  by  al-Uiriini.  The  lati- 
tudes of  the  Brail  ma-Siddluiht::  aUnuiv  vimially  tin*  same  with  tlvsOiof 
the  SiddJiAnta  Ciivm.-uii,  their  •lidenMin-s  ih-mt  amounting,  nivc  in  a 
single  instance,  to  mure  than  3':  but  tin:  latitude.*  of  the  Khmuhi-Kataka 
often  vary  considerably  from  both.  Tlie  Hialia  Laghava.  the  only  other 
authority  acce.-siblo  to  us,  presents  a series  ol'  vari-uioin  *»f  it.*  own,  inde- 
pendent of  those  of  cither  of  the  other  treat i^.  All  tlu\->c  ditferenees 
are  reported  by  us  below,  in  treating  of  separate  aMcrism.  The 
presiding  divinities  of  the  uM/tmiii  v. give  upon  ilu*  aulhority  of  the 
Taittiriya-Sunhitu  (iv.  4. 10.  l-.ij,  the  'raitlirjya-Umluuiina  (iii.  1.  1,2,  as 
cited  by  Weber,  Zeit^  h.  f.  d.  K.  d.  -Mur",  vu.  2UG  ot*-.,  and  Ind.  Stud., 
i.  00  etc.),  the  Miihurta-t  'intiuunni,  and  Odci-mokc : those  of  about 
half  the  astcrism*  arc  also  indirectly  given  in  *»ur  text,  in  the  form  of 
appellations  for  the  aMcrisms  derived  from  them. 

The  names  and  situations  of  the  Arab  lunar  station*  arc  taken  from 


Ideler’.s  ITnterswliuiigi'.ii  iiber  die  Sterniianieii : for  tlie  (.’hinuse  man- 
sions and  their  defcermiijinir  stars  we  rely  solely  upon  the  articles  of 
Biot,  to  which  we  have  already  referred. 

It  has  scenic  1 to  us  advisable,  notwithstanding  the  prior  treatment  by 
Colebrooke  of  the  same  Mihject,  to  enter  into  a careful  re-cxaini nation 


and  identification  of  the  Hindu  astcrisms,  because  we  could  not  accept 
in  the  bulk,  and  without  modification,  the  conclusions  at  w hich  he  arrived. 
' Tffce  identifications  by  Ideler  of  the  Arab  mansions,  more  thorough  and 
fegjjpggct  than  any  which  had  been  previously^  made,  and  Biot's  com  pari- 
of  the  ChiipM  sieu,  have  placed  new  and  valuable  materials  in  our 


* 


Translation  and  Notes . 


188 


riii.  0.] 

hands : and  thQsc — together  with  a more  exact  comparison  than  was 
attempted  by  Colebrooke  or  the  positions  given  by  the  Hindus  to  their 
junction-stars  with  the  data  uf  the  modern  catalogues,  and  a new  and 
independent  combination  of  the  various  materials  which  lie  himself  fur- 
nishes— while  they  have  led  us  to  accept  th#  greater  number  of  his  iden- 
tifications, often  establishing  them  more  confidently  than  he  was  able  to 
do,  have  also  enabled  us  in  many  cases  to  alter  and  amend  his  results. 
Such  a re-examination  was  necessary,  in  unler  to  furnish  safe  ground  for 
a more  detailed  comparison  uf  the  three  systems,  which,  as  will  be  seen 
hereafter,  lends  to  important  conclusions  respecting  their  historical  relar 
lions  to  one  another. 

1.  Awint ; thp  treatise  exhibits  the  firm  ar^ini ; in  tlin  older  lists, 
as  also  often  elsewhere,  we  have  the  dual  ircc/m/n,  arnti/ujav,  “the  two 
horsemen,  or  Arvins”  The  Arvins  are  persona*"'*  in  the  ancient  Hindus 
mythology  somewhat  nearly  corresponding  to  the  Castor  and  Pollux  of 
the  Greeks.  They  arc  the  «li\  initios  of  the  aftterisin,  which  is  named 
from  them.  The  group  is  figured  as  a horse’s  head,  doubtless  in  allusion 
to  its  presiding  duitic*,  and  not  from  any  imagined  resemblance.  The 
dual  name  leads  us  to  c\pi*d  t«»  tind  it  composed  of  two  >U\ rs,  and  that 
is  the  number  nlhul*ad  t-»  ih"  um-i'mii  l«\  ilie  (Vitalya  and  Khanda- 
Kntnka.  The  Suna-Siddhanu  (lv!ow.  v.  inj  designates  the  northern 
member  of  the  "roup  a*  i'*  junction  >t:ir  : that  thb  is  the  star  3 AriefcU 
(magn.  8.*J),  an«l  imi  •«  \ r:--i :s  imagn.  - 1,  a-  a^uuicd  b\  ( ‘olebrooke,  is 
shown  bv  1 lie  following  rninmri*oii  of  lurdilous : 

. i • m 

Acviiu  ....  long..  A.  D.  feiO,  nu  rnf  ....  hit.  9*  n'N. 
d Arietis  . . . •)««.  i i*  . . . do.  X. 

a Arietn  d».  . do.  90  37'  X. 

Colebrooke  was  mbled  in  this  iii'iaucc  by  adopting.  lor  the  number 
of  star*  in  the  asterism,  three,  a*  -t.it  .-il  by  tin*  later  authorities,  and  then 
applying  to  the  group  a*  thus  cuinpos«d  the  designation  given  by  our 
text  of  the  relatiw  position  uf  the  juneiion-iar  a*  the  northern,  and  he 
accordingly  mcrlookcd  the  wry  bcrimi*  error  in  the  determination  of 
the  longitude  thence  roMilting.  Indeed,  throughout  his  comparison,  ho 
"ives  loo  great,  weight  to  the  determination  of  latitude,  and  too  little  to 
that  of  longitude  : we  shall  see  farther  on  that  the  accuracy  of  the  lat- 
ter is,  upon  the  whole,  much  more  to  be  depended  upon  than  that  of  the 
former. 

Considered  as  a group  of  two  stars,  A<;viui  is  composed  of  j?and  y 
Arietia  (iiiagn.  1.3):  as  a group  of  three,  it  comprises  also  a in  the  same 
constellation. 

There  is  no  discordance  among  the  different  iv  tlioritn.,  examined  by 
us  as  regards  the  portion  of  the  junction-star  ot  Acviui.  cither  in  lati- 
tude or  in  longitude.  The  case  is  the  same  with,  the  &th,  10th,  12th, 
and  13th  a^terisms,  and  with  them  alone. 

The  first  Arab  inanzil  is  likewise  composed  of  0 aiul  y*Arietis,  to 
which  Homo  add  a:  it  is  called  ash-Shuratan,  the  two  tokens” — that  is 
to  say,  of  the  opening  year. 

. The  Chinese  series*  of  "licit  commences,  as  did  anciently  the  Hind** 
Hystein  of  asterianis,  with  that  which  is  later  the  third  asterisui.  The 


184  S&rya*Siddhdnta , [viii.  0. 

twenty-seventh  flier/,  named  Lou  (M.  Biot  has  omitted  to  {jive  ns  the 
signification  of  these  titles),  is  (i  Arietis,  the  Hindu  junction-star. 

2.  Bfuirant ; also,  as  plural,  bharanyas ; from  the  root  bhar,  “carry”: 
in  the  T&ittiriya  lists  the  form  apabharani,  “ hearer  away,”  in  singular 
and  plural,  is  also  found.  l|p  divinity  is  Varna,  the  ruler  of  the  world 
of  departed  spirits ; it  is  figured  a*  the  yoni , or  pudendum  inuliebre. 
All  authorities  agree  in  assigning  it  three  stars,  and  the  southernmost  is 
pointed  out  hclow  (v.  IS)  as  its  junction-star.  The  group  is  unquestion- 
ably to  be  identified  with  the  triangle  of  faint  stars  lying  north  of  the 
back  of  the  Ram,  or  35.  30,  and  41  Arietis  : they  are  figured  hv  some  as 
a distinct  ••onstollation,  under  the  name  of  Mu^ea  Itoroulis.  The  desig- 
nation of  the  southern  as  the  junction-star  is  not  altogether  unambigu- 
ous, as  35  and  41  were,  in  A.  D.  500.  very  nearly  eipiyUstanl  from  the 
equator;  the  latter  would  >eem  mure  likely  to  be  trc  one  intended, 
since  it  is  nearer  the  ecliptic,  and  the  brightest  of  1 1n*  group — being  of 
the  third  magnitude,  while  the  other  twu  are  of  the  fourth  : the  defined 
position,  however,  agrees  better  with  35,  ami  the  error  in  longitude,  as 
compared  with  41,  is  greater  than  t hat  of  any  other  star  in  the  series  : 

Ifiianu.ii 3-iJ  JV  . . . . ii°  <V  X. 

S.ri  Ariulia  («  Miw.-)  . . 'Vi1'  . . . . ii3i?' N. 

11  Arietis  (»■  Mu-cirj  . . in1  ....  ii«°  a(i'  N. 

Tin1  Tri-aha-Liigliava  giu-s  I Ilia  rani  1°  more  of  polar  longitude:  this 
would  reduce  by  the  same  amount  the  error  in  the  determination  of  its 
lgpgitiidc  by  the  oilier  anthorii 

JtJThc  second  Arab  innuzih  al-lJutain.  ‘the  Ilf  tic.-  belly” — i.  c„  of  the 
Ram — is  by  mod  author'd  ic*  defined  a*,  rompridiig  tin*  three  slurs  in  the 
haunch  of  ihc  R;mi,  «»r  r,  A,  and  »■*  (*ir  i-N«-  *)  Arietis.  Some,  however, 
have  regarded  it  a-  the  same  with  Mu-ca:  and  we  cannot  but  think  that 
al-Biriini,  in  identifying,  as  he  doe-,  liliarrmi  -with  al-lhitain,  meant  to 
indicate  by  the  latter  name  the  group  of  which  the  Hindu  astcrism  is 
actually  composed. 

The  last  Chinese  fl/Y”,  Oi-i,  is  the  >tar  Arietis,  <n-  a Miimcic. 

JCrtlika  ; or,  as  plural,  krttifois  ■ tin-  appellaiiw  meaning  of  the 
word  is  doubtful.  Tins  regent  of  I In-  asti-ri  hi  is  Agni,  the  g*»d  of  fire. 
The  group,  coinpov.  d of  d\*  >tar<,  is  1 lint  knot'll  to  us  as  the  PU-iadcs. 
It  is  figured  by  some,  a-  a name,  dmiMh*^  in  allusimi  to  its  prodding 
divinity:  the  more  usual  representation  of  ir  is  a razor,  and  in  tin*  choice 
of  l hi*  symbol  is  fu  he  recognized  il.e  inllueiiec  of  the  etymology  of  the 
name,  which  ma\  be  denied  from  the  mot  bxrt%  “cut in  the. configur- 
ation of  the  group,  too,  may  be  seen,  by  a sufficiently  prosaic,  eye,  a 
broad-bladed  knife,  with  a short  handle.  If  the.  designation  given  below 
(v.  IS)  of  tnc  southern  member  of  the.  group  as  its  junction-star,  be 
strictly  true,  ihi-  is  not  Alcyone,  or  \ Tauri  (magn.  3),  the  brightest  of 
the  sis,  but  either  Atlas  (27  Tauri:  magn.  4)  or  Alcrope  (23  Tauri: 
magn.  5);  tin*.  two  latter  wore  very  nearly  equally  distant  from  the 
equator  of  ‘A.lJ.  560,  but  Atlas  is  a little  nearer  to  the  ecliptic.  The 
defined  portion  agrees  best  with  Alcyone,  nor  can  we  hesitate  to  regard 
this  as  actually  the  junction-star  of  the  astcrism.  We  compare  the  pori-' 
tiems  below  : 


viii.  O.J  Translation  and  Notes.  185 

KrllilsA 39a  S'  . . . . . 4°44'tf. 

Alcyone  . ...  39*  5ft'  .....  4°  i' N’- 

27  Tauri  ....  4»°  *>' 3°  53'  N. 

23  Tauri  . . . - 3y°  4i' 3*  55'  S. 


The  Si«  I cl]  i ft.ii  tn-CJJi  ron  imii  etc.  give  KrUiftu.  2'  less  of  polar  longitude 
than  the  SftrvA-Siddhanta,  mid  Hie  Hraha-Lugluiva,  on  the  other  hand, 
30' more:  the  latter,  with  the  Khanchi-Kiitaku,  agree  with  our  text  as 
regards  the  polar  latitude,  which  the  others  reckon  af  4°  30 instead  of  5°. 

The  Pleiades  constitute  the  third  ma nzU  of  the  Arab*,  which  is  de- 
nominated ath-TImraiui,  “the  little  thick-set  group,"  or  an-Najm,  “the 
constellation.”  Alcyone  is  likewise  the  first  (‘hinese  sicu7  which  is 
styled  .Mao. 

4.  RnhM , “ruddy*1;  nauicil  from  the  line  of  its  principal  star. 
ITajupuli.  •■the  lor* l of  created  brings"  is  the  divinity  of  the  asterisix). 
Tt  contains  five  >tars,  in  the  grouping  «>:  \\  lii«-h  Hindu  fancy  has  scon  the 
figure  of  a wain  (compare  v.  1 :st  bi-low);  *niin,I  however,  figure  it  as  a 
temple.  Tin;  enlisted  hit  hm  is  liu*  well-kimwu  o;i«*  in  tie;  face  of  Taurus 
to  which  we  gi\e  the  name  of  the  Ilyad-**,  cnnlaming  *,  *X  */,  t)}a  Tauri; 
the  lalier.  the  iim4  en-lrrlv  (n.  !'.»’)  ami  tin*  brightest  of  the  group — 
being  the  brilliant  ^lar  of  lie;  I’im  magnitude  known  a1'  Aklebriran— is 
the  junction-star,  a*  is  -hnwu  l»\  the  annexed  comparison  of  positions: 

Ib'hini 4V  «/ j9  rf  S. 

,;V  . . . . j * J.1  s*. 

The  Si'hihauta-i/iroiiiani  ct»\  linv  again  pre.-mt  the  insignificant  vari- 
ation fr*»m  1 1n*  polar  I- •nufw n.Ii“  «»f  our  t*  "i'  ml'  l.-s : the  former  also 
makc^iK  polar  latiimle  1 uu':  the  Hruku-I.iigliava  rends  for  the  polar 
longitude,  Hi  . All  1 lif— 1 \.auiati"ii-  a id  i*»  the  error  «»f  defined  position. 

The.  fourth  Arab  iiuinJi  is  •■ompoM-l  «»f  the  llya-i.-s  : its  name  is  ad- 
Pabaran,  “the  follower1—  i.  «■.,  *»f  tin-  Pleiads.  \\  i*  would  suggest  the 
inquiry  whether  ihi-  name  may  not  1 .»  taken  as  an  indication  that  the 
Arab  system  of  mansion*  oi;-e  began,  like  the  ChincM-,  and  like  the 
Hindu  system  originally,  with  the  Pleiades  There  is,  certainly,  no  very 
obvious  proprion  in  naming  any  but  the  second  of  a series  the  “follow- 
ing" (sn{  tints  or  sirtnrins).  Modern  astronomy  ha*  retained  the  title  as 
that  of  tho  principal  star  in  the  group,  to  whi'di  alone  it  was  often  also 
applied  by  the  Arab*. 

The  second  ('hiiiescjt'fi/,  Vi,  is  the  northernmost  member  of  the  same 
group,  or  f Tauri,  a star  of  the  iliinl  to  fourth  magnitude. 

5.  Jlfryanrsha,  or  m ran  ft  ms , “ antelope’*  head"  : with  this  name  the 
figure  assigned  to  the  asterNm  corresponds  : il  c reason  for  the  designa- 
tion we  have  not  been  aide  to  discover.  Tis  uiviuity  i*  Soma,  or  the 
moon.  It.  contains  three  stars,  of  which  the  i.  irthern  (v.  13)  is  the 
determinative.  TIjo^p  three  can  be  no  other  than  the  faint  cluster  in  the 
head  of  Orion,  or  1,  ijp1,  t2  Orimiis,  although  the  Hindu  measurement 
of  the  position  of  the  junction-star,  A (magn.  4),  is  far  fropi  accurate, 
especially  as  regards  its  latitude : 

„ Mrgm/irslia  ....  *h°  3'  . . . . 90  49'  8. 

X Ofiouis  ....  td®  .jo'  ■ • ■ . 1 3°  a5'  8. 


186  S&iTfa-Siddhdnta}  [viii.  0. 

. Jfn  this  ftrroneous  determination  of  the  latitude  all  authoritiesagree: 
the  Gralia-Lughava  adds  1°  to  the  error  in  polar  longitude,  reading  02° 
instead  of  Oil0. 

Hero  again  there  is  an  entire  harmony  among  the  three  systems  com* 
pared.  The  Arab  wu  mil,  al-llak'ah,  is  composed  of  the  same  stars 
. which  make  up  the  Hindu  ns  tor  ism : the  third  aiVw,  named  Tsc,  is  tho 
. Hindujiincti'»n-*tar,  * Orionis. 

6.  Ardrft , ■■  moist  :M  tilt1  appellation  very  probably  has  some  meteoro- 
logical ground,  which  we  have  not  traced  out. : this  is  indicated  also  by 
the  choice  of  Kudra,  the  storm-god,  as  regent  of  the  asterisni.  It  com- 

;*:priscs  a single  star  only,  and  is  figured  as  a gem.  It  is  impossible  not  to 
^regard  the  bright,  star  of  the  first  magnitude  in  Orion’s  right  shoulder, 
Orionis,  as  the  one  hero  meant  t«»  he  designated,  notwithstanding 
the  very  grave  errors  in  the  definition  of  its  position  given  hy  our  text- : 
the  only  visible  star  of  which  the  situation  at.  all  nearly  answers  to  that 
definition  is  lflo  Tauri,  of  the  >i\th  magnitude;  we  add  its  position 
below,  with  that  of  a Orionis  : 

Anlni in3  r).r  . . . . 8*’  W S. 

a Orionis  . . . . usJ  4V  ....  ni3  4' IS. 

135  Tauri  . . . 3S#  ....  tp  iof  S. 

A The  distance  from  the  sun  at  which  the  heliacal  rising  and  sotting  of 
Afdr&  is  stated  below  (ix.  14)  t* » take  pla-"1  would  iudieajr-a  star  of  about 
the  third  magnitude;  this  adds  lo  the  «li llii-ull y «»f  its  identification  with 
either  of  the  two  ►tars  nonpared.  Wu  couli>s  ourselves  unable  to 
i“*-iMCOunt  for  the  confusion  existing  with  regard  1 «*  thi< asterisni,  of  which 
al-Biruni  also  eouM  obtain  no  intelligible  account  from  hi*.  Indian 
f teachers.  P.ur  it  i<  io  bp  ohsened  that  all  tin-  authorities,  excepting  our 
text  and  the  yakalya-Sanhita,  give  Ardrii  1 1°  of  polar  latitude  instead 
of  0°,  which  would  reduce  the  error  of  latitude,  as  compared  with  a 
Orionis,  to  an  amount  very  little  greater  than  will  he  met  with  in  one  or 
tW6  other  cases  below,  where  the  star  js  situated  .smith  of  the  ecliptic; 
and  it  is  contrary  to  all  the  analogies  of  the  sy-tesn  that  a faint  star 
should  have  been  selected  to  form  b\  itself  an  aster  ism.  The  Siddhanta- 
firomani  etc.  make  the  polar  longitude  of  the  asterisni  20'  less  than  that 
given  by  the  Sfiryu-riidd!  uinta.  and  the  t iraha-Lagha\a  1°  20'  lc.*s : these 
wonld  add  so  much  to  the  error  of  longitude. 

Here,  for  the  first  time,  the  three  systems  which  we  are  comparing 
disagree  with  one  another  entirely.  The  < ’hincse  have  adopted  for  the 
determinative  of  their  fourth  JvtVa,  which  is  styled  Tsan,  the  upper  star 
in  Orion’s  licit,  or  S Orionis  (2) — a strange,  und  arbitrary  selection,  for 
which  At.  Biol  is  unable  to  find  any  explanation.  The  Araks  have  estab- 
lished their  sixth  station  close  to  the  ecliptic,  in  the  feet  of  L'ollux,  nam- 
ing it  al-Haii'ali,  “the  pile11 : it  comprises  the  two  stars  y (2.8)  and  S 
(4.8)  Geminoruin  : some  authorities,  however,  extend  the  limits  of  the 
mansion  so  far  as  to  include  also  the  stars  in  the  foot  of  the  other  twin, 
or.’/,  y,  /*  Giminorum ; of  which  the  latter  is  the  next  Chinese  sieu . 

7.  Punarvasu ; in  all  tho  more  ancient  lists  the  name  appears  as  a 
dnal,  punarvas& : it  is  derived  from  jrnnar,  “ again,”  and  vatu,  “good, 
brilliant'9 : the  reason  of  the  designation  is  not  apparent.  The  regent 


viii.  9.]  ’’  Translation  and  Notes, 

of  the  osterism  is  Aditi,  the  mother  of  the  Adityas.  Its  dual  title  indi- 
cates that  it  is  composed  of  two  stars,  of  nearly  equal  brilliancy,  and 
two  is  the  number  allotted  to  it  by  the  £&kalya  and  Khanda-Kataka,  the 
eastern  being  pointed  out  below  (v.  19)  as  the  junction-star.  The  pair 
are  the  two  bright  stars  in  the  heads  of  the  Twins,  or  a and  (1  Gemino- 
rum,  and  the  latter  (1.2)  is  the  junction-star.  The  comparison  of  posi- 
tions is  as  follows : 

Punarvasu  . . .■  . 92°  ria'  . . . . f>°  r/ N. 

/3  Gcmi  riorum . . . i4r  . . . . (3°  3yf  N. 

The  Graha-L&gliava  adds  1°  to  the  polar  longitude  of  Punarvasu  a a' 
Stated  by  the  other  authorities. 

Four  stars  are  by  sonic  assigned  to  this  astcrism,  and  with  that  nun):  , 
ber  corresponds  the  representation  of  its  arrangement  by  the  figure 
a house : it  is  •piile  uncertain  which  of  the  neighboring  stars  of  the  sante^ 
constellation  sire  to  be  added  to  tlmsi;  above  mentioned  to  form  the  group 
of  four,  but  we  think  1 (mngn.  1)  and  v (j)  tli*»-m  mo«t  likely  to  have 
been  chosen:  t'nli-brouk1!  sugg* -1*  «/■  (:t.i)  and  r (3.  i). 

The  dc.tmuinuiivc  of  the  tilth  «Vn,  'lVing.  i*  {•  ticiniumuin  (3),  which, 
as  wc  have  seen,  is  reckoned  among  the  stars  composing  the  sixth 
maaril:  the  seventh  incnrjil  includes,  like  tin:  Hindu  astcrism,  a and  0 
Geininorurn  : it  is  named  adh-I>hirsi\  “the  paw” — i.  e..  of  tlic  Lion;  the 
figure  of  Leo  (see  Ideb-r.  p.  l.VJ  etc.)  being  U\  the  Arabs  so  stretched 
out  as  to  co\  »T  parts  of  Hi  mini.  Haiicvr,  tanU  Minor,  and  other  neigh- 
boring constellations. 

8.  Push  mi ; from  the  root  /jus  ft.  iiouvM*..  thrive” : another  frequent 
name,  which  is  the  our  ompb'jed  by  our  treatise,  is  tishmu  which  is  f 
translated  auspicious" : Amara  give*  ah-*  “prosperous.”  Its  - 

divinity  is  ISrhasnati.  the  priest  and  iraclicr  of  tlie  go*l>.  It  comprises 
throe  stars — the  Khanda-Kataka  almie  ai-emsto  give  it  but  one — of  which 
the  middle  0110  is  the  junction-star  of  tin*  a.-teriMii.  This  is  shown  by 
the  position  assigned  to  it  to  be  <5  Caneri  (4) : 

1’iihliya  ....  1 :'i:  n*  . . . . n°  o’  * 

Afuncri.  . . . M«sJ  (j*  ....  n3 X. 

The  other  two  arc  doubtless ) (4.3)  and  0 (til  of  the  same  constellation: 
the  flstmMn  is  figured  a<*  a crescent  and  as  an  arrow,  and  the  arrange- 
ment of  the  group  admits  of  being  regarded  as  representing  a crescent, 
or  the  barbeil  head  of  an  arrow.  Were  the  arrow  the  only  figure  given, 
it  might  be  possible  to  regard  the  group  as  composed  of  /’,*►,  andff  (4), 
the  latter  representing  the  head  of  the  arrow,  and  the  nebulous  cluster, 
Praisope,  between  y and  the  feathering  of  its  shaft:  & (105°  43'— 
0°  48'  S.)  would  then  be  the  junction-slur. 

The  Arab  manzil,  an- Nath  mb,  “the  nose-gap” — i.  o.,  of  the  Lion-— 
comprises  y and  <J Caiicri,  together  with  Prsesepe . 011,  aecording  to  souiV. 
authorities,  Pncscpe  aloiu^Thc  sixth  siVct,  Kind,  is  Canon,  a star 
which  is,  at  present,  only  witli  difficulty  distinguished  by  the  naked  eye. 
Ptolemy  rates  it  as  of  the  fourth  magnitude,  like  y and  A : perhaps  it  is 
one  of  the  stars  of  which  the  brilliancy  lias  sensibly  diminished  during 
the  ptNLtwo  or  three  thousand  years,  or  else  a variable  star  of  very 
long  ppbd.  The  possibility  of  such  changes  requires  to  be  taken  into 
account,  in  comparing  our  heavens  with  those  of  so  remote  a past. 


188 


\ * ■ 

S&rya-Siddh&nta , [viii.  9. 

9.  M flesh  A ; or,  as  plural,  A flesh  As;  the  word  is  also  Written  ApreshA : 
its  appellative  meaning  is  “ entwincr,  embracer.”  With  the  name  accord 
the  divinities  to  whom  the  regency  of  the  astciism  is  assigned,  which 
are  sarpAs , the  serpents.  The  number  of  stars  in  the  group  is  stated  as 
five  by  all  the  authorities  excepting  the  Khnndu-Katnkii,  which  rends  six : 
their  configuration  is  represented  by  a wheel.  The  star  a Cancri  (4)  ia 
pointed  out  by  C.olebrooke  as  the  junction-star  of  Aylcshfi,  apparently 
from  the  near  correspondence  of  its  latitude  witli  that  assigned  to  the 
latter,  for  lie  says  nothing  in  connection  with  it  of  his  native  helpers: 
but  « Cancri  is  not  the  eastern  (v.  1 9)  member  of  any  group  of  five  stars; 
nor,  indeed,  is  it  a member  of  any  distinct  group  at  all.  Now  the  name, 
figure,  and  divinity  of  Aclc'diu.  are  all  distinct i\e,  ami  point  to  a constel- 
lation of  a bent  or  circular  form:  ami  if  we  go  a little  farther  south- 
ward from  the  ecliptic,  we  iiml  precisely  Mich  a constellation,  and  one 
containing,  morcou  r,  the  ^responding  Chinese  determinative.  The 
group  is  that  in  the  head  of  Hydra,  or  v,  o,  «J,  *,  ? ] I vine,  </  and  q being 
of  the  fifth  magnitude,  ami  tins  rest  of  the  fourth:  their  arrangement  is 
conspicuously  circular.  There  can  be  no  duiibl,  therefore.  that  the 
situation  of  the  astcrUm  is  in  the  head  of  lhdra,  ami  r Hydra*.  its 
brightest  star  (being  rated  in  the  Onenw.  t 'at.  as  .»i‘  ina  ^ni tilde  3.4, 
while  A is  4.5),  is  Hu-  junction-star : 

: Ai;Iedm  ....  it*j?  rn/  ....  03  rn'  S. 

t Hydra-.  . . . . ii^-3  ?u*  . . . . uJ  .VS. 

a Cancri  . . . . iij:i  V . . . . V*  Ti'S. 

The  error  of  the.  ILimlu  del  :rmi»aliun  of  ilie  latitude  i>,  indeed,  very 
^B^jhfliderablc,  yet  not  greater  than  we  arc  compelled  in  accept  in  one  or 
1 t#o  other  eases.  The  Khanda-Katuka  im-iva^es  it  r.  giving  the  aster 
ism  6°  instead  ot  75  of  polar  latitude.  Tim  Siddliantu-riromani  etc. 
deduct  1°  from  the  polar  longitude  of  tIic  Kurya-Siddlinnta.  ami  the 
Graha-Laghava  deducts  2 J : both  variations  would  add  to  the  error  in 
longitude. 

The  Arab  manzil  is,  in  tlii*.  mM.-imc.  far  n moved  fn.in  ine  Hindu  aster- 
ism,  being  composed  of  S Camri  (f»)  and  a Leonid  (.*.4),  and  called  at- 
Tarf,  “the  look” — i.  e.t  «*f  the  Lion.  Tin-  -evi-ntl.  < ’liincsc  .«Vv.  Lieu,  is, 
as  already  noticed,  included  in  1 1n-  Hindu  group,  being  A Hydra1. 

10.  Magha ; or,  as  plural.  Mughtis ; - luiglit; The  pi  lams,  Fathers, 

or  manes  of  the  departed,  are  the  regent*  nf  th*.  aMeri<m,  which  is  fig- 
ured as  a house.  It  is,  according  In  most  au  thornier*,  cum  posed  of  five 
stars,  of  which  the  southern  (v.  JH)  ^ the  junction-star.  Four  of  these 
must  be  the  bright  stars  in  the  neck  and  side,  of  tin-  J .ion,  or  y,  tf.  and 
a Leonid,  of  magnitudes  4.5,2,  0.4,  and  1.2  respectively;  hut  which 
should  be  the  fifth  is  not  easy  to  determine,  for  there  is  no  other  single 
star  which  hcoins  to  form  natural  I \ :i  member  of  Ihc  same  group  with 
these:  v (5),  n (5),  or?  (4)  might  In;  fore#  into  a connection  with 
them.  This  difficulty  would  be  removed  by  adopting,  with  the  Klumdu- 
Kataka,  six  as  the  number  of  stars  included  in  tlm  astcrLsui : it  would 
then  be  curt  posed  of  all  the  stars  forming  the  conspicuous  constellation 
familiarly  known  as  “the  Sickle.”  The  star  « Leon  is,  or  Jtcgulus,  the  ; 
most>  brilliant  of  the  group,  is  the  j unction-star,  jpid  its  position  is  defined  . 
with  unusual  precision : * 


viii,  9.] 


Translation  and  Notes. 


189 


* MagM  ....  1 99°  o'  ....  o°  o' 

Rcgulusi  ....  129°  49'  - . - ■ o°  27'  N. 

The  tenth  tnanzil \ aj-Jahhah,  “ the  forehead” — i.  c.,  of  the  Lion — is 
also  composed  of  £,  V , “ Leouis. 

The  eighth,  ninth,  and  tenth  siett  of  the  Chinese  system  altogether 
disagree  in  position  with  the  groups  marking  the  Hindu  and  Arab  man- 
sions, being  situated  far  to  tin-  southward  of  tlx1  ecliptic,  in  proximity, 
according  to  Biot,  to  the  wjuutor  of  the  period  when  they  were  estab- 
lished. The  eighth,  Sing,  i<  « Ilydrie  (-),  having  longitude  (A.  D.  560) 
127°  1G',  latitude  22°  25'  S. 

11,  12.  Phalguni ; or,  a>  plural,  plialganyas ; tlie  dual,  phalgunydu^ 
is  also  found  : this  treatise  presents  the.  derivative  form  phalguni,  which 
is  not  iiifrec]iicnlly  employed  elsewhere.  The  word  likewise  used  to 
designate.  :i  species  of  tig-tree  : its  derivation,  ami  ii-%  meaning,  as  applied 
to  the  iistcrbrus,  is  unknown  to  u-.  Here,  in  two  other  instances, 
later  (the  20tli  and  21*4,  :md  ilm  2<‘>tU  and  12 Till  a-t ori^iii we  have 
two  groups  called  by  the  sann*  irnm-,  an  l dMinguiMicl  from  one  another 
as purva  and  itlUtru , “former"  muI  ••  l:ii  1 • i-*  to  <;«\,  coming  ear- 

lier and  later  to  their  mcridiaiMruiMf.  Tlsn  true  original  iharactcr  and 
composition  of  these  three  double  u^teriMii^  list*  been,  if  we  are  not  mis- 
taken, not  a little  altered  and  ob-cured  in  the  description  of  ilium  fur- 
nished to  u<;  owing,  app.ircii  y,  to  tin-  ignorance  or  csirelo-m-^  of  the 
describor*,  and  imperially  t > tln-ir  in*',  haring  ei.-avly  distinguished  the 
ch.ir:icteri>iio  of  the  •■■»mbin.,d  n.i:M« -la-i! ion  lVoin  llm^e  of  its  separate 
parts.  In  cell  »,:t>o,>{i  •is-  lt  «*r  bed-irsd  (;*•/////< i,  h'aitca,  par punka) j 
given  as  the  iiginv  of  .me  «-r  liorii  of  tin-  part-,  ami  we  recognize  pB 
them  all  tin1  rlium-liTi-t:*-  of  a •■  usi»  !:«uioii  of  four  stars,  fonfr*™ 

hig  together  si  regular  oblong  lignie.  whi-di  admits  of  being  represent-' " 
cd — nut  unsiiilsihiy,  if  mi  her  pn-siicsilh  — b\  a lad.  This  figure,  in  tfajQ 
ease  of  the.  l'h.ilgunm.  is  composed  of  ■»»,  rf,  and  Ii3  Lconis,  a very 
distinei  stud  well-marked  coii'li  ilut  ion.  rniitaiiiiug  two  -tars,  (J  and  j?,  of 
the  second  to  third  magnitude.  one.  .»f  the  third,  and  one,  03,  of  the 
fourth.  The  symbol  of  a be«l,  properly  belonging  1 f » tin-  whole  constel- 
lation, is  given  by  all  the.  autlmrilic-  i«»  both  the  two  parts  into  which  it 
is  divided.  Kaeh  of  lln.-c  l.-uier  has  two  -t;ir<  a^dgnud  to  it,  and  the 
junction -stars  are  said  (\.  lS)t«>  be  the  northern.  The  first  group  is, 
then,  clearly  identifiable  sis  ii  and  Leouis,  the.  former  smd  brighter 


being  the  distinctive >t:ir  : 

ITirva-l'halgimi  . . . i n;0  W . . . . ii°  19’  2S\ 

A Leonid Mi°  i5'  . . . . uj°  19'  N. 

Lcunis i-H" ’-iT  ■ ■ ■ • f;°  N. 


The  Riddlisintsi-t.’ironmni  etc.,  and  tin*  tlraha-Lsigliava.  give  Pftrva- 
Phalgnui  respectively  3°  smd  \°  more  -»f  polar  hm  dt title  than  the  SAryis 
Siddliiinta.  These  sire  more  notable  variations  than  are  found  in  any*' 
other  case,  and  they  appear  to  us  to  indicate  tlisil  these  treatises  intend  to 
designate  the  southern  member  of  the  group,  sis  its  junction-star : we 
have  accordingly  added  its  position  also  above. 

In  the  latter  group,  the  junction-star  is  evidently  ti  Lconis : 

Uttara-Phulgimi  . . . i5o°  io'  . . , . iaQ  5'  N. 


fi  Lconis i5i°  3?'  ....  ia°  17'  X. 

or.  a 


* 


[tuL9. 


This  star,  however,  is  not  the  northern,  bnt  the  souttarn*  of  the  two 
composing  the  asterism : its  description  as  the  southern  we  cannot  hn ft 
regard  as  simply  an  error,  founded  on  a misapprehension  of  the  compo-. 
aition  of  the  double  group.  To  til-Birftnl,  0 Lconis  and  another  star  to 
the  northward,  in  the  Arab  constellation  Coma  Berenices,  were  pointed 
Out  as  forming  the  astorism  TJttam-Plu&lguut.  The  (y&kalya  gives  it  five 
stars,  probably  adding  to  (?  Lconis  the  four  small  stars  in  the  head  of  the 
Virgiu,  £*,  rf  nr,  and  o,  of  magnitudes  four  to  five  and  five. 

The  regents  of  Pfirva  and  Uttara-Phalgunl  are  Bhaga  and  Aryanvm, 
.or  Aryaman  and  Bhaga,  two  of  the  Adityas. 

The  two  corresponding  Arab  mansions  are.  called  az-Zubrah,  “the 
mane" — i.  e.,  of  the  Lion — and  as-Sarfah,  “ the  turn*1 : they  agree  as 
nearly  as  possible  with  the  Hindu  asterisms,  the  former  being  composed 
of  d and  Lconis,  the  latter  of  ft  Lconis  alone.  The  Chinese  sieu , named 
respectively  Chang  and  Y,  are  u1  llydr.e  (5)*  and  aCratcris  (4). 

13.  /fas/a,  “ hand.”  Suvitar.  the  sun,  is  regent  of  the  ostcrism,  which, 
in  accordance  with  its  name,  is  figured  as  a hand,  and  contains  five  stars, 
corresponding  to  the  five  fingers.  These  are  the  five  principal  stars  in 
the  constellation  Corvus,  a well-marked  group,  which  bears,  however, 
no  very  conspicuous  resemblance  to  a hand.  The  stars  are  named — 
counting  from  the  thumb  around  to  the  little  finger,  according  to  our 
apprehension  of  the  figure — ft.  a.  r,  y,  and  d Corvi.  The  text  gives  be- 
low {v.  17)  a very  special  dc'implimi  of  tin-  situation  of  the  junction- 
star  m the  group,  but  one  which  is  unfortunately  quite  hard  to  under- 
stand and  apply : we  regard  it  as  must  probable,  however  (see  note  to 
fg$rl7),  that  y (3)  is  the  star  intended  : the  defined "position,  in  which  all 
sAe  authorities  agree,  would  point  rather  to  d (3)  : 


Hosts 174 3 . . . . io°  G' S. 

y Corvi  ....  1700  ....  1 fJ  »</  B. 

6 Corvi  ....  :-3°  27'  ....  ua  10' S. 


The  Hindu  and  Chinese  systems  return,  in  this  aatcrisin,  to  an  accord- 
ance with  one  another  : the  ele\onth  *irw,  ( liiii,  \>  the  star  y Corvi.  The 
Arab  system  hold*  it*  own  indepi-ndcni  euiirse  one  point  farther:  its 
thirteenth  mansion  comprise*  the  ti\e  bright  Mars  (t,  y,  dv  b Virginia, 
which  form  two  sides,  measuring  about  '5“  ea»hf  of  a great  triangle: 
the  mansion  is  named  ul-Auwa’,  “ the  barking  dog/' 

14.  Citra, , “ brilliant.”  This  is  the  beautiful  star  of  the  first  magni- 
tude a Virginia,  or  Spica,  constituting  an  asteri»:rn  by  itself,  and  figured 
as  a pearl  or  as  a lamp.  Its  divinity  is  Tvashlar,  u the  shaper,  artificer.” 
Its  longitude  is  very  erroneously  defined  by  the  Surya-Siddh&nta  : 

Citrn  ....  1 48'  ....  i°  5o'  S. 

Spica  ....  1&J0  A</  . - . . 2^  a'  S, 

All  the  other  authorities,  however,  saving  the  ^akalya,  remove  this 
error,  by  giving  Citrfc  183°  of  polar  longitude,  instead  of  18Q9.  The 
only  variation  from  the  definition  of  latitude  made  by  our  text  is  offered 
by  the  Siddhhnta-^irotnani,  which,  varying  for  once  from  the  Brahma* 
Siddh&nta,  reads  1*  43'  instead  of  2°. 


• It  is,  apparently,  by  so  original  error  of  the  press*  that  M.  Blot,  in  all  Us 
tables,  calls  this  stir  r1. 


IS ^ititioridtid  jSfote. 


\ SnicA  is  likewise  the  fourteenth  manxil  of  the  Arabs,  styled  by  them  J 
as-Sirfafik,  and  the  twelfth  rieu  of  the  Chinese,  who  call  it  Kio. 

15.  SvAtt,  or  svAti ; the  word  is  said  to  mean  41  sword/  The  TWt- 
tiriy*-Br&hmana  calls  the  asterism  niaktyb,  44  outcast/  possibly  from  its 
remote  northern  situation.  It  is,  like  the  last,  an  asterism  comprising 
but  a single  brilliant  star,  which  is  figured  as  a coral  bead,  gem,  or  pearl. 
In  the  definition  of  its  latitude  all  authorities  agree;  the Graha-IAghava 
makes  its  polar  longitude  198°  only,  instead  of  199°.  The  star  intended 
is  plainly  <*  Bootis,  or  Arcturus : 


Svttti 1 83°  a'  ....  33°  5o'  JT. 

Arcturus.  . . ■ 18 4°  12'  ...  . 3o°  57' N. 

In  this  instance,  the  Hindus  have  gone  far  beyond  the  limits  of  the 
sodiac,  in  order  to  bring  into  their  series  of  asterism*  a brilliant  star 
from  the  northern  heavens : the  other  two  systems  agree  in  remaining 
near  the  ecliptic.  The  fourteenth  Chinese  Kang,  is  * Virginia 
(4.5) : the  Arab  manzil,  al-Ghalr,  44  the.  covering,”  includes  the  came 
star,  together  with  1,  and  either  1 or  Virginia 

16.  VifAkhA,  “ having  spreading  branches”  : in  all  the  earlier  lists  the 
name  appears  as  a dual,  viedkhe.  The  asterism  is  also  placed  under  the 
regency. Of  a dual  divinity,  indr  April,  Indra  and  Agni.  \Y>  should  ex- 
pect, then,  to  find  it  composed,  likn  the  other  two  dnalastcrisms,  the  let 
and  Vth,  of  two  stars,  nearly  ecpial  in  brilliancy,  and  two  is  actually  the 
number  assigned  to  the*  group  l»y  the.  (/akalya  and  the  Khanda-Kataka. 
Now  the  only  two  star.-  in  iliis  re-jimt  uf  the  zodiac  forming  a conspicu- 
ous pair  are  « and  rl  Libot,  lmtli  of  the  second  magnitude,  and  as  thipg 
two  compose  the  corresponding  Arab  mansion,  while  the  former  of  theftl' 
is  the  Chinese  tint,  we  have  the  strungest  reason-,  for  supposing  them  to  ' 
constitute  the  Hindu  asterism  aUo.  There  arc,  however,  difficulties  ijt  • 
the  way  of  this  assumption.  The  later  authorities  gi\e  Vi^klifi  foil t 
stars,  and  the.  defined  position  of  the  jun»-tion-slar  identifies  it  neither 
with  a nor  (t,  but.  with  th*1  faint  star  < (4.3)  in  the  the  same  constell&r 
tion.  Colcbrookc.  overlooking  tlii<  star,  suggests  a or  x Libra*  (5)  : the 
following  comparir*o»  of  portions  will  >liu\v ’that  neither  of  them  can  be 
the  one  meant  to  be  pointed  out : 


Vi^iikhA  . . ai3J.Jr 

cLibrai  . . ail®  u' 

a Libra  . . 2o5°  5' 

x Libra  . . 217°  45' 


. i°  25'  S. 
. i°48'S. 

. o°  23'  3f. 
. o-  2'  N. 


The  group  is  figured  as  a torana:  this  word  Jones  and  Colebrooke 
translate  “festoon/  but  it>  more  proper  meaning  is  4*an  outer  door  or 
gate,  a decorated  gateway/  And  if  wo  change  the  designation  of  situ- 
ation  of  the  junction-star  in  its  group,  given  belo  (v.  10),  from 44  norths 
efnM  to  44  southern/  we  find  without  difficulty  a tpiadrangle  of  stars,  vis. 
»,  a,  (?,  f (4.5)  Librae,  which  admits  very  well  of  being  fignred  os  a gate- 
way. Nor  is  it,  in  our  opinion,  taking  an  unwarrantable  liberty  to  make 
such  an  alteration.  The  whole  scheme  of  designations  we*  regard  as 
■ of  inferior  authenticity,  and  as  partaking  of  the  confusion  anduncer- 
tainty  of  the  later  knowledge  of  the  Hindus  respecting  their  system  of 
astcrismsi  That  they  were  long  ago  doubtful  of  the  position  of  Vig&khfc 


S6rya-8tMhd%  [viii.  0. 

is  shown  by  the  fact.  that  al-Birftni  was  obliged  to  mark  it  in  his  list  as 
“ unknown.”  Very  probably  the  SArya-Siddhilnta,  in  calling  * the  north- 
enfmember  of  the  group,  intended  to  include  with  it  only  the  star  20 
Libne  (3.4),  situated  about  6°  to  the  south  of  it.  Upon  the  whole,  thou, 
while  we  regard  the  identification  of  Victim  ns  in  some  respects  more 
doubtful  than  that  of  any  other  asterUm  in  the  series,  we  yet  believe 
that  it  was  originally  composed  of  the  two  stars  a and  Libra',  and  that 
later  the  group  was  extended  to  include  also  « and  j\  and,  as  so  extended, 
was  figured  as  a gateway.  The  selection,  contrary  to  general  usage,  of 
the  faintest  star  in  the  group  as  its  junction-star,  may  have  been  made 
in  order  to  insure  against  the  retorsion  of  the  astcrism  to  its  original 
dual  form. 

The  variations  of  the  «dln-r  amlmritio  from  the  position  as  stated  in 
our  text  are  of  small  importance:  the.  Siddhautn-tfiroinani  etc.  give 
Yiciiklui  e;V  Icrn  of  polar  longitude,  and  the  < iralia-Lagliava  1°  less;  of 
polar  latitude,  the  Siddhanta-riromani  gives  it  10',  the  < iralia-IAghnvA 
30'  less ; the  Khainln-Kntukn  agrees  here,  a*  also  in  the  two  following 
asterisms,  with  the  Suna-Siddlnmtn. 

The  sixteenth  Arab  nuwziL  rmnpvMiig,  n<  already  noticed,  n and  f? 
Librsc,  is  styled  az-Zuliftnun,  “tin*  two  cIsiwn’— i.  t».t  (.f  tint  Scorpion: 
the  name  of  the  cm'iv-ponding  t'hinese  iiiuurdon,  having  for  its  deter- 
minative a Librce,  is  Ti. 

lT.  Ann  rM  hit : or,  a<  plural,  anunttlhns : the  word  means  “siutcrs.” 
The  dyinity  is  Mitra,  “ friend.”  one  of  the  Ad  it  Ail*.  According  to  the 
(j&kalya,  the  a«tiari«in  i*  compiled  ,»|'  three  -tars,  and  with  this  our  text 
^plainly  agrees  by  designating  (v.  I*)  the  mitUle  as  the  junction-star : 
all  the  other  authorities  give  ir  lour  >t:ir<.  Asa  group  of  three,  it  com- 
prises ft  nr  ^enrpion is,  d (-.:0  being  the  jimetion-star ; the  fourth 
Jdiwnbcr  we  are  doubt I^n  to  add  « Scurpiunis  (.VI).  It  is  figured  as  a 
taUi>T  va!i  ; this  < olebrooke  translate**  “a  row  of  oblation?,”;  wc  do 
not  find,  however,  that  the  word,  although  it  means  Imtli  ‘‘oblation, 
offering,”  ami  “a  row,  Ibid,  riflig',.‘'  is  mod  in  designate  the  two  com- 
bined : perhaps  if  may  better  It  taken  as  simply  “a  row:’4  the  stars 
of  the  astcrism,  whether  coiMdcn-d  :>s  three  *.r  imir.  being  disposed  in 
nearly  a straight-  line.  The  comparison  of  positions  is  as  follow** : 

Auuraillia  . . . . m i'J  .f  V . . . »J  r»jt'  S. 

6 Scot  pi*  mis  . . . If  . . . 

The  SidJliaiitn-Ciromani  and  * bulm-Lughain  estimate  the  latitude  of 
Anurfcdha  somewhat  more  acer.rately,  deducting  from  the  polar  latitude, 
as  given  by  our  text,  1 3 1-V  Mid  1°  respectively:  the  ^iddliaiitad^iroinani, 
etc.  also  add  the  iiisignifi-iint  amount  of  o'  to  tin;  polar  longitude  of  tins 
Sftrya-Siddlmnta. 

The  corresponding  Arab  manztl,  named  al-lklil,  11  the  crown,”  con- 
tains aUo  the  three  stars  {. i , d,  n Scorpion  is,  some  authorities  Adding  q to 
gtlie  group.  The.  Chinese  siat,  Fang,  is  w (3),  the  southernmost  and  the 
faintest  of  *the  three. 

18.  JyeskfhA,  “oldest.”  The  Tuittiriya-Sanhitfi,  in  its  list  of  aster- 
imp,  repeats  here  the  name  rohint , u ruddy,”  which  wc  have  had  above 
aa  that  of  tho  4th  asterisin : the  appellation  has  the  same  ground  in  tbic 


Translation  and  Notes. 


199 


\iii.  0.] 

as  in  the  otlicr  case,  the  junction-star  of  JyeslitliA  being  also  one  of  those 
which  shine  with  a reddish  light.  The  regent  is  Indra,  the  god  of  the 
clear  sky.  The  group  contains,  according  to  all  the  authorities,  three 
stars,  and  the  central  one  (v.  18)  is  the  junction-star.  This  is  the  bril- 
liant star  of  the  first  magnitude  a Scorpion!*,  or  Antarcs ; its  two  com- 
panions arc  a (3.4)  and  t (3.4)  in  the  san^^onstellation  : 

Jycahthft  ....  a3o°  7'  ■ ■ - ■ 3°  Go'  S. 

Antares  ....  239°  44'  ■ - ■ • 4°  3i#  8. 

Hie  constellation  is  figured  as  a ring,  or  ear-ring;  by  this  may  be  un- 
derstood, perhaps,  a pendent  car-jewel,  n<  the  three  stars  of  JyeshthA 
form  nearly  a straight  line,  with  the  brightest  in  the  middle. 

The  Kiddhanta-yiromani  and  Graha-LAghava  add  to  the  polar  longi- 
tude of  the  junction-star  of  the  aster  mu,  as  stated  in  our  text,  .V  and  1° 
mpcclivi-ly,  and  they  deduct  from  its  polar  latitude  30'  and  1*  respect- 
ively, making  the  definition  of  its  position  in  both  respects  less  accurate. 

Antares  forms  the  eight enith  manzil , ami  is  styled  al-Kalb,  “tho 
heart’' — i.  e.,  of  the.  Scorpion  : a and  1 are  called  an-Xiyat.  “tho  pm- 
cortfrVi”.  The  Chinese  . inVw,  Sin,  i<  the  wesl*-riinio<t  of  the  three,  or  a. 

lfi.  Mu  fa,  “root.”  The  pn-iding  <li\  initv  of  th^  asterism  is  nirrti, 

“ calamity,"  w im  is  also  regeni  «»f  ihe  south-western  quarter.  It  com- 
prises, according  to  the  tViknK;',  nine  stars;  their  cm  figuration  is  rep- 
resented by  a liou\s  tail.  The  <tars  intend*  d arc  Umsi;  in  the  tail  of  the 
Scorpion,  or  r,  «,  i„  ti . x,  ry  l Si'orpinnU.  all  of  them  of  the  third, 
or  third  to  fourth,  magnitude.  t>lher  authorities  count  eleven  stars  in 
tho  group,  probably  reckoning  u and  * as  lour  stars;  each  being,  in  fact, 
a group  of  two  eln^olv  appn»xiniarc  star-,  name  I in  our  catalogues  p1 
(3),  ,u-  (4),  Zl  (4.o),  (;!).  The  Kliamla-Kataka  alone  gives  Mula  only 

two  stars,  which  are  identified  hi  nMJirum  with  the  Arab  manzil 
Shauluh,  or  A and  i*  S«‘« *r] »i* »n i>.  The  I'nitriri  va-Sanhita,  too,  gives 
name  of  the  nsb-risin  a-  ‘■llu*  two  rcl#lc:s":  the  YicrtAtt  -Era 

several  times  spoken  of  in  1 h«-  A than  a- Veda  as  two  -tars  of  which  tlio 
rising  promotes  relief  from  lingering  disease  (faArfnyu) : it  is  accord- 
ingly  probabhi  that  these  are  the  1w*«  stars  in  the  sting  of  tho  Scorpion, 
ami  that  they  alone  have  been  regarded  by  some  as  composing  the  aster- 
ism  : their  healing  \irlue  would  doubtless  be  connected  with  the  meteor- 
ological condition*  of  the  time  at  which  their  heliacal  rising  takes  place. 
Our  text.  (v.  It))  designates  the  ea-leru  member  of  the  group  as  its  junc- 
tion-star: it  is  uncertain  whether  the  direction  i*  meant  to  apply  to  the 
group  of  two,  or  to  1 hat  of  nine  stars:  if,  as  seems  probable,  A is  the 
star  pointed  out  by  the  definition  of  position,  it  is  strictly  true  only  of 
the  pair  A and  since  i,  *,  and  ft  are  all  farther  eastward  than  A: 

Mula a.ls°5a'  ....  8°  48' S. 

% Scorpiotii*  . . . »44°  53'  ....  1 3°  44'  S. 

The  Graha-Liighnva  gives  a more  accurate  statement  of  the  longitude, 
adding  1°  to  the  polar  longitude  as  defined  by  all  the  other  euthoritics  : 
hut  it  increases  the  error  in  latitude,  bv  deducting  1°  from  that  presented 
by  our  text : the  Siddhftuta-f  iromani,  in  like  manner,  deducts  30',  while 
the  Khanda-Kntaka  adds  the  same  amount. 


; TAittirlya-SafthM  makes  pitaras,  the  Fathers,  the  presiding 

Hies  of  this  asterism,  as  well  as  of  the  tenth. 

Bentley  states  (Hind.  Astr.,  p.  5)  that  Mftla  was  originally  reckoned  as 
.the- first  of  the  asterism*,  and  was  therefore  so  named,  as  being  their  root 
or  origin ; also  that,  at  another  time,  or  in  a different  system,  the  series 
was  made  to  begin  with  Jymhthfr,  which  thence  received  its  title  of 
“ eldest.’’  These  statcmeniParc  put  forth  with  characteristic  reckless- 
ness, and  apparently,  like  a great  many  others  in  his  pretended  history 
of  Hindu  astronomy,  upon  the  unsupported  authority  of  his  own  conjee- . 
ture.  It  is,  in  many  case*,  by  no  means  easy  to  discover  reasons  for  the 
particular  appellations  by  which  the  nstcrisms  arc  designated:  but  wo 
would  suggest  that  Mftla  may  perhaps  have  been  so  named  from  its  be- 
ing considerably  the  lowest,  or  farthest  to  the  southward,  of  the  whole 
series  of  asterisms,  and  hence  capable  of  being  looked  upon  as  the  root 
out  of  which  they  had  grown  up  the  heavens.  It  would  even  be  possi- 
ble to  trace  the  same  conception  farther,  and  to  regard  JyeshthA  as  so 
styled  because  it  was  the  first,  or  11  oldest,”  outgrowth  from  this  root, 
while  the  Yi^Akhe,  “the  two  diverging  branches,”  were  the  stars  in 
which  the  scries  broke  into  two  lines,  the  one  proceeding  northward,  to 
SvAti  or  Areturus,  the  other  westward,  U»  CitrA  or  Spica.  We  throw 
out  tlic  conjecture  for  what  it  may  be  worth,  not  being  ourselves  at  all 
confident  of  its  accordance  with  the  truth. 

The  nineteenth  Arab  manzil  is  styled  asli-Sliaulah,  “the  sting” — i.  e.f 
of  the  Scorpion — and  comprises,  as  already  noticed,  v and  1 Scornionis. 
The  determinative  of  the  seventeenth  aicu,  Uei,  is  included  in  the  Hindu 
* asterism,  being  ,«2  Scorpionis. 

«1.  Ashdt/ha;  or,  as  plural,  « shArlhA* ; this  treatise  presents  tJio 
ve  form  dskatlka , which  is  not  infrequent  elsewhere : the  word 
‘unsubdued”  Here,  again',  we  have  a double  group,  divided 
> totcrisms,  wliidi  arc  distinguished  as  purva  and  uttnra , 11  former 
er.”  Their  resjjflfethc  divinities  arc  upas,  “the  waters,”  and  vifve 
' dtv&tt,  u the  collective  gods.”  Two  stars  arc  ordinarily  allotted  to  each 
asterism,  and  in  each  case  the  northern  is  designated  16)  ns  the  junc- 
tion-star. By  some  authorities  each  group  is  figured  as  a bed  or  couch; 
by  others,  the' one  as  a bed  and  the  other  as  an  elephant’s  tusk;  and 
here,  again,  there  is  a difference  of  opinion  as  to  which  is  the  bed  and 
which  Sic  tusk.  The  true  solution  of  this  confusion  is,  ns  we  conceive, 
that  the  two  asterisma  taken  together  are  figured  as  a bed,  while  cither 
of  them  alone  is  represented  by  an  elephant’s  tusk.  The  former  group 
most  comprise  (3.4)  and  e (3.2)  Sagittarii,  the  former  being  the  june ■ 
i tion-star;  this  is  shown  by  the  following  comparison  of  positions: 


PArra-AshAdhA  ....  a54°  39'  . . . . 5°  a8'  S. 
3 Sagittarii a 54°  3a'  . . . . 6°  a5'  S. 


The  OraliarLAghava  gives  Pftrva-AshAdhA  1°  more  of  polar  longitude, 
And  80'  less  of  polar  latitude,  than  the  Sfirya-SiddhAnta:  the  SiddhAnYa- 
: (Ktomani  etc.  give  it  10'  less  of  the  latter. 

The  latter  of  the  two  groups  contains,  as  its  southern  star,  t Sagittarii 
(jM}i  end  its  northern  and  junction-star  can  bo  no  other  than  <r  (2.3)  in 
constellation,  notwithstanding  the  error  in  the  Hindu  detenpk 


.taptiob  of  itk  latitude,  which  led  Colehrooke  to 
. star  intended  i we  subjoin  the  positions : 

Uttam-AihftdhA  ....  a6o°  tV  . . . . 4°  59'  S. 


0 Sagittarii 262°  21'  ....  3°  a4'  S. 

* Bagittarii 264°  48'  ....  5°  1'  S. 


The  only  variation  from  the  position  of  the  junction-star  of  this  aster- 
ism  as  stated  in  our  text  is  presented  by  the  Graha-L&ghava,  which 
makes  its  polar  longitude  261°  instead  of  2ti0°. 

The  Q&kalya  (according  to  Colehrooke : our  MS.  is  defective  at  this 
point)  And  the  Khanda-Kataka  assign  four  stars  to  each  of  the  Ash&dh&s, 
and  the  former  represents  each  sis  a bed.  Tt  would  not  he  difficult  to 
establish  two  four-sided  figures  in  this  region  of  the  constellation  Sagit- 
tarius, each  including  the  stars  above  mentioned,  with  two  others : the. 
one  would  be  composed  of  y2  (4.3),  d,  t,  rt  (4 — the  star  is  also  called  $ 
Telescopii),  the  otlu-r  of  tp  (4.3).  cr,  t,  and  ^ : such  is  unquestionably  the 
constitution  of  the  two  asterisms,  considered  as  groups  of  four  stars ; 
they  are  thus  identified  also,  it  may  be  remarked,  by  al-Birhnl.  The 
junction-stars  would  still  be  d and  c/,  which  are  the  northernmost  in  their 
respective  constellations;  nor  is  there  any  question  as  to  which  four 
among  the  eight  arc  selected  to  make  up  the  double  astcrism,  since  d,  c, 

J,  and  e both  form  the  most  regular  quadrangular  figure,  and  are  the 
brightest  stars. 

The  detcriniuath  cs  uf  the  eighteenth  and  nineteenth  mansions  of  the 
Chinese,  Ki  and  Ten,  are  y 2 ami  r/  Sagittarii,  which  are  included  in  the 
two  quadruple  groups  >tatcd  above.  The  twentieth  manzil  compre- 
hends all  the  eight  stars  which  we  have  mentioned,  and  is  styled  an- 
Na’&ini,  “ the  pasturing  cattle”  : some  also  understand  each 
four  as  representing  an  ostrich,  niiVun.  The  twenty-first  manuL  MmUk 
other  hand,  ul-Bulduh,  “ the  town.”  is  described  as  a vacant  spifejs  abomp 
the  head  of  Sagittarius,  hounded  by  faint  stars,  among  which  the  nigal'-' 
conspicuous  is  tt  Sagittarii  (4.f>). 

22.  Abhijit , “ conquering.”  The  regent  of  the  astcrism  is  Brahma. 
The  position  assigned  to  its  jv.  net  ion-star,  which  is  described  as  the 
brightest  (v.  19)  in  a group  of  three,  identities  it  with  a Lyra?,  or.  Vega, 
a star  which  is  exceeded  in  brilliancy  by  only  one  or  two  others  ill  the 
heavens : 

Abhijit  ....  a64°  10'  ...  . r>9°  58f  N. 

Vega  ....  aG5°  i5'  . . . . 61 0 46'  N. 

The  other  authorities  compared  (excepting  the  £&kalya)  define  the 
position  in  latitude  of  Abhijit  more  accurately,  adding  2°  to  the  polar 
latitude  given  by  the  Surya-Kiddli&utft : the  GraLi-Laghava  also  improves 
the  position  in  longitude  by  adding  1°  2U#,  while  t'le  Biddlianta-Qiroma^i 
etc.  increase  the  error  by*  deducting  1°  40'. 

The  T&ittiriya-SanhitA  (iv.  4. 10)  omits  Abhijit  from  its  list  of  the  aa- 
teriams ; the  probable  reason  of  its  omission  in  some  authorities,  or  in 
certain  connections!  and  its  retention  in  others,  wo  shall  diaouae  far- 
ther on. 

■y;  Abhqit  is  figured  as  a triangle,  or  as  the  triangular  nut  of  the  ffngltia, 
'■’an  aquatic  plant;  thi*  very  distinctly  represents  the  grouping  of  a Lyra 


r (4.8)  w 


196'  Sdrya-Siddhdnta^  fviii.  9. 


with  the  two  other  fainter  stars  of  the  same  constellation,  * and  5,  both 
of  the  fifth  magnitude. 

v In  this  and  the  two  following  asterisms — as  once  before,  in  the  fifteenth 
of  the  series — the  Hindus  have  gone  far  from  the  zodiac,  in  order  to 
bring  into  their  system  brilliant  stars  from  the  northern  heavens,  while 
the  Chinese  and  the  Arab  systems  agree  in  remaining  in  the  immediate 
neighborhood  of  the  ecliptic.  The  twentieth  situ  is  named  Nieu,  and 
is  the  star  p Capricorn  (.1),  situated  in  the  head  of  the  (jloat. : the  twen- 
ty-second taanzil , SsiM  adli-1  iluibih.  “ felicity  of  the  sacrilicer/’  contains 
the  same  star,  the  group  being  o (composed  of  two  stars,  each  of  mag- 
nitude -1.4)  and  p Capricorn i. 

23.  (7rarana,  hearing,  earM ; from  the  root  jtk,  “ hear” : another 
name  for  the  asterism.  fronu , found  oeeurring  in  the  Tnittiriya  lists,  is 
perhaps  from  the  same  root,  but  tin*  word  means  also  “lame/"  (,'ravaiin 
comprises  throe -tars,  of  which  the  middle  one  (v.  is)  is  the  junction- 
star  : they  are  to  be  found  in  the  back  and  neck  of  the  Kaule,  namely 
as  yt  «,  and  p Aijuihc;  «,  the  detcrniiii.ilhc.  in  a >tar  uf  the.  first  to  sec- 
ond magnitude,  while  y and  p an*  of  the  third  and  fourth  respect ively  : 


t/ravana  ....  v±j°  •>*/  ....  5i'  N. 

a Aquiku  . . . i 3 \ i ' . . . . 1 1 ' X. 


All  the  authorities  agree  as  to  the  polar  latitude  of  Trio  ana:  the 
SiddMnt a-^i roman i ete.  give  it  *jc  lc—  (,f  polar  huuriiiidc  than  our  trea- 
tise, and  the  Craha-Laghava  ewii  a-  niiicJi  a<  .V  lr-  . 

The  regent  of  I Ik-  aMeris  n i-  Vidinu,  and  ii>  figure  or  >yml»ol  curres- 

Jionds  therewith,  being  three  lboir-ieps.  iviiivM-iitalites  of  I In*  three  steps 
y which  Vishnu  i>  said,  in  tin*  c:irl\  Hindu  mv  l lu . to  have  strode 
gh  liuuveu.  The  (^akidva,  however,  iri\e^  a trident  as  the  figure 
; to  (^ravaua.  1’omiUiIy  the  iiuim-  is  to  be  regarded  as  indie  a- 
tmt  it  was  originally  figured  as  an  ear., 
lie  Chi iio-o  sim  corre.-pom ling  in  rank  with  Oaian.i  is  called  Nit, 
and  is  the  faint  star  t Aqiiarii  (I.H).  Tin-  Arab  r mtuzil  Su’d  Hula1, 
“felicity  of  a demurer,”  or  al-lliila",  *■  the  dc\i«u:cr/’  ete.,  i ne hides  the 
same  star,  being  composed  «»f  ;•  ( l.-M,  <•  ( > Aqiiurii,  or.  according  to 

others,, of  t and  7 (0)  Aquaiii.  ur  of  n a.nl  #■. 

24.  firaviaht/nf ; tin-  word  i-  a >up»  i l.i.ive  lorniation  lV"in  the  same 
root  frotn  which  came  the  name  of  ti  c |»jv.  -:ding  a-U-ri.-m,  und  means, 
probably,  “mo>t  famous.11  Aiiotlur  and  hardly  les-  frequent  uppcllur 
tion  is  dhaniuhthu , an  irregular  superlative  from  ilhuiini , 11  wealthy/’  The 
class  of  deities  known  as  the  i/cmhj,  “bright,  good/'  an1  the  regents  of 
the  asterism.  It  comprise:'  four  stars,  or,  according  to  tlm  (,'akulya  and 
Khanda-Kataka,  five : the  former,  which  is  given  l»y  so  early  a list  as 
that  of  the  Taittiriya-ihahiuami,  is  doiilitlo.-.-  the  original  number.  The 
group  is  the  conspicuous  one  in  the  head  of  the  Jtolphiu,  composed  of 
iJulphiiii,  all  of  them  stars  of  t lie-  third,  or  third  to  fourth,  mug* 
Attitude,  and  closely  disposed  in  diamond  or  lozenge-form:  they  are  tig- 
" ured  by  the  Hindus  as  a drum  or  tabor.  The  junction-star,  which  is  Um 
western  (v.  17),  is  p : 


<?nviflhthA  . ...  296*  5'  ....  35®  33'  S. 
ji  Delphini  ....  29G0  19'  ...  . 3i°  5y'  8. 


' %■■ 


Translation  and  Nbtes. 


19% 


% 


The' only  variation  from  tlie  position  assigned  in  onr  text  to  thVjnuc- 
tion-star  of  ^ravishthi  is  presented  by  the  CJraha-L&ghava,  which  gives 
.'it  280°,  instead  of  290°,  of  polar  longitude.  Perhaps  its  intention  isto 
point  out  C (5)  as  the  junction-star : this  is  doubtless  the  o^('ndtpd|t|^: 
the  other  four,  on  account  of  its  close  proximity  to  them,  to  make  tip  the 
-group  of , five ; it  lies  only  .about  half  a degree  westward  from  (?.  ^ 

■■  The  name  of  the  twenty-fourth  mansi 7,  Sa?d  as-Sn’ud,  ‘^felicity  of 

a|cities1v — i.  c., 44  most  felicitous*’ — exhibits  an  accordance  with  that  of 
I Hindu  astcrism  which  possibly  is  not  accidental.  The  two  are,  how- 


(0).  The  corresponding  jdtw,  iiiii,  the  fir-t  or  them,  or  8 Aquavit. 

25.  CJatabhixlwj*  kl ha\  ing  a hundred  plivd« -huis" : the  form  y aiabkisk d,  ‘ 
which  seems  to  be  inert.* iy  u rorniptiou  of  the  ocher,  also  occurs  in  later 
writings.  It  is,  as  «-c  ••hoi. Id  cvp***-:.  rV  »’ii  th** 
of  a hundred  stars,  nf  wm»*!i  the  b»-i».i,.e.r.  (\ 

This,  from  its  defined  p.»-i:ion,  c.-n  vwr  !•:■  a 


titie,  said  to  be  composed 
1 f9j  is  the  junction-star. 

,»pi  iiii  ( 1) : 


-.5 1 ■ 


c/ataUiMiij  . 

7.  AfjuarLi  . . . 

The  rest  of  the  a*b-ri>m  is  t 
the  knee  of  Aquarius,  m ! 
ber  one  hundred  i-*  ii"‘  ' > ’•.*  i:»  •*  -m 
pose  it  pns>ii*ii“  to  tr,*v  ■ «i’  i 
to  the  group,  whi  -h  i>  n i*:  ■ T 
Birum,  givis  CaiabuM.:*j  «*,  i\  a - 
of  the  Arab  trsixelli-r : h * i-  i ’.v*'.!.- 
Aquarius  is  to  be  *vgai‘-i«-  i n-emi-ii 
The  regent  of  the 

tics,  is  Vanina,  the  chief  « iV*  Ad.V 
the  Tiiilliriya-Nmhit.i  «lu!:e  *_riw-  in 


3 -.i- 

:•  3'  . . . . 

!•.»  among  th* 

-mv1!::!  frniii  iti-  ■"ir : 


■ 9f  S. 

■ vi  t fainter  stars  in 
os’  C"urwf  iiie  nutt- 


f.u  • 


■r  one,  nor  are  wo  to  sup- 
r !?\  ss  iisc  figure  assigned 

..  !\i::ird  «-  :\ntaka,  ac^iniinir  to  al- 
ii" -isir. . ’.it  i!i'n  is  probably  an  errorj 
;n  p.ui.t  fin  which  of  the  stars 
iniing  t • l . • a-tori.-m. 

\ t«»  ii«*nrlv  all  the  a nth 

' i-.  i'  ll  hit.  r the  god  of  the  waters: 
h ;s:  d t • the  1-1  ill  astorbm.  as  well 


as  to  the  18th,  ti!«lw  as  jin-.i.*iiiii;  mi  isshv  : tl»N  i>  perhaps  mere  blun- 
dering. 

The  t.lraha-Iiigliaxa  phi.v*  t1ir«  uuie*.ion-<i:ir  of  f’.itabhishaj  precisely 
on  the  ecliptic:  the  Siddiuiiita-yiruinniii  **ie.  give  i:  -‘O',  instead  of  30, 
of  polar  latiiudf  south. 

ithe  cunvspoinling  lunar  mansion  of  the  Arabs,  SaM  al-Akhlriyah, 
Mtlie  felicity  of  ieuKM  comprises  the  three  stars  in  the.  right  wrist 
hand  of  the  Water-lwarcr,  or  y (M),  % ( 1),  v (4)  Aquavit,  together  with  m 
fourth,  which  Ideler  suppose-  t«»  be  n (;>).  Since,  however,  the  twenty, 
third  Chinese  de1enniu:iti\e,  iJoci.  i«  « Atpiarii  \*)t  a Slav  so  near  aa<£ 
readily  to  be  brought,  into  the  same  group  with  tl  j other  three,  we  ate 
inclined  to  regard  it  as  altogether  probable  that  the  mansion  was,  it 
least  originally,  composed  of  «,  j*,  and  y. 

20,  27.  Bkudrapodd ; as  plural,  bh&drapnKts : also  bhadrapadd  ; from 
hhudfia,  44  beautiful,  happy,"1  and  /Wtr,  i*f«»nt."?  Another  frequent  appel- 
latiou  is  prosfUhapmla : proxkiku  is  said  to  mean  u carp’1  and  Moxn ; the 
hitter  signification  might  perhaps  apply  here.  We  have  here,  once  more, 

* a double  astcrism,  divided  into  two  parts,  which  are  distinguished  from 
- 1 26 


198' 


SQrjp-SuJdhfata, 


on«  another  tap&rva  and  ultara, 11  former"  and  u latter.”  All  «t»U»0tK" 
tics  agree  in  assigning  two  stars  to  each  of  the  two  groups;  but  there 
not  the  same  accordance  as  regards  the  figures  by  which  they  art  ttp*. 

Stented : by  some  the  one,  by  others  the  other,  is  called  a couch  or  bed,  . 

e alternate  one,  in  either  case,  being  pronounced  a bi-faccd  figure : the 
Muliurta-Cintamani  calls  the  first  a bed,  and  the  second  twins.  It  ad* 
mits,  wc  apprehend,  of  little  or  no  question  that  the  Bh&drapad&s  are 
properly  the  four  bright  stars  f?,  «,  y Pcgasi,  and  a Andromedie— ftll.pf 
them  eoinmouly  reckoned  as  of  the  second  magnitude — which 
together  a nearly  perfect  square,  with  sides  measuring  about  15°:  tnp  i 
constellation,  a very  i-oiihpicuiui*  one,  is  familiarly  known  as  the  “ Square  ' 
of  Pegasus.*’  Tiie  figure  of  a cuiu-h  or  bod,  then,  belongs,  as  in  the 
case  of  the  other  two  double  astcrUins,  already  explained,  to'  the  whole 
constellation,  and  not  to  cither  of  the  two  separate  nstcrisms  into  which 
it  is  divided,  while,  on  the  oilier  hand,  cither  of  these  latter  is  properly 
enough  symbolized  by  a pair  uf  twins,  ur  l*y  a figure  with  a double 
face.  The  appropriatcnc.-*  of  the  designation  41  feet,’*  fiuiml  as  a part  of 
both  the  names  of  the  whole  constellation,  is  aWo  sufficiently  evident,  if 
we  regard  the  group  as  thus  composed.  The  junction-star  of  the  former 
half-asterisin  is,  by  it*;  defined  position,  clearly  shown  to  be  ci  Pegasi: 


Turva-Itliddrapniid 
a .... 


33  P aV 


. 190  *-y  N. 


*The  Graha-LAgliavs&  gives  the  jnuction-tiir  1°  less  of  polar  longitude, 
•X  which  would  bring  itv  jindliui:  to  a yet  cI.wit  accordance,  in  respect  to 
longitude,,  with  u Pegasi : the  error  in  latiludc,  which  is  common  to  all 
:*£tbe  authorities,  i-  nut  greater  than  we  hii\c  met  with  sc> oral  times  elsC- 
£S£kerc.  lint  we  arc  told  below  (v.  Hi)  ilial  tin1  principal  star  of  each  of 
jfflBkssc  asterisms  is  the  northern,  and  this  would  exclude  rf  Pegasi  alto- 
IrjjBther,  bringing  in  as  the  other  member  of  the  first  pair  some  more 
Youth  ern  star,  perhaps  j J V-jrsi*i  1 ).  The  n.i. ibsion  i>  not  less  marked, 
-although  of  another  cliar:i«,t«,r,  in  the  *-a««*  of  ili«-  astcrism : in 

the  definition  of  position  > .f  juii*-tio!i-stnr  w«'  filial  a longitude  given 
which  is  that  of  ouc  member  of  ilm  irroup.  and  *i  latitude  which  is  that 
of  the  other,  a*  i*  .shown  by  tin'  fallowing  comparison  : 


U ttHra- Bliudnipadu  . , . 3.f7°  i&  ....  a43  i'  N. 


yPetrasi :uv°  h1  . . . . ia°  35'  N. 

a Andromeda; 3*3 p 17'  ...  . af)°  4i'  N, 


If  we  accept  either  of  tlioo  two  stars  as  the  one  of  which  the  posi-  ' 
tion  is  meant  to  be  defined,  w e shall  ho  obliged  to  admit  an  error  in  the 
determination  either  of  its  longitude  or  of  its  latitude  considerably 
greater  than  we  have  met.  with  elsewhere.  Nor  is  the  matter  mended 
by  any  of  llie  other  authorities  : the  only  variation  from  the  data  of  our 
text  is  presented  by  the  Graha-L&ghnva,  which  reads,  as  the  polar  lati- 
tude ol  Uttara-lJhudrapada,  21°  instead  of  20°.  There  can  be  no 
• doubt  that  the  two  stars  recognized  ns  composing  the  nstcrism  are  y Pe- 
/ ^d  u Andromedie,  hut  there  has  evidently  been  a blundering  con- 
^fnsjpn  of  the  two  in  making  out  the  definition  of  position  of  the  junc? 

We  would  suggest  the  following  as  A possible  explanation  of 


iMt+.&y?'-  * *r-'  ' ' ■ ■ 


/.  ' I0& 

w ■■  i , 

;(JSU  cbjiftision : that  originally  a and  y Pegasi  were  designated  airdt  de- 
-.  scribed  'as  junction-stars  of  the  two  half-groups,  of  which  they  wcro 


riontv  of  a northern  star — the  rank  of  junction-star  was  sought  to  be 
transferred  from  the  southern  to  the  northern  stars  of  both  asterisins  i ~ 
that,  in1  making  the  transfer,  the  original  constitution  of  tlxe  former 
group  was  neglected,  while  in  the  latter  the  attempt  was  made  to  define 
the  real  position  of  the  northern  star,  hut  by  .simply  adding  to  the  polar 
latitude  already  stated  for  y Pcgnsi,  without  altering  its  polar  longitude 
also.  Al-Birfinl,  it  should  be  remarked,  was  unable  to  obtain  from  his 
Hindu  informants  any  satisfactory  identification  of  either  of  these  aster- 
isms,  and  marks  both  in  his  catalogue  as  kCniikniiwii.v1 

The  view  we  have  taken  of  the  true  character  nf  the  two  Bh&drapa- 
dfts  is  powerfully  supported  by  their  compare  »n  with  the  corresponding 
members  of  the  other  two  systems.  The  twi*nty-«i\ih  aud  twenty- 
seventh  manzil* , nl-Fargli  al-Mukdim  and  al-Fargh  al-Mnkhir.  “the  fore 
and  hind  spouts  of  ihc  water-jar,"  enmprw*  ivhh^i ively  « ami  j?Pcgasi, 
and  y Pegasi  and  « Andromeda*;  the  dctermiiiatives  of  the  twenty- 
fourth  and  twenty-fifth  sieu , Che  and  Pi,  arc  o and  y PcgaM.  . 

The  regents  of  tho>o  two  n*lcrUms  are.  nja  rhipaf  ami  a hi  bndhnya, 
the  “one-footed  goat"  and  the  11  bottom-snake."  two  imriiwal  figures,  of 
obscure  significance,  from  tin*  Vedic  pantheon. 

28.  Recall,  “ wealthy.  :d«iind:mt  ” It*  piv*iding  divinity  is  Pushan, 

“ the  prosperer,”  on**  *»f  tin*  Aditxn*.  li  :*  *?.:d  in  contain  thirty-two 
stars,  which  are  figured,  lik*1  iIiom-  «.f  (’rn.  idsiliu.  l.y  a drum  or  tatiror; 
but  it  would  be  in  vain  to  attempt  t-*  point  out  pr-.^bely  the  thirty- two 
which  arc  ii^ende<l,  or  to  discover  in  their  arrangement  any  rescmblaucei', 
.to  the  figure  chosen  to  represent  it.  The  junciioii-Mnv  of  the  groupjj^V 
said  (v.  18)  to  be  its  southernmost  inemher  : all  authorities  agree  Suv 
placing  it  upon  the  ecliptic,  and  all  eve.-pting  our  treatise  and  tfic' 
Q&kalya  make,  its  position  exactly  mark  tin-  initial  point  of  the  fixed 
sidereal  sphere.  Tin:  star  intended  i*.  as  we  h;no  already  often  had 
occasion  to  notice,  t lie -faint  star  : Pisciun:.  nf  about  the  fifth  magnitude, 
situated  in  the  baud  which  connects  the  two  Fi-iio.  It  :s  indeed  very 
near  to  the  ecliptic,  having  only  l.Tnf  south  latitude.  It  coincided  iu 
longitude  with  the  vernal  c<|uinnx  in  the  year  b T*J  of  our  era. 

At  the  time  of  al-lVmini's  visit  to  India,  the  Hindus  seem  to  bare 


been  already  unable  to  point  out  distinctly  and  with  confidence  the  sit- 
uation in  tliu  heavens  of  that  n»o*l  iir.portnm  point  from  wliich  they 
beld  that  the  motions  of  the.  planets  commenced  it  the  creation,  and  at 
which,  at  successive  intervals,  their  universal  conjunction  "■■'•uld  again 
take  place;  for  he  is  obliged  to  mark  the  sistcrisiii  . ■?  not  certainly  iden- 
tifiable. He  also  assigns  to  it,  as  to  (^atabhishaj,  only  a single  star. 

The  twenty-sixth  Chinese  sieu,  Koei,  is  marked  by  ? Andromedse  (4), 
which  is  situated  only  33#  east  in  longitude  from  £ Pise  in  in,  bnt  which 
lias  17°  36'  of  north  latitude.  The  last  manzil,  Batn  al-Hftt,  “the  fish's 
belly,”  or  ar-Rish&i  “ the  band,”  seems  intended  to  include  the  stftrs  com- 
posing the  northern  Fish,  and  with  them  probably  the  Chinese  deter- 
minative also;  but  it  is  extended  so  far  northward  as  to  take  in  the  bright 


200  ■ 


Stir y a -Siddhdn ta,  [via.  0. 

star  £ Andromcdm  (2),  and  to  this  star  alone  the  name  of  the  mansion 
■ is  sometimes  applied,  although  its  situation,  so  tar  from  the  ecliptic  (in 
. Iftt.  25°  5G'  N.)f  renders  it  by  no  means  suited  to  become  the  distinctive 
Star  of  one  of  the  series  of  lunar  stations. 

..  iVVe  present,  in  the  annexed  table,  a general  conspectus  of  the  corres- 
pondences of  the  three  systems;  and,  in  order  to  bring  out  those  corrca- 
pondunces  in  the  fullest  manner  possible,  we  have  made  the  comparison 
m three  diiferent  ways  : noting,  in  the  iii>t  place,  the*  cities  in  which  the 
three,  agree  with  one  another;  then  those  in  which  each  agrees  with  one 
of  the  others;  and  finally,  tho-e  in  which  each  agrees  with  either  the 
one  or  the  other  of  the  remaining  two. 


Correspondences  of  the  Hindu,  A ran,  and  Chinese  S ft  a tons  of  Aster  isms. 


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4 Tins  supposes  the;  second  mnhr.it  to  ho  compos'd  of  the  stars  in  Mtfrrn,  its 
defined  by  some  . authorities  f 'J'hn  sixth  nwnzil  includes,  according  to  many 
Authorities,  the  fifth  hut  sp  there  is,  at  any  rate,  a discord. 'nice  in  the  order  of 
ji;  eucne^ion,  we  have  not  reckoiifd  Ihn  auifiiig  lies  rorrespnndences.  % Wo  reckon 
these  two  as  rases  of  general  coin.-idrnrc,  bemuse,  mUIiouijIi  the  Chincso  *>cu  is  not 
contained  in  the  Arab  mansion,  the  Hindu  asturisni  includes  them  Loth,  and  the 
" virtual  correspondence  of  the  three  systems  is  beyond  dispute,  § Here  we  Assume 
‘ the  Chinese  sun  to  be  comprised  among  the  stars  forming  the  last  manzil , which  is 
altogether  probable,  although  nowhere  distinctly  stated. 


viii,  0.]  Translation  and  Notes.  201 

Owing  to  the  different  constitution  of  the  systems,  their  correspond- 
ences are  somewliat  diverse  in  character : wo.  account  the  Hindu  aster- 
isms  and  the  Aral)  mansions  to  agree,  when  the  groups  which  mark  the 
two  are  composed,  in  whole  or  in  part,  of  the  same  stars:  we  account 
the  Chinese  system  to  agree  with  the  others,  when  the  determinative  of 
a sieu  is  to  he  found  among  the  stars  composing  their  groups.  We 
have  prefixed  to  the  whole  the  mini  hers  ami  titles  of  the  Hindu  aster- 
isms,  for  the  sake  of  easy  reference  hark  to  the.  preceding  detailed  iden- 
tifications and  comparison-. 

After  this  exhibition  of  the  eon«:ordaiK<»<  existing  among  the  three 
systems,  it  can,  we.  apprehend,  niter  into  ilu*.  mind  of  no  one  to  doubt 
that,  all  have  a common  origin,  and  are  hnl  different  forms  of  one  and 
the  same  system.  The  question'  next.  ari*c — is  either  of  the  three  the 
original  from  which  the  others  have  been  derived  i and  if  so,  which  of  < 
them  i "i  entitled  to  the  honor  of  being  -o  regarded  ? and  arc  the  other 
two  independent  and  direct  derixiuho  from  il,  or  docs  either  of  them 
come  from  the  other,  or  mu-t  hn.h  M-hnowl—lgc  an  ii *. ter medi ate  source? 

Tn  endi'.'ivoring  to  :m-w«T  ilie-'-  ipicMious.  we  will  tir-t  exhibit  the  x’iews 
of  M.  liiot  reipeeling  t!ie  nr i giii  and  •■iijinvler  of  the.  i-hincse  si*h,  as 
stated  in  ilic  volume*  lor  1 x 1 1 * mid  1S.V.»  of  the.  Journal  des  Savants. 

According  t>»  l»i«»t,  the  hint  furni^n  organic  and  integral'  part  of  that 
system  by  which  the  ( 'hinc^e,  from  an  alimM.  iimneinorial  antiquity, 
have  heen  accustomed  loin.inc  their  ear-fnl  an«l  industrious  observations 
of  I'elc-iiiil  plM!i'»incn:i.  'i  heir  ae.d  ineir  mol  hods  of  ob- 
servation, have  he.ii  • * I ■ ■ — • * i \ ina!  with  lliu--  in  u-«*  among  modern 

astronomers  in  tie-  \Y«  -1  : t ln-y  ha1. c ■■mjii- iyi-.  1 a meridian-circle  and  a 
meiiMirc  of  time,  tic*  c|.  p*\dra.  ar!  hav  nh-iTvcd  meridian-transits,  ob- 
taining  rigid.  :i-«,«lii-It-n-  and  i Ii,»".i:::is i« *n^  of  tin*  Indies  ••h>erved.  To  ^ 
reduce  the  error*  of  their  iinp.*rii  1 linn-koepur.-,  they  long  ago  selected  ' ■ 
certain  stars  near  lie-  iipurnr,  of  whi'-li  they  dt i.-rniiued  with  grcafcewe 
the  interval-  in  time,  mid  to  liicM-  \\,  *y  ri  rc.l  lie-  p««xiti.iii'  iff  stars  fcr  , 
planets  coming  (o  the  un Tidlan  In-. ween  tin-in.  " Tl :c  -.tars  thus  chosen 
are  the  mvh.  Tueniy-ioiir  nf  them  were  fixed  uin.n  more  than  two 
thousand  years  l«ffore  our  era  (M.  Ili.»r  -ny*,  ah.-ut  l». i\  *2^57:  blit  it  i» 
obviously  impossible  to  ii \ the  iiai.\  hy  imcrnal  evidence,  within  a cen- 
tury or  two,  nor  i-  tin1  exiernal  ex  Hence  of  a more  definite  character); 
the  considoraiiou-.  which  gnv.-rurd  ilmir  selection  were  three:  proximity 
to  the  equator  of  tiial  period,  distil!**!,  visibility — conspicuous  brilliancy 
not  being  demanded  for  them  - and  near  ngn-mumt  in  respect  to  time 
of  transit-  with  the  upper  and  lower  ineridian-pa—ag'^  of  the  bright  stars 
near  the.  pole,  within  tii1  cjivio  of  pcrpe.ual  apparition:  M.  Biot  finds 
reason  to  believe  ihal  tlic-c  circumpolar  >tar-  *iad  been  earlier  observed 
with  special  care,  and  made,  standard*  of  cmi  Kirison,  and  that,  when 
it  was  afterward  seen  to  he  desirable  to  have  st;. lions  near  the  equator, 
such  stars  were  adopted  as  most  nearly  agreed  w itli  them  in  right  ascen- 
sion. The  other  four,  being  llie  8th,  1-lrli,  2 1 -t,  and  -28th,  the  accession 
of  which  completed  tlm  system  of  t wei it \ -eight,  were  added  in  the  time 
■ of  Chen-Koug,  about  11 0-  1100,  because  they  marked  very,  nearly  the 

Eositions  of  the  equinoxes  and  solstices  at  that  epoch : the  bright  star  of 
lie  Pleiades,  however,  which  had  originally  been  made  the  first  of  the  . 


■■  aerita,  from  its  near  approach  to  tlie  vernal  equinox  of  that  remoter  era, 
, still  maintained,  ns  it  has  ever  since  maintained,  its  rank  as  the  first 
. Since  the  time  of  CIieu-Kong  the  system  has  undergone  no  farther  modi* 
Station,  but  has  been  preserved  unaltered  and  unimproved,  with  the 
obstinate  persistency  so  characteristic  of  the  Chinese,  although  many  of 
. the  determinative  stars  have,  under  the  influence  of  the  precession,  be- 
come far  removed  from  tin?  equator,  one  of  them  even  having  retro- 
graded into  the  preceding  mansion. 

If  the  history  of  the  Chinese  «>k,  as  thus  drawn  out,  is  well-founded 
and  true,  the  question  of  origin  is  already  solved  : the  system  of  twenty- 
eight  celestial  mansions  is  proved  to  he  of  native  Chinese  institution — 
just  as  the  system  of  representation  of  the  planetary  movements  by  epi- 
cycles is  proved  to  he  Greek  by  the  fact  that  we  can  trace  in  tho  history 
of  Greek  science  the  successive  steps  of  its  gradual  elaboration.  That 
history  rests,  at.  present,  upon  the  authority  of  M.  Itiot  alone:  we  are 
not  aware,  at  lcicd.  t lint  any  other  iiinMigulnr  has  gone  independently 
over  the  same  ground;  and  he  lia>  in»t  liim-rlt"  laid  before  u>.  in  their 
original  form,  the  passages  from  Chinese  texts  which  furnish  the  basis 
of  Iris  conclusions.  Hut  we  regard  them  as  entitled  to  be  received, 
upon  bis  authority,  with  no  Might  measure  of  confidence:  his  own  dis- 
tinguished eminence  as  a physicist  mid  astronomer,  his  familiarity  with 
researches  into  the  history  and  .iHiseology  science,  his  acrcvs'to  tho 
abundant  material  for  tin*  hw  >r\  • Miin*  astronomy  collected  and 

worked  up  bv  the  French  mis  i»»nari**-  I Vkin.  and  the  zealous  assist- 
ance of  li  is  M.  Kdimard  1 the  viuin-nl  SinologiM,  whose  prema- 
ture death,  in  has  been  deeply  «l«*pi.ucd  n?  a severe  loss  to  Chi- 

nese studies — all  tliesc  advantages  rarely  mited  in  such  fullness  in  the 
..person  of  any  oup  *.tud»»nt  of  mu-Ii  a *u\\  rt,  giie  u-ry  great  weight  to 
* views  arrived  at  by  m as  the  rt*snl t-.  of  laborious  and  long-continued 
investigation.  X«»ruo  we  m*c  that  any  g-noral  considerations  of  import- 
ance can  be  brought  forward  in  opposition  l«»  iIium-  virus,  it  is,  in  tho 
first  place,  by  no  limans  iviiaoiisisteiii  with  wlial  we  know  in  other  res- 
pects of  the  age  and  character  of  tin1  culture  of  the  Chine  ms,  that  they 
should  have  devised  such  a system  at  so  early  a dale.  They  have,  from 
the  beginning,  been  ns  much  distinguished  by  a tendency  to  observe  and 
record  as  the  Hindus  l»y  the  lack  of  Midi  a tendency  : tiicy  have  always 
attached  extreme  importance  to  n^rniuiiuiea]  labors,’ and  to  the  construc- 
tion and  rectification  «>f  the  calmidar ; and  the  industry  and  accuracy 
of  their  observations  is  aLtoted  l«v  the  iisns  made,  of  them  by  modern 
astronomers — thus,  to  take  a instance,  of  the  cometary  orbits 

which  have  been  calculated,  the  liivl  twenty-five  rest  upon  Chinese  ob- 
servations alone:  and  once  more,  it  is  altogether  in  accordance  with  the 
clever  empiricism  and  practical  shrewdness  of  the  Chinese  character  that 
they  should  have  originated  at  the  very  .start  a system  of  observation 
exceedingly  well  adapted  to  its  purpose,  .stopping  with  that,  working  in- 
•ffustriously  on  thenceforth  in  the  same  beaten  track,  and  never  develop- 
ing out  of  so  promising  a commencement  anything  deserving  the  name 
; ofjfc  scieiMRr,  never  devising  a theory  of  the  planetary  motions,  never 
eyjta  recognizing  and  defining  the  true  character  of  the  cardinal  phe- 
of  the  precession. 


vifi.9,]  Ifomtlatton  xendNotes.  ' 208  ? 

Again,  although  it  might  seem  beforehand  highly  improbable  that  a 
. system  of  Chinese  invention  should  have  found  its  way  into  the  West, 
and  have  been  extensively  accepted  there,  many  centuries  before  the 
Christian  era,  there  are  no  so  insuperable  difficulties  in  the  way  as  should 
destroy  the  force  of  strong  presumptive  evidence  of  the  truth  of  such  a 
communication.  It  is  well  known  that  in  very  ancient  times  the  pro- 
ducts of  the  soil  and  industry  of  China  were  sought  as  objects  of  lux- 
ury in  the  West,  and  mercantile  intercourse  opened  and  maintained 
across  the  deserts  of  Central  Asia ; it  even  appears  that,  as  early  as 
about  B.  C.  600  (Isaiah  xlix.  12),  some  knowledge  of  the  Sinim,  as  a far- 
off  eastern  nation,  had  penetrated  to  Babylon  and  Judea.  On  the  other 
hand,  we  do  not  know  how  much,  if  at  all,  earlier  than  this  it  may  be 
necessary  to  acknowledge  the  system  of  asterisms  to  have  made  its  ap- 
pearance in  India.  The  literary  memorials  of  the  earliest  period,  the 
Vcdic  period  proper,  present  no  evidence  of  the  existence  of  the  system: 
indeed,  it  is  remarkable  how  little  notice  is  taken  of  the  stars  by  the 
Vedic  poets;  even  the  recognition  of  *ome  of  them  as  piancts  does  not 
appear  to  have  inkeu  place  until  considerably  later.  In  tin*  more  recent 
portions  of  the  Vedic  text**— as  in  the  iiiin-i«*i:iith  book  of  the  Athnrva- 
Ycda,  a modern  appendage  in  thsii  modern  collection,  and  in  parts  of 
the  Yajur-Vcda,  of  which  tlu-re  is  reason  to  believe  that  the  canon  was 
not  closed  until  a comparatively  late  period — full  lists  of  the  asterisms 
arc  found.  The.  mo*l  uin*qui\ucal  evidence  of  the  early  date  of  the  sys- 
tem in  India  is  furnish'  d by  the  character  of  the  dh  initios  under  whoso 
regency  the  several  siM'TNUn  are  placed  : UiCm:  an.*  all  from  the  Vcdic 
pantheon  ; the  popular  di\  initii-*  of  later  times  an*  not  t*>  be  found  among 
them  ; but,  on  the  n| her  hand,  iiiniv  than  mu*  whose  consequence  is  lost, 
and  whose  name*  alnm-l  arc  lbrg'»l1«,n.  e\cn  in  the  epic  period  of  Hindu 
history,  appear  in  the  li-x.  Neither  tlih,  however,  nor  any  other  evi- 
dence known  t< » us,  is  sufficient  to  prove,  or  c\on  to  render  strongly  prob- 
able, the  existence  t,f  tie*  asteri-m*  in  India  at  s*»  remote  a period  that 
the  system  might  ik»l  be  b«  Ii-wd  :•»  hau  b.*«jn  introduced,  in  its  fully 
developed  form,  from  Chinn. 

If,  now,  we  make  the  attempt  to  determine,  upon  internal  evidence, 
which  of  the  three  systems  is  the  primitive  one.  a detailed  examination 
of  their  correspondence*  and  difference*  will  lead  us  first  to  the  import- 
ant ncgati\e  conclusion  that  no  one  among  them  can  be  regarded  as  the. 
immediate  source  from  which  cither  of  the  other  two  has  been  deriredv 
It  is  evident  that  the  Hindu  asterisms  and  the  Arab  manazil  constitute," 
in  mail)'  respeet*,  one  and  the  sniuo  system : both  present,  to  us  constel- 
lations  or  groups  of  stars,  in  place  of  the  single  determinatives  of  the- 
Chinese  sicti ; and  not  only  are  those  groups  composed  in  general  of  the 
same  stars,  but  in  *c\eral  cases — as  the  7 th,  loth  lltli,  and  12th  mem- 
bers of  the  series-  where,  they  differ  widely  in  s.tuatioii  from  tho  Chi- 
nese determinatives,  they  exhibit  an  accordance  with  one  another  which 
is  too  close  to  be.  plausibly  looked  upon  as  accidental.  But  if  it  b thu#e 
made  to  appear  that  neither  can  have  come  independently  of  the  other 
from  a Chinese  original,  it  is  no  less  certain  that  neither  can  lg|m  come 
through  the  other  from  such  an  original ; for  each  has  its  ovflKnts  of 
agreement  with  the  tieuf  which  the  other  docs  not  share — the  Hindu  in 


. 204' 


friii.  K. 


the  0th,  13th,  and  21st.  asterisms,  the  Arab  in  the  15th,  22nd,  23rdi„ 
24th*  and^25th  mansions.  The  same  considerations  show,  inversely,  that' 
the  Chinese  system  cannot  be  traced  to  either  of  the  others  as  its  source, 

; since  it  agrees  in  several  points  with  each  one  of  them  where  that  ono 
differs  from  the  third.  1 1 becomes  necessary,  then,  to  introduce  an  addi- 
tional term  into  the  comparison;  to  aclinic  the  existence  of  a fourth 
system,  differing,  in  sonic  particulars  from  each  of  the  others,  in  which 
all  shall  Hud  their  common  point  of  union.  Such  an  assumption  is  not 
to  bo  looked  upon  as  either  gratuitous  or  arbitrary.  Nut  only  do  the 
mutual  relations  ot  the  three  systems  point  distinctly  toward  it,  but  it  is 
also  supported  by  genera]  considerations,  and  will,  we  think,  be  found  to 
remove  many  ol  the  diitfeuities  which  have  embarrassed  the  history  of 
the  general  system.  It  lias  been  urged  a-*  a powerful  objection  to  the  ' 
Chinese  origin  of  the  twenty-ei  gfc-toM  tin  isimi  of  the  J^aveiH,  that  we 
find  traces  of  its  existence  in  *6  many  i.f  the  countries  of  the  West, 
geographically  remote  from  thiiim,  ainl  in  which  € inilnence  tan 
hardly  be  supposed  i»  lieu-  1- on  dinvf!\  f,];.  Ai  d it  i<  imp lmibtedly 
true  that  neither  India  imr  Arabia  ha*  s(ni.d  in  .v.ei.  k In :*  s in  such 

relations  to  China  a-,  should  In  ii  in  1 1 1< 1 tin*  ii m :n-< i *,t i *■  recipient 

of* Chinese  learning,  aiid  tile  mean*1  ■ »t  it -»  iii,iiiiiiiiiiie::iiu,Ii  to  siirroimd- 
ing  people''.  The  great  r« ■ n t « ' c«i"  inti'ivonr'c  iiriiw*aii  i 'I. »i,-i  anil  th«j 
4-Vest  led  over  1 li«*  l ir»le-!.:nd  of  i ,i,nu,al  A-i:1,  a, id  into  north- 
eastern territory  of  i run*  lsm-  -si  ■ »S‘  lii"  Zi-vm-i1. ivli-rioii  ;:ud  cul- 
ture! theiLCi1  tlw*  road-  iiiver*/  ■ \ » o s i.  .••■i"  \»  i . r-.i'd,  t!ie  fi'hor 

SOUtll-Cii.'t  Will'd  illlo  f|.  I . v-  ' v < 'Jn.i.lj'ie  iIIIO 

ite  ol  the  liiiiiau  p>aia.ii.«iii'a.  V.  • ■< in  . -r  n : .< ■■)  jm*-  limits  of  t iii s central 
Iran  we  *'•  «•  tin-  '■■y-lcin  nf  ii >;: n «.!- -:i^  (■•  have  ivcoivcd  time 

; form  of  which  the  JJindii  §mk'  h*itr*nt  and  ;!:■■  r:« i ■ nunmzil  arc*  the 

^somewhat  altered  reprovnlative- ; ji: ■ -i-i-.-  ]v  w iii-re,  and  whether  in  the 
hands  ot  Sbiniii1*  or  or  An.m  reef-.  v .■  wo'di;  n .i  ai  p;'*,.*i,:lt  attempt 
to  say.  There  are,  a**  has  been  iml 1 abuie,  i r.-n,i  — of  an  Iranian  os- 
tein to  be  toinul  in  the  iJim* !•  ; I ■ i ■- 1 t ■ i ■ i>  a \ > ■ ■ i ~ unii-h,  although 

probably  not  later  than  lie*  t j 1 1: »■  - f : -> ■ ■(  •,  i i«  r .% -p# j uiuIit  her 

Sassaniau  ruler.'',  eau  pretem!  t«»  i;u  r.i  di  :■  •.! I>ju::  i and  i».«  lije  traces  have 
ns  yet  been  pointed  out  in  1 Jm:  carle  -s  Iramai*  iiii-niorial.  the  Xendavcsla. 
Weber  (Ind.  LiicriiUirgeM-liii'lite,  p.  - - 1 j.  n.  the  oilier  liaud,  :-i-«s  in  the 
mazzaioth  and  mazzvroth  ,.f  ihi-  S.-ripti.r-s  (.1,.!,  \w\iii.  :jj ; J|  Kings 
xxiii.  5) — words  ra'ii#,aiiy  ‘dfiii  v»m!i  l lx< ■ Arab'*  iunnzil' — iiidiciiliuiis  of 
the  early  exi.-lcnee  ot  the  ‘•_v-i',in  in  oiuMion  ma.-e^  tin*  western  Semites, 
and  suspects  fo:1  it  a Oinlduh*  or  goi:  1 nl  ■ )n»  ;diu-ii.n-  appear  to  ds  too 
obscure  and  erjuivocal  to  hr*  r-iied  upon  as  ju-ooi'  of  thU,  /mr  i*  if  easy 
to  believe  that  such  a method  of  division  of  tin-  heavens  should  liavo 
prc\ ailed  so  far  "to  the  west,  and  from  so  ancient  a time,  without  our 
bearing  of  it  from  the  Greeks  ; and  especially,  if  it  formed  a part  of  the  ■ 
Chaluuii;  astronomy.  Tliis  point,  howevei,  may  fairly  be  passed  over, 
is  ore:  to  be  determined,  perhaps,  by  future  investigations,  and  not  of 
.essential  importance  to  tin-  present  irn|uirv.  Tin;  ([notion  of  originality 
is  it  IcMHeliniiely  settled  adversely  to  the  claims  of  both  the  liindu 
gad  th^Vab  systems,  and  can  only  Jits  between  the  Chinese  and  that 
|i,  system  from  which  the  other  two  have  together  descended.  And  ; 


Translation  and  Notes* 


205 


tin.  9.J 

as; concerns  these,  wo  are  willing  to  accept  the  solution  which  is  fur* 
nished  us  by  the  researches  of  M.  Biot,  supported  as  we  conceive  it  to  be 
by  the  general  probabilities  of  the  case.  Any  one  who  will  trace  out, 
by  the  help  of  a celestial  globe  or  map,*  the  .positions  of  the  Chinese 
determinatives,  cannot  fail  to  perceive  their  general  approach  to  a great 
circle  of  the  sphere  which  is  independent  of  the  ecliptic,  and  which 
accords  more  nearly  with  the  equator  of  B.  C.  2350  than  with  any  other 
later  one.  The  full  explanations  and  tables  of  positions  given  by  Biot 
(Journ.  d.  Saw,  1840,  j»p.  243-254)  also  furnish  evidence,  of  a kind  ap- 
preciable by  all,  that,  the  system  may  have  had  the  origin  which  no 
attributes  to  it,  and  that,  allowing  for  the  limitations  imposed  upon  it  by 
■its  history,  it  is  consistent  with  itself,  and  well  enough  adapted  to  the 
purposes  for  w liich  it  was  designed.  With  the  positions  of  its  determin- 
ative stars  seem  to  have  agreed  those  of  the  constellation*  adopted  by 
the  common  parent  «*f  the  Hindu  ainl  Arab  M«dcin%  excepting  in  five  or 
six  points:  those  points  being  where  thf  rhinc.-e  make  their  one  unac- 
countable1 leap  from  the  head  to  the  bell  of  Orion,  and  again,  where  the 
sieu  are  drawn  off  Far  to  tin1  southward,  in  the  constellations  Hydra  and 
Crater:  and  this,  in  our  \iew,  look*  much  m«*iv  as  if  the  hcries  of  the 
sieu  were  the  original,  who*'1  guidance  had  been  «-hwc'.y  followed  except- 
ing ill  a lew  cases,  than  as  if  the  asterisms  composing  the  other  systems 
had  been" independently  select*  «l  Irmii  tin*  groups  «.f  Mars  .situated  along 
the  zodiac,  with  the  intention  nf  fanning  a x<ujin>anl  series.  It  is  easy  to 
see,  farther,  how  liie >ing!c  dctcmiinati\c"  Mh1  'thm*t  .-limild  have  become 
the  nuclei  for  rmi'icllalioii ; Midi  rs  are  prc.-ciited  by  the  other  systems; 
but  if,  on  the  emit  run . the  sicn  !i:id  been  1 by  the  Chinese,  in 

each  case,  from  group*  pn  \ii-ud\  c.in*.tfouud,  iin-r«-  ap] tears  no  reason 
why  their  brighter  -1  ;* i ^ dimiM  m.i  ha\e  been  di  •**  ■».  a -,  they  were  cho- 
sen later  by  tin*.  Hindus,  in  the  * slab!  Minn  ill  of  jiuicti  m-^tam  for  the 
asterisms.  • 

AVo  would  Miggi1'*,  then,  as  tlic  lh>"iry  h.->t  supported  by  all  ihc  evi- 
dence thus  far  clidlcd.  that  a know ledge  of  tin1  Chiin-e  -iMrunoiuy,  and 
with  it  the  Chines**  syM,*m  of  dixiM-wi  nf  tin*  Inuuens  isi:*»  twenty-eight 
mansions,  wa<  earrie*|  into  Western  .Wia  at  a peril* l hoL  much  later 
than  B.  1 lO'b  ami  was  tlnuv  adopied  by  ^-mie  weM‘irn  people,  cither 
Semitic  or  Iranian.  That  in  their  hands  it  ivccncd  a m-.v  form,  such  as 
adnplcd  it  t«»  a vud-T  and  less  ^i-ii-ni ilir  im-mIio*!  «»f  ohscrv.it i >n,  the-  limit- 
ing star*  of  the  mansions  being  com  cried  into  zodiacal  groups  or  con- 
stellations, ami  in  Mime  iinsiances  altered  in  p ir-iiion,  so  a*  to  be  brought 
nearer  to  llic  general  planetary  padi  of  the  '-.'liptic.  That  in  this 
changed  form,  having  become  a means  of  roughly  determining  and  de- 
scribing the  places  and  iiuocmeiits  of  the  plain  is,  it  pilled  into  the 
keeping  of  the  Hindus — very  probably  along  will  the  first,  knowledge 
of  the  planets  tiicmsehe.s — ami  entered  upon  an  independent  career  of 
liiAtory  in  India.  Thai,  it  still  maintained  its^f  in  iu>  old  seat,  leaving  its 
traces  later  in  the  Bundehesh  ; and  that,  it  made  it*  way  so  far  westward 
as  finally  to  become  known  to,  and  adopted  by,  the  Arabs£  The  farther 


additional  notes,  such  a map  of  the  zodiacal  zone  of  the  heavens  u will  sufficiently 
illustrato  the  character  and  mutual  relations  of  the  three  systems  compared. 

27 


soe 


S&r^Siddh&nfy 


tnodifitmfa'ons  introduced  into  it  by  the  latter  people  all  bare'  in  view 
v dpglft  purpose,  that  of  establishing  its  stations  in  the  immediate  neigh- 
borhood of  the  ecliptic : to  this  purpose  the  whole  Arab  system  is  not  - 
lew  constantly  faithful  than  is  the  Chinese  to  its  own  guiding  principle# 
L.The  Hindu  sustains  in  this  respect  but  an  unfavorable  comparison  with  ; 
the  others  : the  arbitrary  introduction,  in  the  15th,  22nd,  23rd,  and  24th 
astcrisms,  of  remote  northern  stars,  greatly  impairs  its  unity,  and  also 
furnishes  an  additional  argument  of  no  slight  force  against  its  original* 
ity ; for,  on  the  one  hand,  tlic  derivation  of  the  others  from  it  becomes 
thereby  vastly  more  difficult,  and,  on  the  other,  we  can  hardly  believe 
that  a system  of  organic  Indian  growth  could  have  become  disfigured  in 
India  by  such  inconsistencies ; they  wear  the  aspect,  rather,  of  arbitrary 
alterations  made,  at  the  time  of  ils  adoption,  in  an  institution  imported 
from  abroad. 

It  might,  at  first  sight,  appear  that  the  adoption  by  the  Arabs  of  the 
Uiajttii  corresponding  to  A^vini  as  the.  fir^t  of  their  series  indicated  that 
they  had  derived  it  from  India  posterior  to  the  transfer  by  the  Hindus 
of  the  first  rank  from  Krttika,  the  first  of  the  to  Agvini : but  the 
eircumstancc  seems  readily  to  admit  of  another  interpretation.  The 
names  of  many  of  the  Arab  mansions  show  the  inllucnce  of  the  Greek 
astronomy,  being  derived  from  the  Greek  constellations : the  same  influ- 
ence would  fully  explain  an  arrangement  which  made  the  series  begin 
with  the  group  coinciding  most  nearly  with  the  beginning  of  the  Greek 
zodiac.  The  transfer  on  the*  part  of  tlic  Hindus,  likewise,  was  unques- 
tionably made  at  the  time  of  the  general  reconstruction  of  their  astro- 
nomical system  under  the  influence*  of  western  science.  The  two  series 
are  thus  to  be  regarded  as  having  been  brought  into  accordance  in  this 
reaptfCtby  the  separate  and  independent  working  of  the  same  cause. 

’ bL  Biot  insists  strongly,  as  a proof  of  tlu:  non-originality  of  the  sys- 
tem of  asterisms  aifiong  the  Hindus,  upon  its  gross  and  palpable  lack 
of  adaptedness  to  the  purpose  for  whirh  they  used  it;  he  compares  it 
to  a gimlet  out  of  which  they  have  tried  to  make  a saw.  In  this  view 
we  can  by  no  means  agree  with  him  : we  wmiM  rather  liken  it  to  a 
hatcliet,  which,  with  its  edge  flailed  and  broken,  has  been  turned  and 
made  to  do  duty  as  a hammer,  and  which  is  not  ill  suited  to  its  new  and 
coarser  office.  Indeed,  taking  the  Hindu  system  in  its  more  perfect 
and  consistent  form,  ns  applied  bv  the  Arabs,  and  comparing  it  with  the 
Chinese  tieu  at  any  time  within  the  past  two  thousand  years,  we  are  by 
no  means  sure  that  the  advantage  in  respect  to  adaptation  would  not  bo 
generally  pronounced  to  be  upon  the  side  of  the  former.  The  distance 
of  many  of  the  iieu  during  that  period  from  the  equator,  the  faintness 
of  some  among  them,  the  great  irregularity  of  their  intervals,  render 
them  anything  but  a model  system  for  measuring  distances  in  right 
ascension.  On  thcr  other  band,  to  adopt  a scries  of  conspicuous  constel- 
lations along  the  zodiac,  Vf  their  proximity  to  which  the  movements  of 
the  planets  shall  be  marked,  is  no  unmotived  proceeding:  just  such  a 
division  of  tin  ecliptic  among  twelve  constellations  preceded  and  led  the 

S to  the  Greek  method  of  measuring  by  signs,  having  exact  limits, 

; independent  of  the  groups  of  stars  which  originally  gave  name,  to  ' 
SL  Clot's  error  Resin  his  misapprehension, in  two  important 


's  • § m 

respects*  of  the  character  of  the  Hindu  asterisms ; in  the  first  place,  he 
constantly  treats  them  as  if  they  were,  like  the  «>«,  tingle  stars,  the  in* 
.rtdhralt  between  whose  circlet  of  declination  constituted  the  accepted 
divisions  of  the  zodiac ; and  in  the  second  place,  he  assumes  them  to 
have-  been  established  for  the  purpose  of  marking  the  moon’s  daily,  pro- 
gram from  point  to  point  along  the  ecliptic.  Now,  as  regards  the  first 
of  these  points,  we  have  already  shown  above  that  the  conversion  of  the 
Chinese  determinatives  into  constellations  took  place,  in  all  probability, 
'before  their  introduction  to  the  knowledge  of  the  Hindus:  there  is,  in- 
deed*, an  entire  unanimity  of  evidence  to  the  effect  that  fhe  Hindu  sys- 
tem  is  from  its  inception  one  of  groups  of  stars:  this  is  conclusively 
shown  by  the  original  dual  and  plural  names  of  the  asterisms,  or  by  their 
otherwise  significant  titles — compare  especially  those  of  the  13th  and 
25tli  of  the  scries.  The  selection  of  a 41  junction-star ” to  represent  the 
asterism  appears  to  be  something  comparatively  modern:  wc  regard  it 
aa  posterior  to  the  reconstruction  of  the  Hindu  astronomy  upon  a truly 
scientific  basis,  and  the  determination,  by  calculation,  of  the  precise  pla- 
ces of  the  planets  : this  would  naturally  awaken  a desire  for,  and  lead 
* to,  a similarly  exact,  determination  of  the  posit bm  of  some  star  repre- 
senting each  asterism,  which  might  be  employed  in  the  calculation  of 
conjunctions,  for  astrological  purposes;  the  astronomical  uses  of  the 
system  being  no  longer  of  much  account  after  the  division  of  the  ecliptic 
into  signs.  And  the  choice  of  the  junction-star  has  fallen,  in  the  mar 
jority  of  cases,  not  upon  the  Chinese  determinative  itself,  but  upon  some 
other  and  more  conspicuous  member  of  the.  group  originally  formed 
about  the  latter.  Aguii^  there  is  an  ent  ire  absence  of  evidence  that  the 
“ portions”  of  the  arterisins,  or  the  arcs  of  the  ecliptic  named  from  them, 
were  ever  measured  from  junction-star  to  junet ion-star  : whatever  may 
be  the  discordance  among  the  different  authorities  respecting  their  extent 
and  limits,  they  arc  always  freely,  and  often  arbitrarily,  taken  from  parts 
of  the  ecliptic  adjacent  to,  or  not  far  removed  from,  the  successive  con- 
stellations. jffc 

regards  the  other  point  noticed,  it  is,  indeed,  not  at  ull  to  Do  won- 
dered at  that  M.  Hiol  should  treat  the  Hindu  nakshatra 9 as  a system, 
bearing  special  relations  to  the  moon,  since,  by  those  who  have  treated 
of  them,  they  have  always  been  styled  “houses  of  the  moon,"  “moon- 
stations,”  “lunar  asterisms, M and  the  like.  Nevertheless,  these  designa- 
tions seem  to  be  founded  only  in  carelessness,  or  in  misapprehension. 
In  the  SOrya-Siddh&uta,  certainly,  there  is  no  hint  to  be  discovered  of 
any  particular  connection  between  them  aud  the  moon,  and  for  this  rea- 
son we  .have  been  careful  never  to  translate  the  term  nak&hatra  by  any 
other  word  thau  simply  44  asterism.”  Nor  docs  the  ease  appear  to  have 
been  otherwise  from  the  beginning.  No  one  of  *ho  general  names  for 
the  astcrisms  ( mkzhatra , bha,  dhishnya)  means  literally  any  tiling^  more 
than  “star”  or  “constellation”:  their  most  ancient  and  usual  appella- 
tion, nakihatra,  is  a word  of  doubtful  etymology  (it  may  be  radically 
. akin  with  nakla,  nox,  **54,  “night”),  but  it.  is  not  infrequently  met  with 
lit a the  Vedic  writings,  with  the  geucral  signification  of  “star,”*  or 
; 41  group  of  atan” : the  moon  is  several  times  designated  a* “sovereign 
>ior  the  nakthatra*”  but  evidently  in  no  other  sense  than  that  in  w^eh 


we  stylo  her  11  queen  of  night'’ ; for  the  same  title  is  in  other*  passages 
given  to  the  sun,  and  even  also  to  the  Milky  . Way.  When  the  name 
came  to  be  especially  applied  to  the  system  of  zodiacal  asterisms,  we 
have  seen  above  that  a single  one  of  the  series,  the  6th,  was  placed  un- 
der the  regency  of  the  moon,  as  another,  the  13th,  under  that  of  the 
'sun  : this,  too,  by  no  means  looks  as  if  the  whole  design  of  the  system 
was  to  mark  the  moon’s  daily  motions.  Naturally  enough,  since  the 
moon  is  the  most  conspicuous  of  the  nightly  luminaries,  and  her  revolu- 
tions more  rapid  and  far  more  important  than  those  of  the  others,  the 
astcrisins  would  practically  be  brought  into  much  more  frequent  use  in 
connection  with  her  movement** : tlu*ir  number,  likewise,  being  nearly 
accordant  with  the  number  of  days  of  her  sidereal  revolution,  could  not 
but  tempt  those  who  thus  employed  them  to  set  up  an  artificial  relation 
between  the  two.  lienee  the  Arabs  distinctly  call  tlieif  divisions  of  the 
zodiac,' ami  the  constellations  which  mark  them,  “houses of  the  moon,!1' 
and,  until  the  researches  of  M.  J>iolt  no  one,  so  far  as  wo  are  aware,  had 
ever  questioned  that  the  number  of  the  aslcriMiis  or  mansions,  wherever 1 
found,  was  derived  from  and  dependent  on  that  of  the  days  in  the 
moon's  revolution.  It  was  most  natural,  then,  that  Western  scholars, 
having  first  made  acquaintance  with  the  Arab  system,  should,  on  finding 
tli0  same  in  India,  call  it  by  the  same  name:  nor  is  it  very  strange,  oven, 
that  Idcler  should  have  gone  a step  farther,  and  applied  the  familiar  title 
of  “lunar  stations"  to  the  Chimse  bit- ft  also;  an  error  for  which  he  is 
sharply  criticised  by  il.  lJiot  (.Imini.  d.  Sa\„  l'CiO,  p.  4*0).  The  latter 
cites  from  al-Hirujii  Mourn.  •!.  Sav.  JHO,  p.  Ill;  Ih.V.i,  pp.  1*7-8)  two 
passages  derived  by  liim  from  Varaha-mihira  aiul  lirahningiipLa  respect- 
ively, in  which  are  recorded  attempts  to  *s1»l »ndi  a systematic  relation 
between  the  a.**ti-risms  ami  the  inooiiV  true  and  mean  daily  motions. 
One  of  tiio-se  jiasftige-  is  exceedingly  ol-*<,ure.  and  both  are  irrceoneila- 
blc  with  one  another,  ami  with  what  we  kimw  of  1 lie;  s\sr.em  of  a«tcr- 
ism*  from  other  sources:  two  ri»m;liMi>ii',  !io\\e\er,  bearing  .upon  t lie 
presenj^fiattcr,  are  clearly  derixable  from  them  : tirst.  that,  as  the  “por- 
tions" assigned  to  the  sisterMii**  li;nl  no  natural  ami  fixed  limits,  it  was 
possible  for  any  Hindu  system-maker  hi  to  define  them  a**  to  bring  them 
into  a connection  with  the  momi's  d.vlv  motions:  and  secondly^  that 
such  a connection  was  never  deemed  an  cnemial  feature  of  the  system, 
and  lienee  no  one  form  of  it  was  generally  recognized  and  accepted. 
The  considerations  adduced  by  above  are,  we  think,  fully  sufKcicnt  to 
account  for  any  such  isolated  attempts  at  tlie  establishment  of  a con- 
nection as  al-Itfruni,  who  naturally  sought  to  find  in  the  Hindu  nakvha- 
tras  the  correlatives  of  Ills  own  man  fail  alkamar,  was  able  to  discover 
among  the  works  of  Hindu  astronomers  : there  is  no  good  reason  why 
we  should  deprive  the  former  of  their  true  character,  which  is  that  of 
zodiacal  constellations,  rudely  marking  out  divisions  of  the  ecliptic,  and 
employable  for  all  the  purposes  for  which  such  a division  is  demanded. 

The  reason  of  the  variation  in  the  number  of  the  astcriams,  which  are 
reckoned  now  Da  twenty-eight  and  now  os  twenty-seven,  is  a point  of  no 

a l difficulty  in  the  history  of  the  system.  M.  Hiot  makes  the  acute 
estion  that  the  omission  of  Abhijit  from  the  series  took  jSTace  be-. 
5 the  mansion  belonging  to  that  asterism  was  on  the  point  of  becoth- 


' , ftwalatum-and  tfotea.  ' 209 

ing  extiftgffiahed,  the  circloflifrf  declination  of  its  jnnction-sttttobcing 
brought  of  the  precessior^bo  a coincidence  with  that  of  the  juncfffii-star 
of  the  preceding  ‘astcrism  about  A.D.  072.  Bnt  it  has  been  shown 
above  that  M.  Biot's  view  of  the  nature  of  a nakskatra — that  it  is, 
namely*  the  arc  of  the  ecliptic  intercepted  between  the  circles  of.  declinar 
lion  of  two  successive  junction-stars — is  altogether  erroneous:  hoVcvcr 
nearly  those  circles  might  approach  one  another,  there  would  still  be  no 
difficulty  in  assigning  to  each  astcrism  its  “ portion”  from  the  neighbor*  1 
ing  region  of  the  ecliptic.  Again,  this  explanation  would  not  account; 
for  the  early  dale,  of  the  omission  of  Abhijit,  which,  as  already  noticed, 
is  found  wanting  in  one  of  the  most  ancient  lists,  that  of  the  T&ittirfya- 
SanhitA  It  is  to  be  observed,  moreover,  that  il.  Biot,  in  calculating  the 
period  of  Abhijit’s  disappearance,  lias  adopted  t Sagittarii  as  the  junc^ 
tion-stnr  of  Utt&ra- Asha  dim,  while  we  have  shown  above  that  <r,  and 
not  t,4b  to  be  so  regarded  : and  this  substitution  would  defer  until  sev- 
eral centuries  later  the.  date  of  mim-idem  c of  the  two  circles  of  declinar 
tion.  According  to  the  Hindu  nicaMiii'eu.ents,  indeed  (see  the  table. of 
positions  of  the  junction-stars,  near  tin;  beginning  of  this  note),  Abhijit 
is  farther  removed  from  tin*  preceding  astcrism,  both  in  polar  longitude 
and  in  right  ascension,  than  are  tile  of  the  other  aster  isms  from  their 
respective  predecessors : nor  does  the  llim hi  astronomical  system  ae- 
knowledgc  or  make  allowaiiee  for  the  alteration  of  position  of  iho .circlet 
of  declination  under  the  influence  of  the  pivi-i  ^iuii : their  places,  as 
data  for  the  calculation  of  r«  injunction*,  are  ostensibly  laid  down  for  all 
future  time.  For  tb«kM!  various  n^ons,  M.  Biot's  explanation  is  to  be 
rejected  ih  iusuflieiiMit.  A more  salisfaetorv  one.  in  our  opinion,  may  ■ 
be  found  in  the  la>-t.  illustrated  above  (nlc  Fig.  31,  beginning  of  this 
note),  that  the  asteri-ins  are  in  general  *«•  di.-tributed  as  to  accord  quite 
well  with  a division  of  the.  ecliptic  into  twvntv-suv cn  ctpial  portions, 
but  not  with  a divi>ion  into  twenty-eight  equal  portions;  that  the 
region  where  they  are  too  nuu  li  crowded  together  is  that  from  the  20tb 
to  the  23rd  astcrism,  and  that,  among  ilnw1  >ituated  in  this  crowded 
quarter,  Abhijit  is  farthest  removed  from  the  ecliptic,  and  so  is  more 
easily  left  out  than  any  of  the  others,  in  dividing  the  ecliptic  into  por- 
tions. We  cannot  consider  it  ai  all  doubtful  that  Abhijit  is  as  originally 
nnd  truly  a part  of  the  system  of  usterisms  as  nnv  other  constellation 
in  the  scries,  which  is  properly  composed  uf  twenty-eight  members,  and 
not  of  twenty-seven  : the  analogy  of  the  other  systems,  mid  the  fact 
that  treatises  like  this  Siddlumta,  which  reckon  only  twenty-seven  divi- 
sions of  the  ecliptic,  are  yet  obliged,  in  treating  of  the  aslcriams  as  con- 
stellations, to  regard  them  as  twenty-eight,  are  conclusive  upon  this 
poiqt.  The  whole  difficulty  and  source  of  discordance  «ecms  to  lie  in 
this — how  shall  there,  in  any  systematic  metlmd  of  division  of  the  eclip- 
tic, be  found  a place  and  a poriion  for  a twenty -eighth  astcrism?  Hie 
' Khanda-Kutakii,  os  cited  bv  al-Bir&ni — in  making  oat,  by  ft  method 
which  is  altogether  irrespective  of  the  actual  positions  of  the  asterisins 
with  reference  to  the  zodiac,  the  accordance  already  referred  to  between 
their  portions  and  the  moon’s  daily  motions — allots  to  Abhijit  bo  nedttdi. 
of  the  tfcliptic  as  is  equivalent  to  the  mean  motion  of  the  moon  dating 
the  part  of  a day  by  which  her  revolution  exceeds  twenty-seven  days.. 


OtfeMaridW  it  a ahare  in  the  proper  poifpns  of  tire  two' 

j1  ' ^ »r..LA_i_  mu  _ l-x 


asternpft : thus  the  MuhArta-MAlA,  a late  wo 
*fcays : 11  the  last  quarter  of  Uttara-Ash&dhA^ 

Qravana  together  constitute  Abhijit:  it  is  so  to  be  accounted,  when;i 


ode,  of  date  u«®idwn  ta:o£^ 
A and  the  first  fifteeutjl;^^ 


.twenty-eight  asterisms  arc  reckoned  ; not  otherwise."  Ordinarily,  how* 
.^6ver,  the. division  of  the  ecliptic  into  twenty-seven  equal  “ portions”  is 
/made,  and  Abhijit  is  simply  passed  by  in  their  distribution.  After  the' 
^introduction  of  the  modern  method  of  dividing  the  circle  intoJdegreea1 

« minutes,  this  last  way  of  settling  the  difficulty  would  obviously  re* 
o a powerful  support,  ami  an  increased  currency,  from  the  fact  that  *. 
|e  division  by  twenty-seven  gave  each  portion  an  evon  number  of  min-  \ 
"b tea,  800,  while  a division  by  twenty-eight  yielded  the  awkward  and 
unmaiiegeablc  quotient  7 7 1 £ . 

t*  yet  remains  to  be  done,  before  the  history  and  use  of  the  .sys- 
^isterisins,  as  a part  of  the  ancient  Jlindu  astronomy  aadqjpFtrol- 
11  be  fully  understood.  There  is  in  existence  an  abundantlitei1- 
ancient  and  modern,  upon  the  subject,  which  will  doubtless  at  . 
fee  time  provoke  laborious  investigation,  and  repay  it  with  interesting 
Jpnlts.  To  us  hardly  any  of  that  literature  is  Accessible,  and  only  the  ‘ 

■ results  of  wide-extended  and  long-eon  tin  ued  studies  upon  it  cuuld 
1. place  here.  We  have  already  allotted  to  the  Mifahatras  more 
jyt)ian  to  some  may  seem  advisable:  ourexeusc  must  he  the  iu- 
^Stf.the  history  of  the  system,  as  part  of  the  ancient  history  of 
f and  spread  of  astronomical  science ; the  importance  attaching 
*$othe  researches  of  M.  Itiot,  the  inadequate  attcqjtion  hitherto  paid 
ttthfrfe,and  the  recent  renewal  of  their  discussion  in  the  Journal  dea  8a- 
prauts;  and  finally  and  especially,  the  fact  that  in  and  with  the  asterisms 
bound  up  the  whole  history  of  Hindu  astronomy,  prior  to  its  trans- 
'.^ypnatioTL  under  the  overpowering  influence  of  western  science.  In  the 
‘ modern  astronomy  of  India,  the  nakshatras  are  of  subordinate  conse- 
quence only,  and  appear  as  hardly  more  than  reminiscences  of  a former 
OtdjMTof  filings : from  the  Surva-Siddhanta  might  be  struck  out  every 
preferring  to  them,  without  serious  alteration  of  the  character  of  the 

_ \ bringing  this  note  to  a close,  v e present,  in  the  annexed  table, 

^homparison  of  the  true  longitudes  and  latitudes  of  the  junction-stars 
tfdtbe  jtaj  enty-eiglit  asterisms,  as  derived  b\  calculation  lVorn  the  posi- 
ixw  &m  uur  tcxt>  w»th  the  actual  longitudes  and  latitudes  of  that 
stare  wjwi'wriiich  they  are  probably  to  lm  identified.  In  a single  case, . 
(the  2ffh  asterism),  we  compare  the  longitude  of  one  star  and  the  lati- 
tude of  another ; the  reason  of  this  is  explained  above,  in  connection 
with  the  identification  of  the  asterism.  We  add  columns  giving  the 
errors  of  . the  Hindu  determinations  of  position  : iu  that  for  the  latitude 
north  djh^tion  itrqgafdcd  as  positive,  and  south  direction  as  negative. 

IJ  y>on  e^^imogpbjB  column  of  errors  of  latitude  presented  in  this  >. 
table,  hgjjfolirthat  they  are  too  considerable,  and^oo  irregular, 

..Jjjotli  in  fed  in  direction,  to  be  plausibly  Accounted  for  other  . 

n as  direct  errors  of  observation  and  calcurfttion.  The  j 

> aa  baa  already  hew  pointed  out,  are  ctffcmHAgd  in  jthe  i 


southern] 


: of  eonsiderabb  amdimVind  theyj 


' 211 

■'Ernrt  if  Petition,  of  the  Junction-Start  offhe  AttiritHti: 
Loagltnd f5L  I).  .500.  Latitude.  ~ f ’ , ' 

mo..  I ! Hindu  . i _ i Hlnila  SUi  MAPfni 


Hindu.  Tree.  j ,IIb4b 
error. 


■*  Afvinl, 
ft  Bfertf  !, 

3 KrttikA, 

4 RoMfli, 

5 iftgtfinhM, 

6 Ardid, 

■7  Pun  arrow, 

8 Pushya, 

9 AfMiA, 

10  MagliA, 

it  P.-Phalgnnf,  1139  j 

12  U.-Phalguni, 

13  Husta,  >174  : 

14  CilrA,  -i 80  , 

15  SrAti,  ;i83 

t6  VifAkhA,  ’ |2 1 3 . 

17  AnurAdhA,  1374  , 

18  JyeahthA,  ja3n 

19  Mdla,  la4a 

20  P.-AshAdhA,  .254 

11  U.-AshAdhA,  '2Go 

» Abhijit,  |a64 

a3  (Jravuna,  282 

a4  fravishthA,  (296 

a5  (atabhishaj,  319 

26  P.-BhAdrapadA,  334 

27  U.-BhAtfrapaclA,  34? 

28  Hcvatl,  359 


[57]  9 1 1 N. 
1 1911  6 “ 

) 5ol  4 44  u 
r 36  4 49  8. 
*3-7  9 49  “ 

1 53  8 53  “ 
>22  6 oN\ 
t 42  o o 
i 21  6 56  8. 
14900 

1711  19N 
[27  12  5 41 
> 55  10  6 8. 
J 1 i 1 5o  11 
i io'33  5o  NT. 
1 3ij  1 2 5 S. 
>10;  2 5a  11 
j 2!  3 5>» 11 
r 4i-  « 48  “ 

■>  5 28 11 

1 58'  4 r>9  “ 
i 5 69  58  N. 
» 48  29  54 
1 r4  35  Ji  “ 

1 43,  c jS  8. 
1 58  22  N- 
1 52!2  J 1 “ 


! 8 28  N. 
1 1 17  14 
4 1 “ 
j 5 3o  S. 
i3  a5  44 
16  4 "■ 
639N. 

0 4“ 

11  8 8. 
| 027N. 
'i4  19  11 

12  17  44 

12  IO  8- 
2 2 14 

30  r.7  N. 
. 1 48  8. 

1 57  4k 

4 3i  “ 

1 3 44  “ 
6 25  11 
3 24  41 

61  46 X. 
29  19  44 

31  77  - 
•j  23  S 
19  25  N 
ari  4i  “ 

' o 1 3 S 


+ o 43  3 Arietta. 

| — o 1 1 1 85  ArifltifcftMoscai 
1 + o 43  7 TfturCalcymufc/ 
■■  + <»  4i  a Tiiari,  Aldetl&K. 
! + 3 36  * Orionfa.  ■ TfSl 
■!  + 7 1 1|*  Oribnifc' « 
. - o 39 1 3 Gcmin.,  PSuax.  ” 
j-o  4j8  Cancri.  ■ . 

■|  + 4 12U  Hydrw.^- 

; - 3 o‘5  Lconi^^p^J^'*  j 

- +2  4;5  Corvi. 

: + o 1 2 jo  Virginia,  Spiffffi 
. + 2 53  a Bootis,  ArctQnts. 

. +oi3i  Libre. 

' - o 55  S ScorpionUt 
+ o 4 1 a Scorp.,  AfHHlLA 
f-  4 56  x Scorpiqttpu^^^ 
+ o 5-»  6 SagituiSfi.  . 

- 1 25  a Sugittaro.' 

. - 1 43  o Lyre,  Yejflk 
+ 6 35  a Aquile,  Atair.  .-4 
+ 3 36 .3  DvlpMoi.  *4 
. - o 5 a.  Aquiirii. 

. + 3 5 a Pegasi. 

- 1 4f»  y Peg.  A a AndriftL 
..  i-  o i3  i Piscium. 


all  in  the  name  direction,  giving  the  star  a place  too  far  to  the  north*. 
The  column  of  errors  in  longitude,  on  the  other  hand,  shows  a 
marked  preponderance  of  minus  errors,  their  sum  being  33°  54'f  srfftte 
the  sum  of  plus  errors  is  only  7°  5V!'.  Upon  taking  the  diflwedeie  of 
these  sums,  and  dividing  it.  by  twenty-eight,  we  find  the  average'  etror 
of  longitude  to  be  -50',  the  greatest  deviation  from  it  in  citherfriirect&on 
being  -2°  4'  and  + 3°  2V1.*  So  far  ns  this  goes,  it  would  iuAoato  that 
the  Hindu  measurements  of  position  wrerc  made  from  a verbal  equinox 
situated  about  1°  to  the  eastward  of  that  of  A.  1).  560,  and  so  at  a time 
seventy  years  previous  to  the  date  we  have  assumed  for  them,  or  about 
A.D.  490.  In  our  present  ignorance  of  the  methods  of  observation 


ft  In  a comparison  in  which  a high  degree  of  exactness  was  desired,  and  was  not, 
in  the  nature  qf  the  case,  unattainable,  it  would  of  course  bftJMtassftty  to.  take  into 
account  the  proper  motions  of  the  stars  compared.  This  wt.Mvft  wit"  thought  it 
V«rih  while,  in  the  prawnt  instance,  to  do.  We  may  the 

ibnctU'ii-etar  of  the  15ti  oatcrism,  Arcturus,  has  a much  greater  pripi^.  motion  tlsuA 
any  otiMfeln  the  series  j and  that,  if  this  were  allowed  for,  s«#ordingjti  He  vatal fpt 
jkimmmt  bell aiftiMem.'Roy.  Astr.  Soc^  vol.  xix,  4to,  1881),  tho  Hindu  .Ayf 
MgiUftda  wftSBbeftuninisked  about  88',  bat  that  of 


1 " * ' i'  B j ; 

by  the  Hindu*  for  this  purpose,  such  a determination  of  data 
T canpot,  indeed,  be  relied  upon  os  exact  or  OTiclusive,-  yet  itis  the  beat' 
and  surest  that  we  can  attain.  The  genera  conclusion,  at  any  rate, 
stands  fast,  that  the  positions  of  the  junction-stars  of  the  asterisms  were  1 
filed  not  far  from  the  time  when  the  vernal  equinox  coincided  with  the 
"initial  point  of  the  Hindu  sidereal  sphere,  or  during  the  sixth  ccnturt" 
of  our  era. 

Since,  according  to  the  Hindu  theory,  the  initial  point  of  the  sidereal 
'inhere  is  also,  for  all  time,  the  mean  place  of  the  vernal  equinox, "which 
always  reverts  to  it  after  a lihration  of  27°  in  either  direction  (see  above, 
f iii.  ft— 1 2),  we  are  not  surprised  to  find  the  positions  of  the  asterisms  prfr1 
” inarily  defined  upon  the  supposition  of  their  coincidence.  But  it  is  not 
a little  strange  that  the  effect  of  the  precession  in  altering  the  direction 
of  the  circles  of  declination  drawn  through  the  junction-stars,  and  so  the 
poJpjMgitadw  and  latitudes  of  the  latter,  should  he  made  no  account 

fjjjw,  however,  the  latter  half  of  v.  1 *2,  below,  and  the  note  upon  it), 
that  directions  for  calculating  the  conjunctions  of  the  planets  with 
Asterisms  according  to  their  positions  as  thus  Mated  should  be  given, 
(jry*  14-15),  unaccompanied  l»y  any  hint  I hut  a modification  of  the  data 
“ he  process  would  ever  he.  found  necessary.  This  carelessness  is  per- 
Irtb  be  regarded  as  an  additional  evidence  of  the  small  importance 
lied,  after  the  roei instruct i"ii  of  the  Hindu  astronomy,  to  calcula- 
which  tin1  asterisms  were  concerned:  although  it  also  tends 
strofl^y  to  prove  what  we  have  suggested  above  (note  to  iii.  '.>--12),  that 
>rint1ie  construction  of  the  ilindu  astronomical  system  the  precession  was 
^ignored  altogether.  It  is  to  he  noticed  that  the  two  systems  of  yoqax  (see 
ii.'  65,  and  additional  note  upon  that  passage),  original!}  founded 
upon  actual  conjunctions  with  the  aMmsms  have  been  divorced  from 
Any  real  connection  with  them.  A like  eonsidr- ration  might  restrain  us 
from  accepting  the  determinations  of  position  here  presented  as^thc  host 
results  which  Hindu  observers  and  instruments  were  capable  of  attaining ; 
j-yeCgitt  the  absence,  of  other  of  their  powers,  we  cannot  well  help 
Hog  the  conclusion  that  the  Accuracy  of  a Hindu  observation  is  not 
J relied  on  within  a degree  or  two. 


is  at  the  end  of  Gemini,  and  eighty  degrees  south ; 
and  Jfrgavyadha  is  situated  in  the.  twentieth  degree  of  Gemini; 

11.  llis  latitude  (uikshepa),  reckoned  from  his  point  of  declina- 
tion(a/Miira^io),  is  forty  degrees  south:  Agni  (hutubhuj) and Brali- 
xnabrdaya  arc  in  Taurus,  the  twenty-second  degree; 

12.  And  they  are  removed  in  latitude  ( vik*ltipln\  northward,  ' 
eight  and  thirty  degrees  respectively.  ... 

In  connection  with  the.  more  proper  subject  of  this  chapter  we  also 
have  laid  before  ns,  here  and  in  a subsequent,  passage  (vV.  20-21),  the 
defined  positions  of  a few.  fixed  stars  which  arc  not,  included  in  the  sys- 
tem of  zodiacal  asterisms.  The  definition  is  made  in  (heimic  manner 
i^i  before,  bypolar  longitudes  and  latitudes.  It  iaftrt  ftt  'flM  difficult  ty 
1 J — &>*}'  die  stars  referred  to  in  these  verses ; they  correct  I vnoiu  ted 

Colehrookc,  in  his  article  already  cited  (As.  xjffi Agajfe^.* 

! « Xavis,  or  Canopus,  a star  of  the  first  magaH^q^  mRf  one  of.  |m» 

** 


tiii.  i*»is  : x rmmmmm  umimea  : $ \*  .^15  - 

: ■ Up.  *&.  '■-;■>/*.  ;~£ 

moat  b^Umat  in  thesonthern  heavens.  Its  remote^  southern  podtirifok 
Vo Mf  37°  fragtt  She  pole,  renders  it  invisible  to  an  observer  stationed  much  7 
V to  the  nctfuward  of  the  Iropic  of  Cancer.  Its  Hindu  name  is  that  of 
■ pne  of  the  old  Vedie  rsAit,  or  inspired  sages.  ' The  comparison  of  its 
Vtrue  position  with  that  assigned  it  by  onr  text — which,  in  this  instance, 
does  not  require  to  be  reduced  to  true  longitude  and  latitude*— is  at. 1 
follows: 

Agaotya  ....  900  o'  ...  . 8o°  o'  8. 

& Cunopus  ....  85°  4'  ....  75°  5o'  S. 

The  error  of  position  is  here  very  considerable,  and  the  variations  < 
i other  authorities  from  the  data  of  our  text  arc  correspondingly  great. ^ 
The  Siddh&nta-yiroin&ni  and  (according  to  Colobrookc)  the  Brahma-*’1' 
Siddh&nta  give  Agastya  87°  of  polar  longitude,  and  77°  of  latitude, 
which  is  a fair  approximation  to  the  truth : the  Grab a-LAghavav-alsO 
places  it  correctly  in  lat.  7GJ  S.,  but  makes  its  longitude  only  80®j^ 
is  as  gross  an  error  ns  that  of  the  Surya-Siddhiinta,  but  in  the  opj 
direction.  Tlie  ^akidya-Sanhita  agrees  precisely  with,  our  treatise 
respects  the  positions  of  these  four  stars,  as  it  docs  generally  in 
numerical  data  of  its  astronomical  system. 

Migavyftdhr,  14  dl‘o^-lIUllter,, — it  is  also  called  Lubdhaka,  ■“hunte?1£ 
is  a Cams  Mai  oris,  or  Sinus,  the  brightest  of  the  fixed  stars  : , $ 

Alrs:avyft<lh:i  ....  7G0  a 3'  . . . . 3r/>5a'S. 


Sirius 84°  7' 


ji/j  32'  a. 


Here,  while  all  authorities  agree  with  tlic  correct  determinatio^flf  the -■ 
latitude  of  Sirius  presented  by  our  text,  the  $iddhanta-£iromm^jstc. 
greatly  reduce  its  error  uf  longitude,  bv  giving  the  star  86°,  instead  ofj. 
80°,  of  polar  longitude : the  Graha-L&ghava  reads  81°. 

The  star  named  after  the  god  of  tire,  Agni,  and  called  in  the  text  lfitx 
one  of  his  frequent  epithets,  hutabh/ij , devourer  of  the  sacrifice,”  is  W 
one  which  is  situated  at  the  extremity  of  the  northern  horn  of  theBijtP, 
or  p Tauri:  it  alone  of  tiie  four  is  of  the  second  magnitude  only  : . 

A$ni 34°  5'  ....  70  44'  N. 

ft  Tauri  ....  62°  3a'  ....  5°  22'  N.  =jp>  ■ 

The  very  gross  error  in  the  determination  of  the  longitude  of  Ibis  star 
is  but  slightly  reduced  l»y  the  Graha-Laghava,  which  gives  it  53°,  iititead 
of  52°,  of  polar  longitude.  The  Siddhaiita-£iromani  and  Brabma-Sid- 
djhiEttta  omit  ail  notice  of  any  of  the  fixed  stars  excepting  Canopus  and 
Sirius. 

Brahmahrdaya,  “ Brahma's  heart,”  is  a Aurig&\  or  Capella : 

Brnliinnhrdnyii  ....  6o°  39'  ...  . a83  53'  X. 

Capella tii°  5o'  . . - . 20  5a'  A. 

-The  GraliadU^bava,  leaving  this  erroneous  determination  of  latitude 
unamended,  jdds  a greater  error  of  longitude,  in  the  opposite  direction 
“ giving  the  star  4°  more  of  pobir  longitude. 
m comparisons  in  a tabular  form  a&  tqo  end  of  tjag% 
with  the  other  passage  of  similar import. 

constructed  a sphere,  one  may  examine:l|tt 
Atitude  and  polar  longitude  {<m*uvi tka\  0$ 


to  that  of  dj^Ptext, 
We  shall  present 
. ; chapter,  ip  connect! 


2% 


i^Sbaiis 

( tfjfirdto* 


12— 


S&rya-Siddk&nta, 


tbp  true  meaning  and  scope  of  this  passage,  is  a qntajen  with 

1 • i a! j;ir _ jj  _ _ ■ * fjC  .-T;  r*  ji 


which  there  may  bo  some  difference  of  opiftifcf&^xhc  crftti- 
metitator  explains  it  as  intended  to  satisfy  the  inquiry  whetMhAlu1  polar 
longitudes  and  latitudes,  as  stated  in  the  text,  are  constant  or  whether 
they  are  subject,  to  variation.  Now  although,  he  says,  owing  to  thq 
precession,  the  values  of  these  quantities  arc  not  unalterably  fixed,  yet 
they  are  given  by  the  text  as  they  were  at  its  period,  and  as  if  they  were 
constant,  while  the  Astronomer  is  directed  to  determine  them  for  his  own 
time  by  actual  observation.  For  this  purpose  he  is  to  take  such  a sphere 
as  is  described  below  (chap,  xiii) — of  which  the  principal  parts,  and  tho: 
only  ones  which  would  be  brought  into  use  in  this  process,  are  hoops  or' 
circles  representing  the  column,  the  equator,  and  the  ecliptic — and  is  to 
impend  upon  its  poles  an  additional  movable  circle,  graduated  to  de- 
grees : this  would  be,  of  course,  a revolving  circle  of  declination.  The 
sphere  is  next  to  be.  adjusted  in  such  manner  that  its  axis  shall  point  to 
tie  pole,  and  that  its  horizon  shall  be  water-level.  Then,  in  the  night, 
lie  Junction-star  of  llevali  (X  I’isciuni)  is  to  be.  looked  at  through  a hole 
the  centre  of  the  instrument,  and  the  corresponding  point  of  tho 
Jigjliptic,  which  is  10'  east  of  the  end  of  the  constellation  Pisces,  is  to  be 
ght  over  it;  after  that,  it  will  be  necessary  only  to  bring  the  revolv- 
Ifrcle  of  declination,  as  observed  through  the  hole  in  the  centre  of 
iinicnt,  over  anv  other  star  of  which  it  is  desired  to  determine 
Sion,  and  its  polar  longitude  and  latitude  may  be  read  off'  directly 
lie  ecliptic  and  the  movable  circle  respectively. 

CoWbrooke  (As.  lies.,  ix.  320:  Essays,  ii.  324)  found  this  passage 
similarly  explained  in  other  commentaries  upon  tlic  Sftrya-Siddh&nta  to 
which  he  had  access,  and  also  met  with  like  directions  iu  the  commen- 
taries on  the  Siddhantii-£i roman i. 

■ There  are,  however,  very  serious  objections  to  such  an  interpretation 
of  the  brief  direction  contained  in  the  text.  It  is  altogether  inconsist- 
ent with  the  whole  plan  and  method  of  a Hindu  astronomical  treatise  to 
leave,  and  even  to  order,  matters  nf  this  character  to  be  determined  by 
observation.  Observation  has  no  such  important  place  assigned  to  it  hi 
the  astronomical  sv-tem  : with  tile  except  ion.  of  terrestrial  longitude  and 
latitude,  which,  in  the  nature  of  things,  arc  beyond  the  rcuc.h  of  a trea- 
tise, it  is  intended  that  the  astronomer  tlmuM  find  in  bis  Icxl-book  every- 
thing which  be  needs  for  the  determination  of  celestial  phenomena,  and 
should  resort  to  instruments  and  observation  only  by  way  of  illustration. 
The  sphere  of  which  the  construction  is  prescribed  in  the  thirteenth 
chapter  id  not  an  instrument  for  observation : it  is  expressly  stated  to  lie 
“ for  the  instruction  of  the  pupil,*’  and  it  is  encumbered  with  such  ji 
number  and  variety  of  different  circles,  including  parallels  of  declination 
for  all  the  asterisms  and  for  the  observed  fixed  stars,  that  it  could  not 
be  used  for  any  other  purpose:  it  will  be  noticed,  too,  that  the  com- 
mentary in  itself  obliged  to  order  here  the  addition  of  the  only  Appli- 
ances— the  revolving  circle  of  declination  and  the  hole  through  the  cen- 
tre— which  make  of  it  an  instrument  for  observation.  The  simple,  npd 
original  meaning  of  the  passage  seemsjto  be  that,  having  constructed  a 
■there  in  the  manner  to  be  hereafter, described,  one  may  examine  the 
of  the  aateriyina  as  marked  hj&bn  At,  ancLjipte  their  coincidence 


viiU*3:^ 


Translation  and  Nobs. 


7 if  , ■»  . ■ 

frith  the  actual  positions  of  the  stars  in  the  heavens.  And  we  frofU* 
regard  the  other  interpretation  as  forced  upon  the  passage  by  the  com- 
mentators, to  order  to  avoid  the  difficulty  pointed  out  by  us  above  (near 
the  end  of  the  note  on  the  last  passage  but  one)  and  to  free  the  Sid- 
.dh&nta  from  the  imputation  of  having  neglected  the  p recessional  varia- 
tion of  "the  circles  of  declination.  M.  Biot  pronounces  the  method  of 
observation  explained  by  the  commentators  44  almost  impracticable,” 
and  it  can,  accordingly,  hardly  be  that  by  which  the  positions  of  the  aa- 
terjsms  were  at  first  laid  down,  or  by  wbich  they  could  be  made  to  un- 
dergo the  necessary  corrections.  Another  method,  more  in  accordance 
with  the  rules  and  processes  of  the  third  chapter,  and  which  appears  to 
us  to  be  more  authentic  and  of  higher  value,  is  described  by  Colebrooke 
(as  above)  from  the  Siddhaiita-Sarvahlj&uina,  being  there  cited  from  Aft 
Siddh&nta-Sundara ; it  is  as  follows : 

44  A tube,  adapted  to  the  summit  of  the  gnomon,  is  directed  toward 
the  star  on  the  meridian  : and  the  line  of  the  tube,  pointed  to  the  star, 
is  prolonged  by  a thread  to  tlic  ground.  The  line  from  the  summit 
the  gnomon  to  the  base  is  the  hypothenusc ; the  height  of  tlic  gnomox^ 
is  the  perpendicular  ; and  its  distance  from  the  extremity  of  the  thread? 
is  the  base  of  the  triangle.  Therefore,  as  the  hypothenusc  is  to  its 
so  iB  the  rudins  to  a base,  from  which  the  sine  of  the  angle, 'and  c£w*‘- 
quently  the  angle  itself,  are  known.  If  it  exceed  tlic  latitude 
place  of  observation  |,  tlic  declination  is  south  ; or,  if  the  contra^Jl^r 


north.  The  right,  ascension-  *»f  the  star  is  calculated  from  the  l|fp|L of 
night,  and  from  the  right  :lm  cn*iun  of  the  sun  for  that  time.  Th#«pi- 
nation  of  the  corresponding  point  of  the  ecliptic  being  found,  the  'itun 
or  difference  of  the  declinations,  according  ;»s  the)  are  of  the  same  or  of  • 
different  denomination?*,  U the  distance  of  the  star  from  the  ecliptic.  The 
longitude  of  the  same  point  is  computed  ; and  from  these  elements,  with 
the  actual  precession  of  the  equinox,  may  be  calculated  the  true  longi- 
tude of  the  star;  as  also  its  latitude  on  a circle  passing  through  the  polos 
of  the  ecliptic.” 

The  Siddh&nlu-Sarvabluiuma  also  gives  the  true  longitudes  and  lati- 
tudes of  tlic  aMcrisms,  professedly  as  thus*  obtained  by  observation  ana 
calculation,  and  they  are  reported  by  Colebrooke  in  his  general  table  of 
data  respecting  the  astorism-. 

If  we  arc  not  uii>1akcu,  the  amount  and  character  of  the  errors  in  the 
stated  latitudes  of  the  astcrisms  tend  to  prove  that  this,  or  some  kindred 
process,  was  that  Jby  which  their  positions  were  actually  determined. 

13.  In  Taurus,  the  seventeenth  degree,  a planet  of  which  the 
latitude  is  a little  more  than  two  degrees,  <outh,  will  split  the 
wain  of  llohii.ii. 


The  osterism  Roliini,  as  has  been  seen  above,  is  composed  of  the  live 
principal  stars  in  the  head  of  Taurus,  in  the  constellation  of  which  is 
seen  the  figflA  of  a wain.  The  divinity  is  Praj&pati..  The  distances  of 
its  atari'  in  longitude  from  the  initial  point  of  the  sphere  vary  from  45° 
40'  (y)  to  49°  45' (a):  hence  the  seventeenth  degree  of  the  second 
sign — the  reckoning  commencing  at  the  initial  point  of  the  sphere,  taken, 
•as  coinciding  also  with  the  vernal  equinox — is  very  nearly  the  middle^Qif 


s\  ■ 1 ■■  1 1 " - - «*  ‘ 

iTOfcwaiiu  The  latitude  of  its  stare,  again?  varies  from  2°  36'  (a)  to  5*  , 
hence,  to  come  into  collision  with,  or  to  enter,  the  wain,  a ; 
.planet  mast  have  more  than  two  degrees  of  south  latitude.  The  Sid- 
dh&nta  does  not  inform  us  what  would  be  the  consequences  of  soph  an 
bceurfence ; that  belongs  rather  to  the  domain  of  astrology  than  of  ^ 
tronomy.  We  cite  from  the  Paficatantra  (vv.  238-241)  the  following* 
description  of  these  consequences,  derived  from  the  astrological  writings  . 
of  Varkha-mihira:* 


“When  Saturn  splits  the  wain  of  Robin!  here  in  the  world, then 
M&dhava  rains  not  upon  the  earth  for  twelve  years. 

11  When  the  wain  of  Prajapati’s  asterism  is  split,  the  earth,  having 
as  it  were  committed  a sin,  performs,  in  a manner,  her  surface  being 
strewn  with  ashes  and  bones,  the  k&palika  penance.  '* 

1 u If  Saturn,.  Mars,  or  the  descending  node  splits  the  wain  of  Rqhigt, 
why  need  I sav  that,  in  a sen  of  misfortune,  destruction  befalls  the  world  I 
41  When  the  moon  is  stationed  in  the  urid«t  of  Kohinl’s  wain,  then 
men  wander  recklessly  about,  deprived  of  shelter,  eating  the  cooked 
■jrjBesh  of  children,  drinking  water  from  vessels  burnt  by  the  sun” 

^JJpon  what  conception  this  curious  feature  of  the  ancient  Hindu  as- 
^ founded,  we  arc  entirely  ignorant. 

|g?JL4.  Calculate,  as  in  the  case  of  tlic  planets,  the  clay  and  night 
IW'the  asterisms,  and  perforin  the  operation  for  apparent  longi- 
tude (dfkkarman)}  as  before : the  rest  is  bv  the  rules  for  the  con- 
junction (mclalca)  of  planets,  using  the  daily  motion  of  the  planet 
as  a divisor:  the  same  is  the  case  as  regards  the  time. 

.'15.  When  the  longitude  of  the  planet,  is  less  than  the  polar  . 
longitude  (« dhruvalca ) of  the  asterism,  the  conjunction  {yoga)  is  to 
come ; when  greater,  it  is  past : when  the  planet  is  retrograding 
(vakragati),  the  contrary  is  to  be  recognized  as  true  of  the  con- 
junction (samdgama). 


^ The  rules  given  in  the  preceding  chapter  for  calculating  the  conjunc- 
tion of  two  planets  with  one  another  apply,  of  course,  with  certain  mod- 
ification^ to  the  calculation  of  the  conjunctions  of  the  planets  with  the 
aateriama.  The  text,  however,  omits  to  specify  the  most  important  of 
these  modifications — that,  namely,  in  determining  the  apparent  longi- 
tude of  an  asterism,  one  part  of  the  process  prescribed  in  the  ease  of  $ 
planet,  the  ayanadrkkarmaa , or  correction  for  ecliptic  deviation,  is  to  be 
omitted  altogether;  since  the  polar  longitude  of  the  asterism,  which  is 

S’ven,  corresponds  in  character  with  the  ay  ana  graha , or  longitude  of 
e planet  as  affected  by  ecliptic  deviation,  which  must  be  ascertained 
by  tne  ayanadrkkarman.  The  commentary  notices  the  omission,  bat 
offers  neither  explanation  nor  excuse  for  it.  The  other  essential  raodifi- 
. cation — thftt,  the  asterism  being  fixed,  the  motion  of  the  planet  alone  is 


# Our  translation  represents  the  verses  as  amended  .in  their  readinge  by  Benfey 
(Vtytfeehatantra  eta.  2r  Theil,  no.  284-287).  In  the  third  of  the  verses,  however, 
Aejjgadiog  of  the  published  text,  fmfi,  “ moon,”  would  seem  decidedly  preferable  to 
3mkkLl “ descending  node”:  since  the  node,  being  always -.neefiearily  » the  ecliptic, 
some  into  eollieion with  Robins  wmbl  ' ^ *' 


VuLltfJ* 

to  be  arid  ap  divisor  in  determining  the  piece  end  time  of  I 
tion — is  duly  noticed.  ^ ; 

.The  iqpccurocies  in  the  Hindu  process  for  determining  f^xiueent  fon- 
gitadesj-which,  as  above  noticed,  are  kept  within  bounds,- wheye  the 
plgpetsalone  are  concerned,  by  the  small  amount  of  their ' latitudes,  - 
* would-  be  liable  in  the  case  of  many  of  the  astcrisms  to  lead  to  gravrer- 
rors  of  result. 

18.  Of  the  .two  Phalgunis,  the  two  Bhadrapadas,  and  likewise, 
the  two  Ashadhas,  of  Viyakha,  Agvini,  and  MrgagTrsha  ($&tpnycfy 
the  junction-star  (yogat&va)  is  stated  to  be  the  northe^i  (of 

17.  That  which  is  the  western  northern  star,  being  th*H| 
situated  westward,  that  is  the  junction-star  of  Hasfta;  ** 
yishthfi  it  is  the  western : 

Of  Jyeshthu,  £ravana,  Anuradlui  ( maitrd ),  and  Pushyfi 
( [bdrhaspatya),  it  is  the  middle  star : of  Bharai.ii,  Krttika  (dgneya)h. 
and  Magha  ( pitryd ),  and  likewise  of  itevntf,  it  is  the  southern: 

19.  Of  Roll iri i,  Punarvaau  ((Mitya),  audllula,  it  is  the  eastern^ 

and  so  ahtffeof  Aglcsha  (.s arjia)  : in  the  case  of  each  of  the  otheflfc 
the  juncti<m-siar  (yogalaraku)  is  the  great  (sthula)  one.  ■ \'^Z 

We  have  had  occasion  nboio,  in  treating  of  ll.r  kleftification  of-dfe 
astcrisms,  to  question  tins  accuracy  of  smiie  of  those  designations -ofrtBeK 
relative  position  of  the  junction -stars  in  llic  groups  containing  them.  . 
We  do  not  regard  the  passage  as  having  the  same  authenticity'  and 
authority  with  that  in  which  the  determinations  of  the  polar  longitudes 
and  latitudes  are  given;  and  indeed,  \\v  are  inclined  to  suspect  that  all 
which  follows  the  fifteenth  verse  in  tin*  chapter  may  he  a later  addition 
to  its  original  content.  It  is  difficult  to  see  otherwise  why  the  stated 
ments  given  in  verses  20  and  21  of  the  positions  of  certain  stars  should 
be  separated  from  those  presented  above,  in  verso  10-12.  A designa- 
tion of  the  relative  position  of  Ihe  junction-star  in  each  group  ought  also 
properly  to  be  connected  witli  a definition  of  the  number  of  stars  com~ 
posing  each,  and  a description  of  its  configuration — sueh  as  are  presented 
along  with  it  by  other  treatises,  ns  the  (^iikalva-Snnhita.  The  first  is  even 
in  sonic  points  ambiguous  unless  accompanied  by  the  others,  since  there 
are  cases  in  which  the  same  star  lias  a different,  position  in  its  asterism 
;-l#ccordiug  as  the  hitter  is  to  be  regarded  as  including  a less  or  a greater 
number  of  stars.  In  this  respect  also,  then,  the  passage  looks  like  a dis- 
connected fragment.  Nor  is  the  method  of  designation  so  clear  and 
systematic  as  to  inspire-  us  with  confidence  in  its  accuracy.  Upon  a 
consideration  of  the  whole  series  of  astcrisms,  it  is  obvious  that  the 
. brightest  member  of  each  group  is  generally  sclered  as  its  junctiotf-star. 
Hence  wc  should  expect  to  find  a general  rule  t-o  that  effect  laid-  down, 
and  then  the  exceptions  to  it  specially  noted,  together  with  ihe  cnee  in 
which  such  a designation  would  be  equivocal.  Instead  of  this,  we. have 
the  ju action-stars  of  only  two  astcrisms  containing  more  than,  one  star, 
namely  Abhijit  and  ^atabliishaj,  described  by  their  'superior  brilliapcy, 
while  that  of  the  former  is  not  less  capable  of  being  pointed  out  by  its 
position  than  are  any  of  the  others  in  the  seriea.  Again,  there  are  ^es 


23,8.  v Silrya-Siddh&fita,  / [vitt.lfc- 

. in  which  it  is  questionable  which  star  is  meant  to  be  pointed  out  in  4 
group  of  which  the  constitution  is  not  doubtful,  owing  to  the  very  near 
correspondence  of  more  than  011c  star  with  the  position  as  defined.  And 
once  more;  where,  in  a single  instance,  a special  effort  has  apparently  ' 
been  made  to  fix  the  position  of  the  junction-star  beyond  all  doubt  or 
cavil,  the  result  is  a failure ; for  it  still  remains  a matter  of  dispute  how 
the  description  is  to  be  understood,  and  which  member  of  the  group  is 
intended.  The  case  referred  to  is  that  of  llastn,  which  occupies  nearly 
all  of  verse  If.  That  Colcbrooke  was  not  satisfied  as  to  the  meaning  of 
the  description  is  clear  from  the  fact  that  lie  specifics,  as  the  star  referred 
to,  “)'  or  o (jjprvi.”  Ilis  translation  of  the  verse,  “ 2nd  \V.  of  1st  N.  W % 
conveys  to  us  no  intelligible  meaning  whatever,  as  applied  to  the  actual 
group.  He  evidently  'understood  porcimottaratdrayd  as  a single  word,' 
standing  by  euphony  for  -tardy  its,  ablative  of  -tdrd.  Our  own  render* 
ing  supposes  it  divided  into  the  two  independent  words  papcifijptia- 
ratdrd  yd , or  the  three  paccimu  uttarutdrd  yd.  This  interpretation!^  in 
^the  first  place,  supported  by  the  corresponding  passage  in  the  y&kalyap 
* SanhiUi,  which  reads,  “of  llasta.  the  north-western  ( rayavi ):  it  is  also 
the  second  western.17  Again,  it  applies  without  dilliculty  to  one  of  the 
etarain  the  group,  namely  to  y,  which  we  think  most  lik®t  be  tlie 
outpointed  out — and  mainly,  because  either  of  the  others  would  tidmit 
of  being  more  sift  ply  and  brielly  designated,  d a>  the  northern;  P as  thc- 
&fe&stern,  a as  the  southern,  and  r a*  tin*  western  star.  We  should,  then, 
■regard  the  description  as  imainhigiioiis.  were  it  not  for  what  is  farther 
added,  “ being  the  second  siti'at*  d westward for  y is  tlie  first  or  most 
westerly  of  the  five  in  longitude,  ami  tin;  third  in  right  ascension,  while 
the  second  iir longitude  and  in  right  ascension  respectively  arc  the  two 
faint  stars  and  n.  We  confess  that  we  do  not  sec  liow  the  difficulty  is 
to  be  solved  without  some  emendalioii  of  the  text. 

We  conceive  ourselves  to  bo  justified,  then,  in  regarding  this  passage 
as  of  doubtful  authenticity  ami  inferior  authority:  as  already  partaking, 
in  short,  of  that  ignorance  and  f urelessiu-*-*  which  lias  rendered  the 
Hindu  astronomers  unable,  at  any  time  during  tlie.  p\st  thousand  years, 
to  point  out  in  the  heavens  the  nmiplcif  series  of  the  groups  of  stars 
composing  their  system  of  usterisms.  X«um  of  the  other  authorities 
accessible  to  us  gives  a description  «»f  the  reiatisc  places  of  the  junction- 
stars,  excepting  the  (^aknlya-Sanhita,  and  «>ur  manuscript,  of  its  text  is 
so  defective  and  corrupt  at  this  point  that  we  arc  able  to  derive  from  it, 
with  confidence  the  positions  of  only  about  a third  of  the  stars.  ■■  So 
far,  it  accords  with  the  S&rya-Siddliuiita,  save  that  it  points  out  as  the 
junction-star  of  Purva-Asldullik  the  brightest,  instead  of  the  northern- 
most, member  of  the  group ; and  here  tin-re  is  a difference  in  the  mode  of 
designation  only,  and  not  a disagreement  as  regards  the  star  designated. 

20.  Situated  five  degrees  eastward  from  Brahmalirdaya  is  Pra- 
jfipatl : it  is  at  the  end  of  Taurus,  and  thirty-eight  degrees  north. 

21.  Apfimvatsa  is  five  degrees  north  from  CitrS : somewhat 
greater  than  if^  as  also  six  degrees  to*the  north  of  it,  is;  Apas. 

The  three  stars  whose  positions  are  defined  in  thh  passage  arc  not 
meggianed  in  the  ^&kulya-Saubit&,  nor  in  the  Siddhhuta-Qiiomani  and 


219 


tilL'  21  Trandai ion  and  Notes, 

Recording  tor  Colebrookc)  the  Brahma-Siddh&nta ; only  th*  latter  of 
them,  Apas,  is  omitted  by  the  Gralm-Laghava,  being  noticed  in  the 
SftryarSiddh&nta  alone.  It  may  fairly  be  questioned,  for  mMeasovt  re- 
marked above,  whether  the  original  text  of  our  treatise  itselff contained 
the  last  two  verses  of  this  chapter : moreover,  at  the*  end  of-  the  next 
chapter  (ix.  18),  where  those  stars  are  spoken  of  which  never  set  heli- 
acally,  on  account  of  their  high  northern  situation,  ITaj&pati  is  wt 
mentioned  among  them,  as  it  ought  to  he,  if  its  position  had  been  pb-  * 
viously  stated  in  tin*,  treatise.  Still  farther  on  (xiii.  9),  in  the  descrip- 
tion of  .the  arniillarv  sphere,  it  is  referred  to  hy  the  name  of  Brahma* 
which,  according  to  the  coimnentnr\  on  this  passage,  and  to,jC«debrooke, 
it.  also  customarily  beat's.  Perhaps  another  evidence  of  the  nnauthen- 
tknfty  of  the  passage  is  to  be  seen  in  the  fact  that  the  two  definitions  of  - 
the  polar  longitude  of  l ’rnjapali  do  n«»t,  if  taken  in  cenneetion  with  verso 
11,  appear  to  agree  with  one  another:  a star  which  is  3°  east  from  the 

KSltlon  of  Hrahinalirdava,  as  there  stated,  is  not  “ at  the  end  of  Taurus,” 
t at  its  twenty-seventh  degree  : this  may,  however,  be  merely  an  ina&?  ^ 
curate  expression,  intended  to  mean  that  tin*  star  is  in  the  latter  part,  or 
near  the  end,  of  Taurus.  The  (■rnlui-lAghavu,  which  defines  the  ' posi- 
tion^ ,of  allViese  stars  direel  iy,  by  degrees  of  polar  longitude  and  l&ti- 
fudc^'nnd  not  by  reference  either  to  the  signs  or  to  oilier  stars,  gives  FTa- 
j&pAti  61°  of  polar  longitude,  or  i»°  m-»re  than  it  assigned  to  Brahniabf'* 
data:  it  also  adds  1°  to  the  polar  latitude  as  stated  in  our  text.  Tfe4;|| 
star  referred  to  can  hardly  be  any  other  than  that  in  tlie  head' of  the  ~ 


Wagoner,  or  d Auriga;  ( i) : 

Projitpati  . . . . ir°  u'  . . . . 3G*  49* 

& Auri£.r<!  . . . . (iy3  ri  V . . . . 3o°  49*  JT. 


The  error  of  latitude  i«*  about  the  same  with  that  which  was  commit- 
ted with  reference  to  Hraliitiuhrduyu,  or  Capelin.  Why  so  faint  and  in- 
conspicuous a star  should  be.  found  aiming  the.  few  of  which  the  Ilindn 
astronomers  have  taken  particular  notice  i^  not  easy  to  discover. 

The  portion  of  the  star  named  Apamvatsa,  Waters5  Child,”  is  de- 
scribed in  our  text  by  reference  to  Citra,  or  Spica  Virginia  : it  is  said  to 
bo  in  the  same  longitude,  180°,  and  5°  farther  north;  and  this,  since 
Citr&  itself  is  in  lat.  2°  £.,  would  make  the  latitude  of  Apumvatsa  &°  N. 
The  Graha-Laghava  gives  it  this  latitude  directly,  and  also  makes  its  lon- 

S'tude  agree  with  that  of  Spica,  which,  as  already  noticed,  it  places  at 
e diatanco  of  183°  from  tlie  origin  of  the  sphere.  Apas, 11  Waters” 
(the  commentary,  however,  treats  tlie  word  as  a singular  masculine,  Apa), 
'is  put  6°  north  of  Apamvatsa,  or  in  lat.  9°  N.  It  i*  identified  by  Cole- 
brooke  with  $ Virginia  (3),  and  doubtless  correctly : 

Apas 176°  33'  . . . . 8C  i5'N. 

5 Virginia  ....  1710  28'  ....  8°  38'  If. 

Colcbrooko  pronounces  Apamvatsa  to  comprise  44  the  nebulous  -j^an" 
marked  b 1,  2,  3”  in  Virgo.  ■ We  can  find,  however,  no  sncli  stars  Spoil 
any  map,  or  in  any  catalogue,  accessible  to  us,  and  hence  presume  that 
Colebro-ikc  must  have  been  misled  here  by  some  error  &f  the  authdritv 
on  which  lie  relied.  There  is,  ou  the  other  hand,  a star,  # Virgiuis  (4), 


jdt&Ated  directly  between  Spica  and  d,  and  at  such  a distant*  from  eadfe^ 
’ jBt^b°ws  almost  beyond  question  that  it  is  the  star  intended : 

ApAmviitsa  ....  178°  48'  ....  a*4Sf.N.  ' 

^ i:':  v 9.  Virginia  ....  178°  1 a'  . . . . i°45'!f.  ^ i 

It  i^inot  less  difiieult  in  this  than  in  the  former  case  to  account*lbr  the 
' selection  of  these  stars,  among  the  hundreds  equalling  or  excelling  them 
in^rilliancy,  as  objects  of  special  attention  to  the  astronomical  observers 
WVhcicnt  India.  Perhaps  we  have  here  only  the  scattered  and  dfeQph^ 
^nected  fragments  of  a more  complete  and  shapely  system  of  Stella^ 

' tronomy,  which  flourished  in  India  before  the  scion  title  reconstruct  tanm. 5 
the  Hindu  qjlronomy  transferred  the  field  of  labor  of  the  astronomer^ 
from  the  skies  to  his  text-books  and  his  tables  of  calculation.  ■ 

The  annexed  table  gives  a comparative  view  of  the  positions  of  tne  * 
seven  stars  spoken  of  in  this  and'  a preceding  passage  (vv.  10—12)  j 
defined  by  our  text  and  as  determined  by  modern  ubservers  : 


Positions  of  certain  Fixed  Stars. 
Hindu  position  : True  position: 


■i  1 


1 loilff. 

Itlt. 

long. 

1 1st. 

0 1 

c r 

0 I 

c » 

80  o S ; 90  o 80  o S. 
'4o  o S.i  -6  a 3 39  f«j  s. 

‘ 8 oN.|  r>4  '/  7 4 \S. 
,3o  oNV  (Vi  29  78  03  N.' 
3S  oX.j  '17  ji  3(i  49  N. 

! 1 O _V.;i-8  4«:  5 41*  N. 

, 9 nN.jr'i  a3,  K r>  X. 


8r>  4 71)  5o».;o  Ar 
8.1  7 39  3a  S ;urnniBllaj.B8 
<»?  3a‘  5 j-2  N.'.d  Tauri. 
fn  Go  jjl  5a  V.  a Aurigrc,  Cnpella.j 
*>9  04 3o  49N.18  Aurigrc. 

S Virginia. 

8 Virginia. 


17K  13.  1 45  N. 
i7i  a8  8 38  N. 


Prajap&ti, 

ApOtnvatsa, 

Apes, 

The  gross  errors  in  the.  dctcruiinutiims  of  position  of  thesi*  stars  give 
us  a yet  lower  idea  of  the  r hara'  ter  of  Hindu  observations  than  we 
derived  from  our  examination  of  tin*  jimctioiWars  of  the  ristcrisms. 
f-  The  essay  of  Culobrooke  in  the  ninth  volume  of  the  iVsjatic  Re- 
searches,  to  which  we  have  already  so  often  referred,  fivers  farther  inform 
mation  of  much  interest  resj meeting  such  matters  connected  with  the  Hindu 


performance  of  certain  religious  ceremonies,  lb*,  also  presents  a view; of 
the  Hindu  doctrine  of  the  Seven  Sages,  or  rsh is,  by  which  naiuo.jlre^ . 
known  the  bright  stars  in  Ursa  Major  forming  the  well-known  constella-? 
t ion  of  the  Wain,  or  Dipper.  To  these  stars  the  ancient. astronomers SkV- 
India,  and  many  of  the  modern  upon  their  authority,  have  attributed  #«*’,' 
independent  motion  about  the  pole  of  the  heavens,  at  the  rate  of  8'  yearly^  ’ 
or  of  a complete  revolution  in  2700  years.  The  S&rya-Siddh&nta  alludes^ 
- in  a later  passage  (xiii.  $))  to  the  Sevan  Sages,  but  it  evidently  is '.to  be 
;.*-UndMtooa  as  rejecting  the  thb&ry  of  their  proper  motion,  which  is  also 
)gd|ed  by  the  Siddhanta-^iromani.  That  so  absurd  a dognia  should  . 
; hayg  originated;  and  gained  a general  currency  in  Iudia,  and  that  it  should 
stilpfoiaintaln  itSelf  in  many  of  the  astronomical  text-books,  is,  however, 
top  striking  and  significant  a circumstance  £0  be  left  out  of  sight  in  esli- 
m0tg-the  character  of  the  ancient  and  ii^iye,2$ndu  astronomy. 


221 


CHAPTER  IX. 


V. 


OF  HELICAL  RISINCJ9  AND  SETTINGS. 

Osirrrrw:— 1,  subject  of  the  chapter;  2-3,  unifor  what  circumstances,  and  at  which 
borifoo,  tlw  planets  rise  anJ  set  heliacally ; 4-5,  method  of  calculating  their  dia-  • 
•lancet  in  oblique  naccnaiun  from  the  aun ; 6-tf,  distances  from  the  eun  at 
thpjyjjwappear  nnil  reappear ; 10-11,  how  to  find  the  time  of  heliacal- setting  or 
tbijogj  past  or  to  come ; 12-15,  distanced  from  the  sun  at  which  the  asterismajund^ 
stars  disappear  and  re  appear  ; 10-17,  mexfe  of  determining  their  times  of 
and  setting ; 18,  what  asterisms  anr]  stars  never  set  heliacally. ' 

■;> 

‘1.  Now- is  set  forth  the  knowledge  of  the  risings  (udaya)  and 
settings  (astamaya)  of  the  heavenly  bodies  of  inferior  brilliancy, 
whose  orbs  arc  overwhelmed  by  tin'-  rays  of  the  sun. 

The  terms  used  for  the  heliacal  *j.*ttings  sm<l  ridings  of  Uic  heavenly 
bqjiea,  or  their  disappearance  in  the  sun's  neighborhood  and  theft  return 
to^ibilitv,  are  precisely  the  same  with  those  employed  to  denpte  their 
rising  {ndaya)  and  setting  (rw/u,  astamaya,  aitumancr)  above  find  bfel<Mfc 
the  &Orizon.  The  title  of  the  chapter,  udayastadhikara f is  literal® 


o' 


jfij 


translated  in  our  head  in 

2.  Jupiter,  Mars,  and  Saturn,  when  their  longitude  is  greater" 
than  that  of  the  sun,  g«»  to  their  sotting  in  the  west;  when  it  is 
less,  to  their  rising  in  the  cusl:  so  likewise  Venus  and  Merouryy; 
when  retrograding. 

S.  The.  moon,  Mercury,  and  Venus,  having  a swifter  motion, 
go  to  their  setting  in  the  cast  when  of  less  longitude  than  the 
sun;  when  of  greater,  to  their  rising  in  the  west. 

These  spec  dilutions  are  of  obvious  meaning  and  evident  correctness. 
The  planets  wliieli  li.-wc  a slower  motion  than  the  sun,  and  <o  are  over- 
taken by  him,  make  their  last  appearance  in  the  west,  after  sunset,  and 

Sperge  again  into  visibility  in  tin:  cast,  before  sunrise : of  those  which 
ove  more  rapidly  than  the  sun,  the  contrary  is  true:  Venus  andMcpii 
enry  belong  to  cither  class,  according  as  their  apparent  motion  is  retreh 
grade  or  direct 

■^4fiS€alouhite  tlie  longitudes  of  the  sun  and  of.  the  planet — in 
^ west,  for  the  time  of  sunset ; in  the  east,  for  that  of  sunrise — 
and,  then  make  also  the  calculation  of  apparent  longitude  (< drlckar - 
mart)  of  the  planet. 

Then  the  ascensional  equivalent,  in  resi 'rations,  of  the  in- 
iferval  between  the  two  (fagndntaraj)rd nds)  will  give,  when  divid- 
ed by  sixty,  the  degrees  of  time  (k wdneds) ; or,  in  the  west,  tike 
^ascensional  equivalent,  in  respirations,  of  the  interval  betwqn 
the  two  when  increased  each  by  six  signs.  ^ ^ . 

.Whether  a planet  will  or.wiU  not  he  visible  in  the  west  after  annset, 
qr  in  the  east  before  sunijf^,  in,  in  this  treatise  made  to  depend  solefy 


m: 


*t  r*  ■ 


apon.the  interval  of  time  by  which  it*,  setting  follows,  or  its  m 
msdes,  that  of  the  sun,  or  upon  its  distance  from  the  sun  in  ob 
ascension ; to  the  neglect  of  those  other  circumstances— as  the  dtcniih ' 
tion  of  the  two  bodies,  and  the  distance  apd  direction  of  the  planet  . 
from  the  ecliptic — which  variously  modify  thtiftimit  of  visibility  as  time  , 
defined.  The  ascertainment  of  the  distance  in  oblique  ascension,  then,  .■ 
is  the  object  of  the  rules  given  in  these  verses.  In  explaining,  the 
method  of  the  process,  we  will  consider  first  the  case  of  a calcmatiqfe  ' 
made  for  the  eastern  horizon.  The  time  of  sunrise  having  been  ■ 
mined,  the  true  longitudes  yd  rates  of  motion  of  the  aun  and  thepiaMt  ' 
in  question  are  found  for  that  moment,  as  also  the  latitude  of  the  planefe? 
Owing  to  the  latter  s removal  in  latitude  from  the  ecliptic,  it  will  not : 
pass  Sic  horizon  at  the  same  moment  with  the  point  of  the  ecliptic 
which  determines  its  longitude,  and  the  point  with  which  it  does  actu- 
ally rise  must  be  found  by  a separate  process.  This  is  accomplished 
by  calculating  the  apparent  longitude  of  the  planet,  according  to  the 
method  taught  in  the  seventh  chapter.  There  is  nothing  in  the  hm- 
. guage  of  the  text  which  indicates  that  the  calculation  is  not  to  be  made 
in  fill,  as  there  prescribed,  and  for  the  given  moment  of  sunrise : gj§so 
f podduelted,  however,  it  would  evidently  yield  an  erroneous  result {Tfor, 
mta -planet  being  above  the  horizon,  the  point  of  the  ecliptic  to  which 
•jtja  then  referred  by  a circle  through  the  north  and  south  points  of  the 
^.horizon  is  not  the  one  to  which  it  was  referred  by  the  horizon  itself  at 
■ Ae  moment  of  its  own  rising.  The  commentary  removes  this  difficulty, 
by  specifying  that  the  akwiadrkktirwan,  or  that  part  of  the  procew 
which  gives  the  correction  for  latitude,  is  to  be  performed  “only  as 
taught  in  the  first  half-verse'' — that  is,  according  to  the  former  part  of 
vii.B,  which  contains  the  rule  for  determining  the  mnount  of  the  correc- 
tion at  the  horizon — omitting  the  after  process,  by  which  its  value  ia 
made  to  correspond  to  the  altitude  of  the  planet  at  the  given  time. 
Having  thus  ascertained  the  points  of  the  ecliptic  which  rise  with  the 
ann  and  with  the  planet  respectively,  the  corresponding  equatorial  inter- 
val, or  the  distance  of  the  planets  in  oblique  ascension,  is  found  by  A 
rate  already  given  (iii.  50).  The  result  is  expressed  in  respirationa  of 
‘ tercel  time,  which  are  equivalent  to  minutes  of  the  equator  (sec  above, 
11-12);  they  are  reduced  to  degrees  h)  dividing  by  sixty:  and  the 
.great  thus  found  receive  the  technical  name  of  “ time-degrees ” 
(£al&nf&9,  kulabhfu/as) ; they  are  alto  called  below  “degrees  of  setting” 
(cijfdnyd*),  and  “degrees  of  visibility”  (drfyanf&s),  y .ft 

If  the  planet  for  which  the  calculation  is  made  lias  greater  los^jtape  ;■ 
thari  the  sun,  the  process,  being  adapted  to  the  time  of  sunset,  and  to  &e 
western  horizon,  requires  a slight  modification,  owing  to  the  fact  that  A*  ■. 
equivalents  of  the  signs  in  oblique  ascension  (iii.  42-45)  are  given  only  * 
as  measured  at  the  eastern  horizon.  Since  180  degrees  of  the  ecliptic  V. 
are  always  above  the  horizon,  any  given  point  of  the  ecliptic  will  set  at  V 
the  seme  moment  that  another  1809  distant  from  it  rises;  by  adding,- '.f 
thin,  six  signs  to  the  calculated  positions  of  the  sun  and  the  planet,  ana 
Ascertaining,  by  iii.  60,  the  ascensional  difference  of  the  two  points  so  ... 
the  interval  between  the  setting  of  the  sun  end  . that  of  (be  planet'S 
"i  determined, 


" Jfaritofofeta W’lWfoa.  933 

feeforA  going  on  to  explain  hew,  from  the  remit  that  obtained,  (he 
time  of  the  planet's  disappearance  or  re-appearance  may  he  derived,  the 
tott  defines  the  distances  from  the  son,  in  oblique  ascension  or  * degrees 
Of  time,"  aft  which  each  planet  is  visible. 

6 The  degrees  of  setting  (astdngds)  are,  for  Jupiter,  eleven; 
for  Saturn,  fifteen ; for  Mars,  moreover,  they  are  seventeen ; 

4 7*  Of  Venus,  the  setting  in  the  west  and  the  ruing  in  theeut 
wee  place,  by  reason  of  her  greatness,  at  eight  degrees;  the 
setting  in  the  east  and  the  rising  in  the  west  occur,  owing  to  her 
inferior  size,  at  ten  degrees  : 

8.  So  also  Mercury  makes  his  setting  and  rising  at  a distance 
from  the  sun  of  twelve  or  fourteen  degrees,  according  as  he  is 
retrograding  or  rapidly  advancing. 

9.  At  distances,  in  degrees  of  time  ( MlahMgds ),  greater  than 
these,  the  planets  become  visible  to  men ; at  less  distances  they 
become  invisible,  tlieir  forms  being  swallowed  up  (yrasto)  by  the 
brightness  of  the  sun. 

The  moon,  it  will  be  noticed,  is  omitted  here : her  heliacal  rising  and 
setting  are  treated  of  at  the  beginning  °f  the  nest  follow  ing'chapter.  * 

In  the  case  of  Mercury  and  Venus,  the  limit  of  Mobility  is  at  a greater 
or  less  distance  fnnn  the  sun  acronlui!>  .v>  the  phnet  is  approaching  its 
inferior  or  superior  conjum  tion,  the  diminution  of  the  illuminated  pop- 
tion  of  the  disk  being  more  than  compensated  by  the  enlargement  of 
the  disk  itself  when  seen  so  iiukIi  ueaii  i to  the  earth. 

Ptolemy  treats,  in  the  last  tluec  chapters  (xui.  7-0)  of  his  work,  of 
the  disappearance  and  re  ippcaranci  ot  the  plaueN  in  the  neighborhood 
of  the  sun,  and  di fines  the  limits  of  usibihu  of  each  planet  when  in 
the  sign  Cancer,  or  wlicic  the  cipiator  and  erl.ptic  are  nearly  parallel. 
His  limits  arc  considerably  ditfci  cut  trnm  those  defined  in  our  text,  being, 
for  Saturn,  14° , tor  Jupiter,  12J  4 o'\  lor  Mars  14°  30' ; for  Venus  and 
Mercury,  in  the  west,  5°  40'  and  11°  30'  respectnely.  v 

10.  The  difference,  in  minutes,  between  tbc  numbers  thus  sta- 
ted aud  the  planet’s  degrees  of  tunc  (kdlunuh),  when  divided  i|||. 
the  difference  of  daily  motions — or,  if  the  planet  be  rctrogradifl^- 
by  the  sum  of  daily  motions — gives  a result  which  is  the  time,  in 
days  etc. 

11.  The  daily  motions,  multiplied  by  tlie  corresponding  ascen- 
sional equivalents  {tuUagndsacaa),  and  dix  ided  by  eighteen  hun« 
dred,  give  the  daily  motions  in  time  (kiilay  >U) ; by  means  of  these 
is  found  tho  distance,  in  days  etc.,  of  the  tu  le  past  or  to  com$> 

Of  these  two  verses,  the  second  prescribes  so  essential  a modifications 
of  the  process  taught  in  the  first,  that  their  arrangement  might  here 
btsn  more  properly  reversed.  If  we  have  ascertained,  by  the  prevtinw 
rules,  fee  distance  of  a planet  in  oblique  ascension  from  fee  sun,  ana  if 
,we  know  fee  distance  in  oblique  ascension  at  which  it  will  disanpate  or 
foappear,  fee  interval  between  fee  given  moment  and  that  at  which  dis- 
appsaance  or  rs-sppearsaes  wiU  take  place  may  be  assdily  found  by 


SQrya>lSdc^dnia, 


: ■ jo 


ascension,  and  not  in  longitude.  The  former  is  derived  from  the  latter  ^ 
by  the  following  proportion : as  a sign  of  the  ecliptic,  or  1800',  is  to.  its  ; 
equivalent  in  oblique  ascension,  as  found  hy  iii.  42-45,  so  ia  the  &tc  of  1 
the  ecliptic  traversed  hy  each  planet  in  a Jay  to  the  equatorial  cquiva-  % 
lent  of  that  arc.  The  daily  rates  of  motion  in  oblique  ascension  thus 
ascertained  sire  styled  the  41  time-motions”  (k&layati),  as  being  commen- 
surate with  the  “ time-degrees”  (kaldnrds). 


is.  svii  Agastya,  Mrgavvadha,  Citru,  Jvcshtha,  Pun&rv&su, 
Abhijit,  and  Hrulirnalmlaya  rise  and  set  at  thirteen  degrees. 

13.  llasta,  QVavaim,  the  Phalgunis,  Qravisblha,  Rohitf,  and 
Maghfi  become  visible  at  fourteen  degrees;  also  Vigil  klia  and 
Agvini. 

14.  Krttika,  Anurfitlhfi  (mfiitra),  and  Mula,  and  likewise  Aglc- 
sha  and  Ardrfi  (mirdrarksha),  are  seen  at  fifteen  degrees;  so,  too, 
the  pair  of  Asliadhas. 

■:fc  15.  Bliaram,  Pushy  a.  and  Mrgagirsha,  owing  to  their  faintness, 
otfe  seen  at  twenty-one  degrees ; the  rest  of  the  astcrisms  become 
■ visible)  and  invisible  at  seventeen  degrees. 

1 These  arc  specifications  of  ihe  di.-tiuices  from  the  sun  in  oblique  as- 
cension {hulanras)  at  which  the  a>lmMiis,  and  those  other  of  the  fixed 
stars  whoso  positions  wen1  defined  in  the  preceding  chapter,  make  their 
heliacal  risings  and  settings.  The  astcrisins  we  are  doubtless  to  regard 
as  represented  hv  their  junction-stars  (tjw/aturd).  The  classification 
here  uiadc  of  the  stars  in  question,  according  to  their  comparative  mag- 
nitude and  brilliancy,  is  in  many  points  a very  strange  and  unaccount- 
able one,  and  by  no  means  calculated  to  give  us  a high  idea  of  the 
'intelligence  and  care  of  those  by  whom  it  was  drawn  up.  Tho  first 
cIqss,  comprising  such  as  are  visible  at  a distance  of  L'*0  from  the  sun, 

«deed,  almost  wholly  composed  of  stars  of  the  first  magnitude;  one, 
Punurvasn  (ft  (icmiuorum),  being  of  the  first  to  second,  niul  hav-^ 
'or  its  fellow  one  of  the  first-  (u  (icndinmini).  But  the  second 
that  of  the  stars  visible  at  14°,  also  contains  four  which  arc  of  the 
magnitude,  or  the  first  to  second  ; namely,  Aldchuraii  (Kohini), 
Hcgtilus  (Magha),  Deneb  or  fi  Leouis  (Pttara-Plialgunl),  and  Atair  or 
a Aquihe  (£mvana) ; and,  along  with  these,  one  of  the  second  to  third 
magnitude,  d Leouis  (Purva  l'hidguid),  three  of  the  third,  and  one, 

* Libras  (VigAkhk),  of  tlie  fourth.  In  this  last,  case,  however,  it  might 
4 -.be  possible  to  regard  « Libra,  of  the  second  magnitude,’  us  the  star 
Which  is  made  to  detennine  the  visibility  of  the  asterism.  Among 
*.  the  stars  of  the  third  class,  again,  wliich  arc  visible  at  15°,  is  one, 
a Ononis  (Ardrfi.),  which,  though  a variable  star,  does  not  fall  below 
the  first  to  second  magnitude ; while  with  it  arc  found  ranked  six  stars 
of  tlie  third  magnitude,  or  of  the  third  to  fourth.  The  class  of  those 
■■wbjjm  are  visible  at  17°,  and  which  are  left  unspecified,  contains  two  - 
'sj^djof  the  fourth  magnitude,  but  also  two  of  the  secoud,  one  of  which. 


v*.w  " 3pntnslQtfon,Md:N6tet>  -V. 

!’■.  1 v ,V,  *•'  *•  * ■*.,  ■’..■<■■ 

-V  ■ 4 ^ .1 

; :•  Androtnedte  or  y Pegasi  (Uttara-BhAdrapadS),  is  mentioned  Mwt; 
(v.  18)  among  those  which  are  never  obscnred  by  the  too  near  approach 
* of  the  sun.  The  stare  forming  the  class  which  are  not  to  be  seen  ' 
within  21°  of  the  sun  arc  all  of  the  fourth  magnitude,  but  they  are  no 
less  distinctly  visible  tlmn  two  of  those  in  the  preceding  class ; and  in- 
deed, Bharanl  is  palpably  more  so,  since  it  contains  a star  Of  the  third 
magnitude,  which  is  perhaps  (sec  above)  to  be  regarded  as  its  juncthfa- 
star.  Since  Agui,  Brahma,  Apainvatsa,  mid  A pas  arc  not  specially  men- 
tioned, it  is  to  be  assumed  that  they  all  belong  in  the  class  of  those 
visible  at  17°,  and  they  are  so  treated  bv  the  commentator : the  first  "of; 
them  ( 3 Tauri)  is  a star  of  the  second  magnitude ; for  the  rest,  sco  thft 
last  note  to  the  preceding  chapter.  ■?*vv 

Some  of  the  apparent  anomalies  of  this  classification  are  mitigated  Of 
removed  by  making  due  allowance  for  the  various  circumstances  by 
which,  apart  from  its  absolute  brilliancy,  the  visibility  of  a star  in  the 
sun's  neighborhood  is  favored  or  the  contrary — such  as  its  distance  and 
. direction  from  the  equator  and  ecliptic,  and  the  part  of  the  ecliptic  in; 
which  the  sun  is  Mtuated  during  its  disappearance.  Many  of  them/ 
however,  do  not  admit  of  such  explanation,  and  we  cannot  av<nd  regard- 
ing, the  whole  scheme  of  classification  as  one  not  founded  mi  careful 
and  long-continued  observation,  but  hastily  and  roughly 'drawn  up  in 
the  beginning,  ami  perhaps  corrupted  later  bv  unintelligent  im 
and  copyists. 

16.  The  degrees  of  visibility  (rfrffllnys),  if  multiplied  b; $ 
eighteen  hundred  and  divided  bv  the  corresponding  ascensional 
equivalent  (uiltii/'i&iuas),  give,  as  a result,  the  corresponding  de- 
grees on  the  ecliptic  (Md nnnfi*)\  bv  means  of  them,  likewise, 
the  time  of  visibility  and  of  invisibility  may-  be  ascertained- 

This  verso  belongs,  in  the  natural  order  of  sequence,  not  after  the  pas- 
sage next  preceding,  with  which  it  has  no  special  connection,  but  after 
verse  1 1.  Instead  of  reducing,  u>  taught  in  that  verso,  the  motions  up- 
on the  ecliptic  to  motions  in  oblique  ascension,  the  ’‘degrees  of  time” 
(k&lanfds)  may  themselves  be  reduced  to  their  equivalent  upon  the  qag 
v responding  part  of  the  ecliptic,  and  then  the  time  of  disAppenrancgeSl 
of  re-appearance  calculated  as  before,  using  as  a divisor  the  sum  eSpl^ 
fercnco  of  daily  motions  along  the  ecliptic.  The  proportion  by 
the  reduction  is  made  is  the  converse  of  .that  before  given ; namely,  at 
the  ascensional  equivalent  of  the  sign  in  which  are  tlie  sun  and  the 
planet  is  to  that  sign  itself,  or  1S00\  so  are  the  “degrees  of  visibility91 
(drpytinf&s,  or  kdldnfdt)  of  the  planet  to  the  equivalent  distance  upon 
that  part  of  the  ecliptic  in  which  it  is  then  situated.  The  technical 
name  given  to  the  result  of  the  proportion  is  ks  *efrdnfds : kshetra  i&dH1 
©rally  “field,  territory.”  and  the  meaning  of  the  compound  may  be  £htu 
paraphrased:  “tlic  iiinit  of  visibility,  in  degrees,  measured  upon*  thal 
part  of  the  ecliptic  which  is,  at  the  time,  the  territory  occupied  by  the 
planets  in  question,  or  their  proper  sphere.” 

IT.  Their  rising  takes  place  in  the  east,  and  their  aetteag  ir 
, the  west ; the  calculation  of  their  apparent  longitude  (thkkarman 


ttilAo  according  to  previous  tales ; the  aseert&idmeftt  ^ 


i 7.  This  verse  should  follow  immediately  after  verse  15,  fo which  it  fit* 

5 fetches  itself  in  the  closest  manner.  The  dislocation  of  arrangement  in  : 
' the  latter  part  of  this  chapter  is  quite  striking,  and  is  calculated  to  eng* 

. geat  a suspicion  of  interpolations.  « 

The  directions  given  in  the  verse  require  no  explanation  : they  afi 
just  snch  an  adaptation  of  the  processes  already  prescribed  tp  the  caei 
of  the  fixed  stars  as  that  made  in  verso.  1 4 of  the  last  chapter.  Hi#1 
commentary  points  out  again  that  the  calculation  of  the  correction  tot 
latitude  ( okahadrkkannan ) is  to  he  made  only  for  the  horizon,  or  jjii 
stated  in  the  first  half-verse  of  the  rule. 


18.'  Abhijit,  Bralimahrdaya,  Svati,  Qravaya  (vdishnava)^  Qra- 
vishtha  (vdsava),  and  Uttara-Bhadrapada  ( ahirbudhnya ),  owing  td 
their  northern  situation,  are  not  extinguished  by  tlie  sun’s  rays. 

It  maisecin  that  it  would  have  been  a more  orderly  proceeding  to 
omit  the%ars  here  mentioneil  from  the.  specifications  of  verses  12-15 
above ; but  there  is,  at  least,  no  inconsistency  or  inaccuracy  iu  the  double 
^.Statement  of  the  text,  since  some  of  the  stars  may  never  attain  that  die- 
Stance  in  oblique  ascension  from  the  sun  which  is  there  pointed  out  as 
^Iheir  limit  of  visibility.  Wc  have  not  thought  it  worth  the  trouble  to 

S>  through  with  the  calculations,  and  ascertain  whether,  according  to 
e data  and  methods  of  this  treatise,  these  six  stars,  and  these  alone, 
of  those  which  the  treatise  notices,  would  never  become  invisible  at 
TJjjayini.  It  is  evident,  however,  as  lias  already  been  noticed  above 
(viii.  20-21),  that  the  star  called  Braluna  or  Pruj;\pati  (5  Aurigae)  is  not 
i here  taken  into  account,  since  it  is  8°  north  of  Bralunalifdaya,  and  con- 
eeqnantly  can  not  become  invisible  u here  the  latter  does  not. 


chapter;:. 

0?  THE  MOON’S  RISING  AND  SETTING,  AND  OF  THE  ELEVATION 

OF  HER  CUSPS. 

Ooirnsm  1,  of  the  heliacal  rising  aurl  setting  of  the  moon  ; 2-5,  how  to  find  the 
interval  from  sunset  to  the  suiting  or  rising  of  the  moon ; 6-8,  method  of  deter* 
mining  the  moon's  relative  altitude  and  distance  from  the  sun  at  sunset;  0,  to  aa> 
r . certain  the  measure  of  the  illuminated  part  of  her  disk ; 10-14,  method  of  define 
. eating  the  moon's  appoamnee  at  sunset;  15,  how  to  make  the* some  oalculatioa 
J and.  delineation  for  sunrise. 

^ *$l.  The  calculation  of  the  heliacal  rising  ( udaya ) and  setting 
(o#(u)of  the  moon,  too,  is  to  be  made  by  the  roles  already  giveq.  ~ 
' JEtHtj'ilve  degrees'  distance  from  the  son  rile  becomes  visible -jit 
^^^^e^.  or  . invisible  in  the  east. 


. ' vT 


V'1 

y§. i - tbetime  of  themootfa  diaan 

M W®  ftn,  or  of  her  emergence  into  visibility  again  beyond  ft*? 
f lipfteA  bf  hie  rays,  no  new  rules  are  required;  the  same  methods  being 
* employed  as  were  made  use  of  in  ascertaining  tlie  time  of  heliacal  set* 
ting  and  rising 'of  the  other  planets:  they  were  stated  in  the  preceding  - 
chapter.  The  ^definition  of  the  moon’s  limit  of  visibility  would  hiave  . 

. been  equally  in  order  in  the  other  chapter,  but  is  deferred  to  ftjpjjh . 
order  that  tne  several  processes  in  which  the  moou  is  concerned  may} 
be  brought  together.  The  title  of  the  chapter,  frngmnatyadki&krap 
“chapter  0f  the  elevation  of  the  moon’s  cusps’  (frnga%  literally  “horn*)? 
properly  applies  ouly  to  that  part  of  it  which  follows  the  fifth  verea»- 

The  degrees  spoken  of  in  this  verse  are,  of  course,  “ degrees  of  tinUjSf 
(k&ldnp&s),  or  in  oblique  ascension.  ^ 

2.  Add  six  signs  to  the  longitudes  of  the  sun  and  moon  re- 
spectively, and  find,  as  in  former  processes,  the  ascensional  eaui*-? 
alent,  in  respirations,  of  their  interval  ( lag ndnta rdsavas) : ir  the 
sun  and  moon  be  in  the  same  sign,  ascertain  their  interval  id 
minutes. 

3.  Multiply  the  daily  motions  of  the  sun  and  moon  by  the  re- 

sult, in  nadis,  and  divide  by  sixty;  add  to  the  longitude  of  each 
the  correction  for  its  motion,  thus  found,  and  find  anew  their  in- 
terval, in  respirations;  -4 

4.  And  so  on,  until  the  interval,  in  respirations,  of  the  su% 
and  moon  is  fixed:  by  so  many  respirations  does  the  moon,  in 
the  light  half-month  {cuMu),  go  to  her  setting  after  the  sun. 

5.  Add  half  a revolution  to  the  sun's  longitude,  and  calculate 

the  corresponding  interval,  in  respirations:  by  so  many  respira- 
tions does  the  moon,  in  the  dark  half-month  ( krshnapakiha\  come** 
to  her  rising  after  sunset.  * 


The  question  here  sought  to  be  solved  i%  how  long  after  sunset  upon 1 
any  given  day  will  take  place  the  setting  of  the  moon  in  the  crescent 
. half-month,  or  from  new  to  full  moon,  and  the  rising  of  the  moon  in 
||ihe  waning  halt-month,  or  from  full  to  new  moon.  The  general  proems* 
is  the  same  with  that  taught  in  the  last  chapter,  for  obtaining  a IHtev 
result  as  regards  the  other  planets  or  fixed  stars:  we  ascertain,  by  ws 
rules  of  the  seventh  chapter — applying  the  correction  for  the  latitude  , 
according  to  its  value  at  the  horizon,  as  determined  by  the  first  part  of 
vii.  8-r-thc  point  of  the  ecliptic  which  sets  with  the  moon ; and  then  ftp 
distance  in  oblique  ascension  between  this  and  the  point  at  which  ft* . 
anti  set  will  measure  the  required  interval  of  time.  An  additional  cor- 
rection, however,  needs  to  be  applied  to  the  res  lit  of  this  process  if.fti 
case  of  tho  moon,  owing  to  her  rapid  motion,  t nd  her  conseq^mtU^t^!; 
Ceptible  change  of  place  between  the  time  of  sunset  aud  that  of  Wfeddn 
Mtting  or  rising : this  is  done  by  calculating  the  amonnt  of  her  'illfeU®® 
during  the  interval  as  first  determined,  and  adding  it*  equivalent!*  # 
Uqne  ascension  to  that  interval;  then  calculating  her  motion,  anew  for 
. : (he  increased  interval  and  adding  its  ascensional  eqiuvaienfc— end  go 
V nfctii  the  deaired  degree  of  accuracy  is  attained. 


jfc 


*■  * ' j*'** 

The*  process  thus  explained,  however,  is  not  precisely  that  : which  is  ; 
prescribed  in  the  text.  We  are  there  directed  to  calculate  the. amount 
•5rf  motion  both  of  the  sun  and  moon  during  the  interval  between  the  ‘ 
lotting  of  the  sun  and  that  of  the  moon,  and,  having  applied  them  to, 
the  longitudes  of  the  two  bodies,  to  take  the  ascensiomu  equivalent  of 
/the  distance  between  them  in  longitude,  as  thus  doubly  corrected,  for 
the  precise  time  of  the  setting  of  the  moon  after  sunset.  In  one' point* 
of  view  this  is  false  and  absurd ; for  when  the  sun  has  once  passed  the 
horizon,  the  interval  to  the  setting  of  the  moon  will  be  affected  only  by 
her  motion,  and  not  at  all  by  his.  In  another  light,  the  process  does  not 
lack  reason  : the  allowance  for  the  sun's  motion  is  equivalent  to  a reduc- 
Mon  of  the  interval  from  sidereal  (nukshatra)  time  to  civil,  or  true  solar 
^(sdvaaa)  time,  or  from  respirations  which  are  tliirty-six-hundrcths  of  tho 
earth's  revolution  on  its  axis  to  such  as  are  like  parts  of  the  time  from 
actual  sunrise  to  actual  sunrise.  Hut  such  a inode  of  measuring  time  is 
unknown  elsewhere  in  this  treatise,  which  defines  (i.  1 1-12)  and  employs 
sidereal  time  alone,  adding  (ii.  •>!))  to  the  sixty  niiclis  which  constitute  a 
sidereal  day  so  much  sidereal  time  as  is  needed  to  make  out  the  length 
of  a day  that  is  reckoned,  by  any  other  method.  It  seems  necessary, 
then,  either  to  suppose  a notable  blunder  in  this  passage,  or  to  recognize 
in  it  such  a departure  from  the  usual  methods  of  the  treatise  as  would 
show  it  to  be  an  interpolation.  Probably  the  latter  is  the  alternative  to 
: be  chosen:  it  is,  at  any  rate,  that  which  the  commentator  prefers;  he 
pronounces  the  two  verses  hi'irinn^g  with  the  second  half  of  verso 
and  ending  at  the  middle  of  vimmo  4,  to  be  spurious,  arid. the.  true  text  of 
the  Siddhiinta  to  comprix*  only  tho  first  half  of  verse  2 and  the  secqud 
of  verse  4;  tlie^e  would  form  together  averse  closely AtialhgoOSihita 
method  and  expression  with  ven«  5,  which  teaches' the  like  psocesjr^  ^^ 
moon-rise,  in  the  waning  half-month.  Fortified  by  the  authority^*1 
^commentator,  wc  are  justified  in  assuming  that' the  Sfirya-Sidf* 

'.  originally  neglected,  in  its  process  for  calculating  the. time  of  the  I 
. ietting,  her  motion  during  the  interval  between  that  time  and  i 
. and  that  the  omission  was  later  supplied  by  another  hand, 

■ other  treatise,  which  reckoned  by  solar  time  instead  of  sidereal  'TWa,.. 
d6es  not,  however,  explain  and  account  for  tho  second  half  of 

J verse;  which,  if  it  has  any  meaning  at  all,  di&srqht;  from  that  copveyra 
in  the  former  part  of  the  same  verse,  seemstq,  signify  that  when  thjMftii. 

. and  moon  arc  so  near  one  another  n<  to  be  in  the  same  sign,  the  discord- 
ance between  distances  on  the  ecliptic  and  their  equivalents  upon  the 
1 eauator  may  be  neglected,  mid  the  difference  of  longitude  in  minutes 
taken  for  the  interval  of  time  in  respirations. 

If  the  time  is  between  new  and  full  moon',  the  object  of  the  process  is 
to  obtain  the  interval  from  sunset  to  the  setting  of  the  moon ; as  both 
. tjdce  place  at  the  western  horizon,  the  two  planets  are  transferred  to  the 

■ eastern  horizon,  in  order  to  the  measurement  of  their  distance  in  ascen- 
i*.  ft  on  the  other  hand,  the  moon  has  passed  her  full,  tho  time  of 

nrii»e  is  sought;  here  the  sun  alone  is  transferred,  by  tho  addition  of 
to  his  longitude,  to  the  eastern  horizon,  as  taught  in  verse  0.  Tho 
' n to  be  applied  to  the  longitude  of  both  planets  is  found  by  the  * 
- proportion— as  sixty  nfcdis  are  to  tho  given  interval  in  niUlli*  so 


— J ' 


■ b the  trae  duly  motion  of  the  planet  to  its  actual  motion 
internl.. 


mg- that 


■ ■ . * 


' 6.  Of  the  declinations  of  the  sun  and  moon,  if  their  direction 
be  the  same,  take  the  difference ; in  the  contrary  case,  take  the 
sum:  the  corresponding  sine  is  to  be  regarded  as  south  or  north,  / 
according  to  the  direction  of  the  moon  from  the  sun.  ':y 

7.  Multiply  this  by  the  hypothenusc  of  the  moon’s  mid-day 
shadow,  and,  when  it  is  north,  subtract  it  from  the  sine  of  laftir  r 
tude  ( aksha ) multiplied  by  twelve ; when  it  is  south,  add  it  t ifc* 
the  same.  a* 

*.8.  The  result,  divided  by  the  sine  of  co-latitude  (Jamto),  gives- 
the  base  (i bluija ),  in  its  own  direction ; the  gnomon  is  the  perpen- 
dicular (koti) ; the  square  root  of  the  sum  of  their  squares  is  the 
liypothenuse. 


In  explaining  tlic  method  uf  this  process,  we  shall  follow  the  guidance 
bf  the  commentator,  pointing  out  afterwards  wlierein  he  varies  from 
the  strict  letter  of  the  text:  for  ilhi*Lrsitiiui  we  refer  to  the  accompany- 
ing figure  (Fig.  :*2). 

The  figure  represents  the  south- western  quarter  of  the  vi>ible  sphere,  ■ 

seen  us  projected  upon  the . 

■ plane  *»f  the  meridian;  Z being.’ 

the  zenith,  V the  south  point, 
\V  Y the  intersection  of  the 
horizontal  and  meridian  planes,  „ 
and  W the  projection  of  thQ* 
west  point.  Let  7.  ii  equal  thb* 
latitude  of  the  place  of  obaer-  r 
vatiou,  and  let  (J  T and  QO.bel 
the  declinations  of  the  sun  atyd'* 
moon  respectively,  at  the  given.  ' 
time : then  \Y<J,  ST,  and  ft O ’ 
will  be  the  projections  of  the  - 
equator  and  of  the  diurnal  cir- 
cles of  the  sun  ami  moon.  Sup-  v 
pose,  now,  the  sun  to  be  upon  * 
the  horizon,  at  S,  and  the  moon  . 

to  have  a certain  altitude,  being  at  M : draw  from  II  the  perpendicular 
to  the  plane  of  the  horizon  M L,  and  join  MS:  it  is  required  to  kuoi£.; 
the  relation  to  one  another  of  the  three  sides  of  the  triangle  SLM,  ut  - 
order  to  the  delineation  of  the  moon's  appeai.incc  when  at  M,  or  at  the * 
moment  of  sunset. 

Now  M L is  evidently  the  sine  of  the  mooi.'s  altitude  at  the  gtotar 
time,  which  may  be  found  by  methods  already  more  than  once  described 
and  illustrated.  And  S L is  composed  of  the  two  parts  S N and  > 

which  the  former  depends  upon  the  distance  of  the  moon  in  decUtiatigd * 
from  the  sun,  and  the  latter  upon  the  moon’s  altitude.  Bnt  SN  is  one/, 
of  the  sides  of  a right-angled  triangle,  in  which  the  angle  NSh  is  equal,;, 
to  the  observer’s  co-latitude,  and  N b to  the  sum  of  ^pine  rf  decli^; 
P turn  of  the  sun.  cb  or  Wo,  and  that  of  the  moon,  JSPfr  Bence  yrtf 

* " ■ ■ ao 


■ (&»* 


f mbBViiViiXiBV 

St  / sin  co  1st : sum  of  sines  of  dflcL::R:B2f 

and  8N  = (RXiumof  sinmof  decL)-S-  am  co-lot 

In  like  manner,  since,  in  the  triangle  MNL,  the  angles  at  M and  N 
are  respectively  equal  to  the  observer’s  latitude  and  co-latitude, 

sip  MNL  ' im  LMN : : M L . N L 
or  sin  co  1st  : Bin  lat  . Bin  alt . N L 

sad  NL  = (sin  nit.  X siu  lat ) — sm  co  lat. 

We  have  thus  found  the  values  of  M L and  the  two  parts  of  SL  in 
terms  atf  the  general  sphere,  or  of  a circle  whose  radius  is  tabular  radius : 
it  is  desired  farther  to  reduce  them  to  terms  of  a circle  in  which  U|i 
shall  equal  the  gnomon,  01  tw  eh  c digits  And  since  the  gnomon  is 
equal  to  the  sine  of  altitude  in  a circle  of  which  the  liypolhenuse  of  the 
corresponding  shadow  is  radius  (compare  above,  lii.  25-27  etc.),  this  re- 
duction may  he  effected  by  multiply  mg  the  quantities  in  question  by  the 
hypothenuse  of  the  shadow  and  dividing  by  ladius.  That  is  to  say,  rep- 
resenting the  reduced  values  of  S N and  N L by  < n aud  n l respectively, 


R : hyp.  «had  M L gnom 
r K hyp.  ibsd  SN  in 

; R.byp  shad  NL  n l 

Substituting,  now,  in  the  bpcoik!  and  thiid  of  these  proportioNLthe  val- 
ues of  S N and  N L found  foi  them  above,  and  substituting  JH^the 
{bird  the  value  of  the  hvpothenuse  of  the  shadow  derived  iroiUTUOTirst, 
we  have 


R ; hyp,  shad. 


RX  sum  Bin decl 
■in  co  lat 


which  reduce  to 


Bit,  and  R 


RXgnom 
Bin  alt. 


■malt  X nn  lat.  , 

. -mi 

■mco-lat 


hyp  Bhad  X snm  sin  decl.  sin  lat  X gnom 

mi=  — — . — • and  fl(= -r—r 

bui  co  lat  am  co-lat 

Hence,  if  the  perpendicular  M L be  assumed  of  the  ccustant  value  of  the 
gnomon,  or  twelve  digits,  we  Lave 

^^(hyp  «had  X sum  Bin  decl ) 4-  («n  lat  X gnom  ) 

■in  co  lat  ~ 


In  the  case  thus  far  considered  the  6un  and  moon  have  been  supposed 
upon  opposite  sides  of  the  equator.  If  they  are  upon  the  same  side, 
the  sun  setting  at  S',  or  if  their  sines  of  declination,  8'd  and  X c,  are  of 
the  same  direction,  the  value  of  S'  N,  the  corresponding  part  of  the 
hose  S'  Lf  will  be  found  by  treating  in  the  same  manner  as  before  the 
difference  of  the  sines,  S'e,  instead  of  their  sum.  In  this  case,  too,  the 
value  of  8'e  being  north,  8'N  will  have  to  be  subtracted  from  NL  to 
give  the  1mm  S'  L Other  positions  of  the  two  luminaries  with  respect 
to  one  another  are  supposable,  blit  those  which  we  have  taken  are  suffl- 
- qjant  to  illustrate  all  the  conditions  of  tlie  problem,  and  the  method  of 
fo  solution. 

is  evident  that,  in  two  points,  the  process  as  thus  explained  by  the 
Hwsptaentator  is  discordant  with  that  which  the  text  prescribes.  The 
^pp^in  the  diet  place,  tells  us  to  take,  not  the  sum  or  difference  of  the 


•toes  of  declination,  but  the  sine  of  the  sum  or  difference  of  (feclinetioni,  ■ 
an  the  ride  4 N of  the  triangle  8 N 6.  This  seeitis  to  be  a men  inaoen.  . 
ncjr  on  the  part  of  the  text,  the  difference  between  the  two  quantities, 
which  could  never  be  of  any  great  amount,  being  neglected : tfc  is,  how- 
ever, yerjr  hard  to  see  why  the  less  accurate  of  the  two  valnetioiis  of  the 
quantity  in  question  should  have  been  selected  by  the  text ; for  it  is,  if 
anything,  rather  less  easy  of  determination  than  the  other.  The  other 
discordance  is  one  of  much  more  magnitude  and  importance  : the  text 
speaks  of  the  ‘‘hypothenuse  of  the  moon's  mid-day  shadow”  ( madhpAh* 
ntnduprabhdkarna ),  for  which  the  commentary  substitutes  that  m the 
shadow  cast  by  the  moon  at  the  given  moment  of  sunset.  The  coni' 
mentator  attempts  to  reconcile  the  discrepancy  by  saying  that  the  text 
means  here  the  moon’s  shadow  as  calculated  after  the  method  of  a noon* 
shadow  4 or  again,  that  the  time  of  sunset  is,  in  effect,  the  middle  of  the 
day,  since  the  civil  day  is  reckoned  from  sunrise  to  sunrise : but  neither 
of  these  explanations  can  be  regarded  as  satisfactory.  The  comment** 
tor  farther  urges  in  support  of  his  understanding  of  the  term,  that  vra 
are  expressly  taught  above  (\ii.  11)  that  the  calculation  of  apparent 
longitude  ( drkkarman ) is  to  be  made  in  the  process  for  finding  the  ele- 
vation of  the  moon’s  cusps ; while,  if  the  hypothenuse  of  the  moon's 
meridian-shadow  be  the  one  found,  there  arises  no  occasion  for  making 
that  calculation.  It  seems  clear  that,  unless  the  commentator's  under- 
standing of  the  true  scope  and  method  of  the  whole  process  be  errone- 
ous, the  substitution  which  he  makes  must  necessarily  be  admitted*  Thin 
is  a point  to  which  we  shall  recur  later. 

9.  The  number  of  minutes  in  the  longitude  of  the  moon  di- 
minished by  that  of  the  sun  gives,  when  divided  by  nine  hun- 
dred, her  illuminated  part  (ruJcla) : this,  multiplied  by  thenum-- 
ber  of  digits  (angida)  of  the  moon's  disk,  and  divided  by  twelve^ 
gives  the  same  corrected  (sphutn). 

The  rule  laid  down  in  this  veisc,  for  determining  the  measure  of  the 
illuminated  part  of  the  moon,  applies  only  to  the  time  between  new 
■ijmoon  and  full  moon,  when  the  moon  is  less  than  180°  from  the  sun: 
when  her  excess  of  longitude  is  more  than  180°,  the  rule  is  to  be  ap- 
plied as  stated  below,  in  verse  1 5.  As  the  whole  diameter  of  the  moon 
is  illuminated  when  she  is  half  a revolution  from  the  sun,  one  half 
her  diameter  at  a quarter  of  a revolution’s  distance,  and  no  part  of  it  at 
the  time  of  conjunction,  it  is  assumed  that  the  illuminated  portion  of  her 
diameter  will  vary  ns  the  part  of  180°  by  which  she  is  distant  from  the 
sun ; and  hence  that,  assuming  the  measure  of  the  diameter  of  hftf 
disk  to  bo  twelve  digits,  the  number  of  digits  iMuminat*  d may  be  fMMf 
by  the  following  proportion:  as  half  a reio  ition,  or  10,800^  tfW 
twelve  digits,  so  is  the  moon’s  distance  from  the  sun  in  minutes  to  the 
corresponding  part  of  the  diameter  illuminated : the  substitution^  ht  the ; 
first  ratio,  of  000  : 1 for  10,800 : 12,  gives  the  rule  as  stated  in  the  fisft 
Here,  it  will  be  noticed,  we  have  for  the  first  and  only  time  the  QVedb 
ftnthod  of  measuring  the  moon’s  diameter,  by  eqnal  twelfths,  or  digits: 
from  this  scale  a farther  reduction  is  made  to  the  proper  Qfhdtt  ses&dft 
determined  by  the  methods  of  the  fourth  chapter  iie*ib*ve,‘iv.  9*3, 


-<* 


' ' W another  proportion : as  twelve  is  to  the  true  diameter  in  digits,  so  is  ' 
. 4he  result  already  found  to  the  true  measure  of  the  part  of  the  diameter. - 
illuminated. 

. v’lt  ia  not  to  be  wondered  at  that  the  Hindus^  .*■ 

: fipticity  of  the  line  forming  the  inner  bouudai^  d^  ihh^iooo’e  lUnminlk- 
, M.p  art:  it  is  more  strange  that  they  ignored  thsdbviouS  diet, 
while  the  illuminated  portion  of  the  nioonii  sphericaltartace  naftiefirom 
the  earth  varies  very  nearly  as  her  diatahee  from"  the  sun,  the  apparent 
•breadth  of  the  bright  part  of  her  disk,  in  which  that  surface  ia |een- pro- 
jected, must  vary  rather  as  tlio  veined  sine  of  her  distance. 

10.  Fix  a point,  calling  it  the  sun : from  that  lay  off  the  base, 
in  its  own  proper  direction  ; then  the  perpendioular,  toward,  the 
west ; and  also  the  hvpothonusc,  passing  through  the  eternity 
of  the  rierpendicular  and  the  central  point. 

11.  From  the  point  of  intersection  of  the  perpendicular  and 
the  hypothenuse  describe  the  moon’s  disk,  according  to  its  di- 
mensions at  the  given  time.  Then,  bv  means  of  the  hypothe- 
-nusc,  first  make  a determination  of  directions ; 

. IS.  jSJ  i.c y oif  'u|puu  ku^^^^W.UGiaioi  ,‘  nunViiiiu  j/uiiiu  unw " 
^intersection  with  the  disk,  in  an  inward  direction,  the  measure  of 
the  illuminated  part:  between  the  limit  of  the  illuminated  part 
and  the  north  and  south  points  draw  two  fish-figures  ( malsya ) ; 

13.  From  the  point  of  intersection  of  the  lines  passing  through 
.^their  midst  describe  an  arc  touching  the  three  points : as  the  disk 
7 already  drawn  appears,  such  is  the.  moon  upon  that  day. 

■ 14.  After  making  a determination  of  directions  by  means  of 
the  perpendicular,  point  out  the  elevated  ( unnala ) cusp  at  the 
extremity  of  the  cross-line : having  made  the  perpendicular 
(iofi)  to  be  erect  (unnata),  that  is  the  appearance  of  the  moon. 

15.  In  the  dark  half-month  subtract  the  longitude  of  the  sun 
'■*  increased  by  six  signs  from  that  of  the  moon,  and  calculate,  in 
^he  same  manner  as  heforoj  her  dark  part.  In  this  case  lay  off 
:■  the  base  in  a reverse  direction,  and  the  circle  of  the  moon  on  the’ 
west  .. 

Having  made  the  calculations  prescribed  in  the  preceding  passages, 
we  are  now  to  project  their  results,  and  to  exhibit  a representation  of 
• the  moon  as  she  will  appear  at  the  given  time.  The  annexed  figure 
(Fig.  33)  will  illustrate  the  method  of  the  projection. 

.,  VWe  first  fix  upon  a point,  as  S,  which  shall  represent  the  position  of 
|he  sun’s  centre  upon  the  western  horizon  at  the  moment  of  sunset,  and 
i;  'we  determine,  in  the  manner  taught  at  the  beginning  of  the  third  chap- 
iter, the  lines  of  cardinal  direction  of  which  it  is  die  centre.  From  this 
4ht  we  then  lay  off  the  base  (bhuja)  8 L,  according  to  its  value  in  dig- 
i as  ascertained  by  the  previous  process,  and  northward  or  southward, 
*ording  to  its  true  direction  as  determined  by  the  same  process.  From 
X>extren)ity,  is  laid  off  the  perpendicular  [koii\  which  has  the  fixed 
r.of  twelve  digits.  This,  being  a line  peipenaicular  to  the  plane  of 
-*-i-tn»ay  be  regarded  as  having  no  proper  direction  of  ita  own 


..ft 


..  ■■  ^v. . ■ ■ - ■ .-■»»■  ft*  - 

Trmtlation  and  Mite*. 


■ V 


upon  the  surface  of  projection : but  the  text  directs  us  to  lay  it  off  wesfr* 

Fin*  to.  ward  from  L,  apparently  in  order  that  H 

the  observer,  standing  upon  the  east-  f 
era  side  of  liis  base  S L,  and  looking 
westward  toward  the  setting  sun, 
may  have  his  figure  duly  before  him;. 
The  western  extremity  of  the  perpen- 
dicular, M,  represents  the  modn’s, 
place,  and  from  that  as  a centre,  and, 
with  a radius  equal  to  the  seini-diam-  : 
eter  of  the  moon  in  digits,  as  ascer-  . 
tained  hv  calculation  for  the  given ... 
moment,  a circle  is  described,  repre-  - 
senting  the  moon’s  disk.  Next  . wo  » 
are  to  prolong  the  hypotbenuse,  8 M,  to  c,  and  to  draw,  by  the  usual 
means,  the  line  sn  at  right  angles  to  it : the  directions  upon  the  disk  J 
thus  determined  hy  the  liypnthemise,  ns  the  text  phrases  it,  are  called  by 
the  commentary  “ moon-directions”  (cawfrarf?V<M).  The  sun  being  at  S, 
the  illuminated  hah*  «»f  the  moon's circumference  will  be  s wn,  tlic  cusps 
will  be  at  8 aiul  n , and  w will  be  the  extremity  of  the  diameter  of  great- 
est illumination.  from  tr,  then,  lay  off  upon  the  hvpotlienuse  an  amount, 
w jr,  equal  to  the  measure  in  digits  of  the  illuminated  part  of  the  diam- 
eter, and  through  «,  r,  and  n describe  an  arc  of  a circle,  in  the  manner 
already  more  than  once  explained  (see  above,  vi.  14-16)  ; the  crescent 
s wnx  will  represent  the  amount  and  direction  of  the  moon's  illumina- 
ted part  at  the  given  time.  Now  we  once  more  make  a determination:  ■. 
of  directions  upon  the  di^k  according  to  the  perpendicular  LU;  that  is., 
to  say,  wc  prolong  1#  M to  r\  and  draw  s’  ri  at  right  angldto  it:  the*- 
directions  thus  established  arc  styled  in  the  commentary  “ sunSfireetions” 
(tflryadifcts),  although  without  obvious  propriety  : they  might  rather  be 
called  “apparent  directions,”  or  “directions  on  the  sphere,”  since  a'*' 
should  represent  a line  parallel  with  the  horizon,  and  i 10V  one  perpendieu- 
lar  to  it.  The  line  r'n#  is  called  in  the  text  the  “ cross-line”  {tiryaksbtra\ 
and  whichever  of  the  moon’s  cusps  is  found  upon  that  line  is,  we  are  told*So 
be  regarded  as  the  elevated  ( unnata ) cusp,  the  other  being  the  depressed 
one  (nata).  'Whenever  there  is  any  base  (bhuja),  as  S L,  or  whenever 
the  moon  and  sun  arc  not  upon  the  same  vertical  line  M L,  there  will 
take  place,  of  course,  a tilting  of  the  moon’s  disk,  by  which  one  of  her 
cusps  will  be  raised  higher  above  the  horizon  than  the  other ; the  rela- 
tive value  of  the  base  to  the  perpendicular  will  determine  the  amount  of  . 
the  tilting,  and  of  the  deflection  of  the  points  of  direction  netw  fri^m 
nVs'tir';  and  the  elevated  cusp  will  always  be  that  upon  the  samqNll|p 
of  the  perpendicular  on  which  the  base  lies.  What  is  meant  bplBb 
latter  half  of  verso  14  is  not  altogether  clear.  The  commentator  explains  .., 
it  in  quite  a different  manner  from  that  in  which  we  have  translated  itr* 
he  .Understands  koti  as  meaning  in  this  instance  11  cusp,”  which  sighing; 
cation  it.  is  by  derivation  well  adapted  to  bear,  and  does  actually  receive^- 
although  not  in  any  other  passage  of  this  treatise : and  he  explains 
verb  krtvd,  “having  made”  by  drshtvd , “having  seen”:  the  phnhigK' 
would  then  read  “beholding  the  elevated  cusp.”  We  cannot  accktyt 


this  explanation  as  a plausible  one : to  nt  the  meaning  seeml  rather  to 
^bo  that  whereas,  in  the  projection,  the  perpendicular  (Mi)  LM  is  drawn 
;otf  a horizontal  surface,  we  are,  in  judging  of  the  projection  as  an  actual 
representation  of  the  moon’s  position,  to  conceive  of  that  line  as 
erected,  set  up  perpendicularly. 

have  thus  far  only  supposed  a case  in  which  the  calculations  are 
. &ade  for  the  moment,  of  sunset,  the  situation  of  the  moon  being  in  the 
western  hemisphere  of  the.  heavens.  In  the  text,  however,  there  is  noth- 
ing whatever  to  limit  or  determine  the  time  of  calculation,  and,it  is  evi- 
dent that  the  process  of  finding  the  base  and  perpendicular  will  be  pre- 
cisely the  same,  if  S (Fig.  32)  he  taken  upon  the  eastern  horizon,  and 
the  triangle  S LM  in  the  eastern  hemisphere.  The  last  verse  supposes 
those  to  be  the  conditions  of  the  problem,  and  layB  down  rules  for  de- 
termining in  such  a case  the  amount  of  illumination,  and  for  drawing  the 
projection.  As  regards  the  measure  of  the  illuminated  part,  we  are  to 
follow  the  same  general  method  as  before,  only  substituting  for  the 
moon’s  distance  in  longitude  from  the  sun  her  distance  from  the  point 
of  opposition,  and  regarding  the  result  obtained  ns  the  measuro  of  that 
part  of  the  diameter  which  is  obscured  (asita,  “ black1') : since,  during 
the  waning  half-month,  darkness  grows  gradually  over  the  moon's  faco 
in  the  same  manner  as  illumination  had  done  during  the  crescent  half- 
month.  But  why  the  base  (bhvja)  is  now  to  be  laid  off  in  the  opposite 
to  its  calculated  direction,  we  find  it  very  hard  to  see.  The  commenta- 
tor says  it  is  because  all  the  conditions  of  the  problem  arc  reversed  by 
OUT  having  to  calculate  and  la\  off  the  obscured,  instead  of  the  illuinina- 
: %ted,  part  of  the  moon's  disk : but  the  force  of  this  reason  is  not  apparent. 

: The  eataUu  diment  in  the  projection  of  a point  representing  the  position 
of  the  sivjifs,  in  effect,  the  one  condition  which  sufficiently  determines 
all  the  flB t:  if  we  arc  to  make  a projection  corresponding  to  that 
' drawn  in  illustration  of  the  other  rise,  we  ought,  it  should  secin,  to 
draw  tho  base  in  its  true  direction,  and,  stationing  the  observer  upon  the 
western  side  of  it,  looking  eastward,  to  lay  off  the  perpendicular  away 
.from  him,  toward  the  cast ; and  then  to  proceed  a*  before,  only  measur- 
ing the  obscured  part  of  the  diameter  from  its  icmoter  extremity,  in- 
1 steed  of  from  that  next  the  sun.  This  latter  direction  is  regarded  by 
the  commentator  as  actually  conveyed  in  tho  final  clause  of  verse  15:  he 
interprets  4%the  circle  ( mnnrlala ) of  the  moon”  to  mean  the  dark  pari  of 
the  moon’s  disk,  or  that  which  is  to  be  pointed  out  as  increasing  during 
the  waning  half-month,  and  “ on  the  west'*  to  mean  on  the  western  side 
of  the  complete  disk,  which  is  tiic  side  now  turned  away  from  the  sun. 

' It  seems  to  us  exceedingly  questionable  whether  the  passage  fairly  admits 
of  this  interpretation,  but  wc  have  no  other  explanation  of  it  to  offer — 

' unless,  indeed,  it  is  to  be  looked  upon  as  a virtual  repetition  of  the  for- 
mer  direction  to  lay  off  the  perpendicular,  which  determines  the  posi- 
V j Jion  of  the  moon's  disk,  towards  the  west. 

' We  must  confess  that  we  feel  less  satisfied  with  our  comprehension  of 
&‘$he  scope  and  methods  of  this  chapter  than  of  any  that  precedes  it.  We 
disappointed  at  finding  the  result  arrived  at  one  of  so  indefinite  a 
jj||Meter,  and  of  bo  little  significance.  The  wholo  laborious  calculation 
, igpito  be  made  simply  for  the  sake  of  delineating  tho  appearance  of 


286 


xi.]  Trckalatian  and  Notes. 

the  moon  at  a given  moment,  and  pointing  out  which  of  her  two  home 
has  tho  greater  altitude.  No  determination  is  made  of  the  amount  of 
angular  deflection,  upon  which  any  consequences,  meteorological,  astro- 
logical,  or  of  any  other  character,  could  be  founded ; nor  is  any  hint 
given  of  the  way  in  which  the  results  of  the  process  are  to  be  turned  to 
account  Moreover,  while  the  object  aimed  at  seems  thus  to  be  merely 
a projection,  a time  is  selected  at  which  the  moon  is  not  ordinarily  visi- 
ble, so  that  she  can  not  be  seen  to  exhibit  an  accordance  with  her  deline- 
ated appearance  1 Once  more,  the  whole  process  is  an  extremely  fanlty 
one : it  is,  in  fact,  only  when  the  moon  is  herself  at  the  horizon  that  her 
visible  disk  can  be  regarded  as  in  the  same  plane  with  lines  parallel  with 
and  perpendicular  to  the  horizon,  or  that  e'  w'  and  n'  s'  (Fig.  33)  repre- 
sent actual  directions  upon  her  face:  anywhere  else,  the  relations  of  tho 
moon's  disk  at  M in  the  first  figure  (Fig.  32)  and  at  M in  the  other  fig- 
ure (Fig.  33)  arc  so  different  that  the  latter  cannot  fairly  represent  the 
former.  It  would  seem,  indeed,  as  if  the  moment  of  the  moon's  owfn  ' 
setting  or  rising  were  the  one  for  which  such  a calculation  and  projec- 
tion as  this  would  have  most  significance : at  that  time,  the  disappear- 
ance or  appearance  of  one  of  her  horns  before  the  other  would  be  such 
a phenomenon  as  might  seem  to  a Hindu  astrouomer  worth  the  trouble 
of  delineating,  as  a decisive  proof  of  the  accuracy  of  his  scientific 
knowledge.  \Vc  have  not  found  it  possible,  however,  to  make  the  rules 
of  the  text  apply  to  such  a case,  and  the  commentary  is  explicit  in  its 
definition  of  the  time  of  the  calculation,  as  sunset  or  sunrise  alone,  to 
the  exclusion  of  ativ  other  moment.  But  the  discordance  existing  at 
more  than  one  point  in  the  chapter  between  the  text  and  the  commen- 1 
tary  suggests  the  conjecture  that  the  original  design  of  the  one  and  the 
traditional  interpretation  of  it  represented  by  the  other  may  be  at  vari- 
ance, and  we  are  not  without  suspicions  that  the  text  may  have  been 
altered,  so  as  not  now  fairly  and  accurately  to  represent  any  one  consist- 
ent process.  A better  understanding  of  the  general  object  of  the  calcu- 
lation and  the  use  made  of  its  results,  and  an  acquaintance  with  the  so- 
lutions of  the  problem  presented  by  other  astronomical  treatises,  might 
throw  additional  light  upon  these  points ; but  we  are  not  able  at  present 
fully  to  avail  ourselves  of  suck  assistance,  nor  is  the  importance  of  the 
subject  such  as  to  render  incumbent  upon  us  its  fuller  elucidation. 

• 

CHAPTER  XI. 

OF  CERTAIN  MALIGNANT  ASPECTS  OF  THE  SUN  AND  MOON.  .-v 

Contents:— 1-6,  definition  and  description  of  the  maligi.  rot  aspects  of  the  sup  and 
moon,  when  of  equal  declination;  6-11,  to  find  the  longitude  of  the  su&’-ahd. 
moon  when  their  declinations  are  equal;  12-13,  to  ascertain  the  corresponding 
time ; ,14-16,  to  determine  tlie  duration  of  the  aspect,  and  the  moment  of  its  be- 
ginning and  end ; 16-18,  its  continuance  and  its  influences  *,  19,  when  such  an  as- 
peo tinny  occur  more  than  once,  or  not  at  all;  SO,  occurrence  of  the  yoga  of  like 
name  and  character ; 21,  of  unlucky  points  in  the  circle  of  asterismt;  22,  caution 
aa  to  these  unlucky  aspects  and  points;  28,  introductory  to  the  following  ehapte* 


2S6  SCirya-Siddh&n&}  [xi.  1- 

1.  When  the  sun  and  moon  are  upon  the  same  side  of  either 
solstice,  and  when,  the  sum  of  their  longitudes  being  a circle, 

' they  arc  of  equal  declination,  it  is  styled  vaidhrta. 

2.  When  the  moon  and  sun  are  upon  opposite  sides  of  either 
solstice,  and  their  minutes  of  declination  are  the  same,  it  is 
vyatipala , the  sum  of  their  longitudes  being  a half-circle. 

3.  Owing  to  the  mingling  of  the  nets  of  their  equal  rays,  the 
lire  arising  from  the  wrath  fulness  of  their  gaze,  being  driven  on 
by  the  provector  {prcuuhn),  is  originated  unto  the  calamity  of 
mortals. 

4.  Since  a fault  (pdht)  at  this  time  often  causes  the  destruction 
of  mortals,  it  is  known  as  vyutipdta,  or,  l»y  a difference  of  title, 
v&idhrti. 

5.  Being  black,  of  frightful  shape,  bloody -eyed,  big-bellied,  the 
source  of  misfortune  to  all,  it  is  produced  again  and  again. 

Of  all  the  chapters  in  the  treatise,  this  is  the  one  \\  liii-h  has  least  in- 
terest and  value.  It  is  styled  puttnlhiktira,  41  chapter  uf  the  and 

concerns  itself  with  giving  a deseript ion  of  the  malignant  fhnrneler  of 
the  times  when  the  sun  and  mumi  have  equal  declination.  upon  the  sanm 
or  opposite  sides  of  the  equator,  and  with  laying  down  rules  by  which 
the  time  of  occurrence  *»f  tlm-c  malignant  aspects  may  be  calculated. 
The  latter  part  alone  properly  falls  within  the  province  of  an  astronom- 
ical treatise  like  the  present  : the  other  would  better  have  been  left  1o 
works  of  a professedly  astrological  character.  The  term  pata,  applied  1«» 
the  aspects  in  question,  mean>  literally  “fall,"  and  hence  also  either 
"fault,  transgression/’  or  “calamity."  \Yc  have  ofiui  met  with  it  above, 
in  the  sense  of  “ node  of  a planet V orbit";  as  so  u<ed,  ii  was  probably  first, 
applied' to  the  moon's  nodes,  because  they  were  the  poinls  of  danger  in 
her  revolution,  near  which  the  sun  or  her<cif  was  liable  to  fall  into  the 
jaws  of  R&hu  (*oe  ahoic,  iv.  0) ; ami  il  Mih  then  tran-fe.ncd  also,  tiiougli 
without  the  same  reason,  to  the  mule-,  of  the  other  planets*.  As  it  i* 
employed  in  this  chapter,  we  translate  it  simply  “ aspect.”  Why  the 
time  when  the  sun  and  lmmii  are  equalh  di^ani  from  the  equator  diuwld 
be  looked  upon  as  so  imperially  unfortunate  i>  not  ea^y  to  discover,  nut  - 
withstanding  the  lucid  explanation  furnished  in  She  third  verse.  For  the 
41  pro  vector”  (pravuha).  the  wind  whi<‘ii  carries  the  planets  forward  in 
their  orbits,  sec  above,  ii.  >al.  When  the  equal  declinations  are  of  oppo- 
site direction,  the  aspect  is  denominated  r&idhrta , or  v&idhrti . Tlii* 
word  is  a secondary  derivative  from  vidhrli , 11  holding  apart,  withhold- 
ing/’ or  from  vidhrta : it  lias  been  noted  above  (under  ii.  Go)  sis  the 
name  of  the  last  yoya ; and  its  use  here  is  not  discordant  with  that, 
since  the  twenty-seventh  yoga  also  occurs  when  the  sum  of  the  longi- 
tudes of  the  sun  and  moon  is  360°.  The  title  of  the  other  aspect  ( pata ), 
which  occurs  when  the  sun  and  moon  are  equally  removed  from  the 
equator  upon  the  same  side  of  it,  is  vyalip&ta , which  may  be  rendered 
■ 41  very  excessive  sin  or  calamity.”  This,  too,  is  the  name  of  one  of  the 
yogas,  but  not  of  that  one  which  occurs  when  the  sum  of  longitudes  of 
the  sun  aud  moon  is  180°:  the  discordance  gives  occusiou  for  the  ex- 


TrdHslation  and  Notes. 


s-ijr 


287* 

i 


^planation  contained  in  verse  20,  below.  The  specification  of  the  text,  ^ 
■ that  the  aspects  take'  place  when  the  sum  of  longitudes  equals  a circlq^' 
or  a half-circlc  respectively,  or  when  the  tvfo  luminaries  are  equally  dia3 
tant  from  either  solstice,  or  either,  equinox,  is  uot  to  be  understood  as 
exact:  this  would  be  the  case  if  the  moon  had  no  motion  in  latitude;  ' 
but  owing  to  that  motion,  the  equality  of  declinations,  which Js  .the  nuriu> 
thing,  occurs  at  a time  somewhat  removed  from llmt  of  equality  of  a! is- 
tance  from  the  equinoxes : the  latter  is  ‘called  in  the  commentary  flto* 
dhyapata , 41  the  mean  occurrence  of  the  aspect/’  The  terra*  translated  - 
by  us  “upoii  tlie  s:une  and  upon  the  opposite  sides  of  cither  sofstice**  . 
arc  ek&yantigjata  and  vipuritayaruHjuta , literally  “situated  in  the  same 
and  in  contrary  ayanas ayanu  being,  as  already  pointed  out  (end  of^ 
note  to  iii.  0-12),  the  name  of  the  halves  into  which  the  ecliptic  is 
.'divided  by  llic  solstices. 


6.  When  the  longitudes  of  llu1  sun  and  moon,  bein<*.increased; 
by  the  degrees  etc.  found  for  the  coincidence  of  the  solstice  with 
its  observed  place,  arc  together  nearly  a circle  or  ncSLrly  a half- 
circle, calculate  the  corresponding  declinations. 

7.  Then,  if  the  declination  of  the  moon,  slu;  being  in  an  odd1 
quadrant,  is,  when  corrected  by  her  latitude  (vil^hepa),  greater 
than  the  declination  of  the  sun,  the  aspect  (jkita)  is  already  past; 

8.  If  less,  it  is  still  to  come:  in  an  even  quadrant,  tKc  contrary*; 
is  the  case.  If  the  nuiuiis  deed ii ml  ion  is  to  be  subtracted  from 
her  latitude,  the  rules  as  to  the  quadrant  are  to  be  reversed. 

As  in  other  processes  of  a simil.ir  < harm-tor  (m-c  above,  iv.  7-8;  vii. 
2-6),  we  arc  supposed  to  have,  found  by  trial,  l"«»r  the  starting-point  of 
the  present  calculation,  the  midnight  m \t  prcyi-ding  or  following  thflr 
occurrence  of  the  aspect  in  qiie<1i‘*n,  and  u»  have  determined  for  that 
moment  the  longitudes  and  rale**  • •f  mnliuii  of  l oti i bodies,  and  the* 
moon’s  latitude.  In  finding  lias  longitudes,  ur  are  to  apply  the  correo 
tion  for  precession this  is  the  un-auing  of  the  cxpn-v*i*»u  in  verse  6, 
drktulyag&dhitdnpdili,  which  may  be  literally  tra delated  41  degrees  etc. 
calculated  for  accordance  with  nhserved  place";  the  inference  is  lo  the 
similar  expression  for  the  provos-ion  contained  in  iii.  11.  Next  the  de- 
clinations are  to  be  found,  and  that  of  the?  moon  as  corrected  for  hep  lat- 
itude. And  since,  in  the  odd  quadrants — that  is  to  say,  the  first  and 
third,  counting  from  the  actual  vernal  equinox — declination  is  increasing, 
while  in  the  others  it  is  decreasing,  if  the  declination  in  an  odd  quad-^ 
rant  of  the  moon,  the  swifter  moving  body,  is  already  greater  than  that 
of  the  sun,  the  time  of  equality  of  declination  is  evidently  already  past,  * 
and  the  converse..  But  if,  on  the  other  hand,  the  moon's  decimation 
(using  that  ternl  in  its  Hindu  sense)  is  so  small,  and  her  latitdde'  eo 
great,  being  of  opposite  directions,  that  her  actual  distance  from  t ho 
equator jjpbjneasured  b f the  excess  of  the  latter  above  the  former,  and  so 
is  of  direction  contrary  to  Chat  of  her  declination,  thcii,  as  declination 
increases,  distance  from  the  eqmgdjr  diminishes,-  or  the  contrary  9 and  the 
conditions  aa  formerly  stated  are  reversed  throughout  ‘ 

' 81 

V 


m WryaySm&a,  . ' [«■»- 

i * ... 

9.  Multiply  the  sines  of  the  two  declinations  by  radius,  and  di- 
vjdft  by  the  sine  of  greatest  declination:  the  difference  of  the 

. corresponding- to  the  Results,  or  half  that  difference,  is  to  bo 

added-  to  the  moon’s  longitude  when  the  aspect  (pdta)  is  to  come ; 

10.  And  is  to  be  subtracted  from  the  moon’s  longitude  when 
djhe  aspeb^  is  past.  If  the  same  quantity.be  multiplied  by  the 
gran’s  motion  and  divided  by  the*  moon’s  motion,  the  result  is  an 
;equation,  in  minutes,  which*  is  to  be  applied  to  the  sun’s  place, 
in  the  same  direction  as  the  other  to  the  moon’s. 

11.  So  also  is  to  be  applied,  in  the  contrary  direction,  a like 
equation  to  the  place  of  the  moon’s  node.  This  operation  is  to 
be  repeated,  until  the  declinations  of  the  two  bodies  edme  to  be 
the  same.  ‘ 

By  this  process  are  ascertained  the  longitudes  of  the  sun  and  moon 
at  the  time  when  their  declinations  arc  equal.  Its  mcthod.may  be  briefly 
explained  as  follows.  At  the  midnight  assumed  us  the  starting-point  of. 
t£e  whole  calculation  there  is  fonnd  to  be  a certain  difference  in  the 
’two  declinations : we  desire  to  determine  how  fur  the  paths  of  the  two 
lnminaries  must  be  traced  forward  or  backward,  in  order  that  that  differ- 
ence may  be  removed ; and  this  must  be  effected  by  menus  of  a scries 
of  approximations.  We  commence  our  calculation  with  the  moon,  as 
being  the  body  of  mora  rapid  motion.  By.  a proportion  the  inverse  of 
that  upon  which  the  rule  lor  deriving  the  declination  from  the  longitude 

SL  28)  is  founded,  we  ascertain  at  what  longitude  the  moon  would  have 
c sun’s'  actual  declination,  and  at  what 'longitude  she  would  have 
her  own  actual  declination,  as  corrected  by  hur  latitude : the  difference 
between  the  two  results  is  a measure  of  the  amount  of  motion  in  longi- 
tude, forward  or  backward,  by  which  she  would  gain  or  lose  the  differ- 
ence of  declination,  if  the  sun  remained  stationary  and  her  own  latitude 
unchanged.  Since,  however,  that  is  not  the  case,  wc  are  compelled  to 
calculate  the  corresponding  motion  of  the  sun,  and  also  the  moon's  lati- 
tude in  her  hew  position ; and  in  order  to  the  latter,  wc  must  correct  the 
pbice  of  the  node  also  for*  its  retrograde  motion  during  the  interval. 
The  motions  of  the  sun  and  node  arc  found  by  the  following  proportion : 
as  the  moon's  daily  motion  is  to  that  of  the  sun,  or  to  that  of  the  node, 
Bo.ia  the  correction  applied  Up  the  moon’s  place  to  that  which  must  be 
appliedto  the  place  of  the  sun,  or  to  that  of  the  node.'  '"A  new  set  of 
positions  in  longitude  having  thus  been  found,  the  declinations  are  again 
to.be  calculated,  and  the  same  approximative  process  repeated — and  . o 
on,  until  the  desired  degree  of  accuracy  is  attained. 

The  text  permits  us  to  apply,  as  the  correction  fi>r  the  place  of  the 
moon,,  either  the  whole  or  the  half  of  the  difference  of  longitude  found 
as  the  mult  of  the  first  proportion : it  is  unessential,  of  course,  in  a 
process  of  this  tentative  character,  wliat  amount  we  assume  as  that  of 
* the  first  correction,  provided  those  which  we  apply  to  the  places  of  the 
sun  and  node  be  made  to  correspond  with  It : and  there  may  bo  cases 
in  which  we-  should  be  conducted  mojp^directly  to  the  final  result  of  the 
.*‘f;pS mess  by  taking  only  half  of  the  difference,  * 


xi.  18.];  3)giifeftttiion  and  ftotct.  28& 

, 12.  The  aspect  (pdfa)  is  at  the  time  of  Quality  of  deelinatiens ; 
if,  then,  the  moon’s  longitude,  as  thus  increased ' Or  dhninished, 
be  less  than  her  longitude  at  midnight,  the  aspect  is  paiti  ir 
greater,  it  is  to  come.  : ' 

13.  The  minutes  of  interval  between  the  tfiobn’a  kmgititde  as 
‘finally  established  and  that  at  midnight  give,  when  multiplied; 
by  sixty  and  divided  by  the  moon’s  duly  motion,  the  time  qf  the 
aspect,  in  n&dis. 

We  had  thus  far  found  only  the  longitudes  of  the'  Bun  and  moon  M 
the  time  Oi  equality  of  declination,  and  not  that  time  itself:  <the  latter 
ia  now  derived  from  the  former  by  this  proportion : as  the  moon’s  daily 
motion  is  to  a day,  or  sixty  n&dls,  so  is  the  difference  between,  the 
moon’s  longitude  at  midnight  and  at  the  time  of  the  aspect  to  the  inter- 
val between  the  latter  time  and  midnight 

* 

14.  Multiply  the  half-sum  of  the  dimensions  (m£na)6frfhe  titftt 
and  moon  by  "sixty,  and  divide  by  the  difference  of  their  daily 
motions:  the  result  is  hall1  the  duration  (sthiti),  in  nadis  etc. 

15.  The  corrected  (spliuta)  time  of  the  aspect  [pak r)  is  the  mid- 
dle: if  that  be  diminished  by  the  half-duration,  the  result  is  the 
time  of  the  commencement ; if  increased  by  the  same,  it  is  the 
time  of  the  end. 

16.  The  time  intervening  between  the  moments  of  the  begin- 
ning and  end  is  to  be  looked  upon  as  exceedingly  terrible,  hav- 
ing the  likeness  of  a consuming  lire,  forbidden  for  all  wfarko. 

The  continuance  of  the  centres  of  the  sun  and  moon  at  the  point  of 
equality  of  declination  is,  of  course,  only  momentary;  but  the  aspect 
and  its  malignant  influences  arc  to  be  lvgardcd.as  lasting  as  long  as  there 
is  virtual  contact  of  the  two  disks  at  that  point,  or  as  long  as  a central 
eclipse  of  the  aim  would  last  if  it  took  place  there.  ltB  half-duration, 
then,  or  tho  interval  from  its  middle  to  its  beginning 'or  end  respectively, 
is  found  by  a proportion,  as  follows : if  in  a day,  or  sixty  n&dls,  the  two 
centres  of:  tlio  aim  and  moon  become  separated  by  a distance  which  is 
equal  to  the  difference  of  their  daily  motions,  in  liow  many  n&gis  will 
they  become  separated  by  a distance  which  is  equal  to  the  sum  of  their 
semi-diametcis!  or 

diflf.  d.  motions : 60  : : sum  somi-diam. : half-duration 

And  if  this  amount  be  subtracted  from  and  added  to  the  time  of  equal- 
ity of  declination,  the  results  will  be  the  moments  at  which  the  aspect 
will  begin  and  end  respectively.  a 

Such  is  the  plain  and  obvious  meaning  of  the  text  in  this  passage; 
Tlio  commentator,  however,  in  accordance  with  his  interpretation,  of  me 
next  following  verse  (see  below),  declares  that  the  aspect  actually  Iststii 
as  lough*  any  portion  of  the  moon’s  disk  has  the  same  declination  with 
any  portion,  of  that  of  the  sun ; And  that,  accordingly,  i^conmvees — . 
the  moon's  declination  being  supposed  to  be  increasing — whatever  her 
remoter  limb*  comes  to  have  the  same  declination  with  tktftKMkr  Ifttib 
of  the  sunr  and  ends  when  her  nearer  li$b  comes  to  have  (bream*  do* 


240  S&rya-Siddhfoiltoti*  [xi.  16- 

dination  with  the  remoter  limb  of  the  sun — the  contrary  beihg  the  case 
when  her  declination  is  decreasing,  lie  acknowledges  that  the  text 
does  not  seem  to  teach  this,  but  puts  in  the  plea  which  is  usual  with  him 
whin  excusing  a palpable  inaccuracy  in  tlio  statements  or  processes  of 
the  treatise ; namely,  that  the  blessod  author  of  the  work,  moved  by  pity 
for  mankind,  permitted  here  the  substitution  of  difference  of  longitude 
for  difference  of  declination,  in  view  of  the  greater*. ease  of  its  calcula- 
tion, and  the  insignificance  of  the  error  involved.  That  error,  however, 
is  quite  the  reverse  of  insignificant ; it  is,  indeed,  so  very  gross  and  pal: 
pablc  that  we  cannot  possibly  suppose  it  to  have  been  committed  inten- 
tionally by  the  text : we  regard  it  as  the  easier  assumption  that  the  con- 
ditions or  the  continuance  of  the  aspect-  arc  differently  estimated  in  the 
text  and  in  the  commentary,  being  by  the  former  taken  to  be  as  we  have 
stated  them  abofc,  in  our  explanation  of  the  process.  The  view  of  the 
matter  taken  by  the  commentator,  it  is  true,  is  decidedly  the  more  nat- 
ural and  plausible  one:  there  seems  no  goo* l reason  why  an  aspect, 
which  depends  upon  equality  of  declinutiou  should  be  determined  as  to 
continuance  by  motion  in  longitnde,  or  why  the  aspect  should  only  oc- 
cur at  all  when  the  two  centres  are  equally  distant  from  the  c<  plat  or ; 
why,  in  short,  there  should  not  l>c  partial  aspects,  like  partial  eclipses  of 
the  sun.  If  the  dor-trine  of  the  commentary  is  a later  development,  or 
an  independent  form,  of  that  which  the  text-  appears  to  represent,  it  is  a 
naturally  suggested  one,  and  such  as  might  have  been  expected  to  arise. 

17.  While  any  parts  of  the  disks,  of  the  sun  and  moon  have 
the  same  declination,  so  long  is  tlirre  a continuance  of  this  aspect, 
causing  the  destruction  of  all  works. 

18.  So.  from  a knowledge  of  the  time  of  its  occurrence,  very 
great  advantage  is  obtained,  by  means  of  bathing,  giving,  prayer, 
ancestral  offerings,  vows,  oblations,  and  other  like  acts. 

We  have  translated  verse  17  in  strict  accordance  with  the  interpreta- 
tion of  it  presented  in  the  c.ofnmeutary,  although  we  must  acknowledge 
that  we  do  not  see  how  that  interpretation  is  to  he  reconciled  with  the 
actual  form  of  the  text.  The  term  cl-  n/fma'/ain,  which  the  commenta- 
tor renders  11  having  equal  declination,”  N the  same  with  that  which  in 
the  first  verso  signified  “ situated  in  the  same  ui/una”  ; mandala,  although 
it  is  sometimes  used  with  the  meaning  “ disk,”  here  attributed  to  it  by 
him,  is  the  word  employed  in  that-  same  verse  for  g 41  circle,”  or  14  UGO0” ; 
and  antarai  which  he  explains  by  ekadega , “ any  part,”  neVer,  so  far  as 
too  know,  is  properly  used  in  that  sense,  while  it  is  of  frequent  occur- 
rence elsewhere  in  this  treatise  with  the  meaning  “interval.”  The  nat- 
ural rendering  of  the  line  would  seem  to  bo  “ when  there  is  between  the 
sun  and  moon  the  interval  of  a circle,  situated  ill  the  same  ayafia.” 
This,  however,  yields  no  useful  meaning,  since  such  a description  could 
only  apply  to  an  actual  conjunction  of  the  sun  and  moon.  Wc  do  not 
ecu  how  the  difficulty  is  to  be  solved,  unless  ifcbe  allowed  us,  in-view  of 
the  discordance  already  pointed  out  as  existing  between  Jhe  plain  mean- 
ing of  the  prdVions  passage  and  that  attributed  to  it  by  the  commenta- 
1 tor,  to  assume  that  the  text  has  bccn(  tampered  with  in  this  vene,  and 
made  to  furnish  a different  sense  from  that  it  originally  had,  partly  by  a 


241 


*i-  23.]  Tifcn datum  and  Notes.  , 

.0 

forced  interpretation!  but  partly  also  by  such  an  alteration  of  its  readings' 
as  disables  it  from  yielding  auy  other  intelligible  meaning.  " 

19.  When  the  equality  of  declinations  of  the  sun  and  moon 

takes  place  in  the  neighborhood  of  the  equator,  the  aspect  may 
then  again  occur  a second  time : in  the  contrary  case,  it  may  tail 
to  occur.  v 

Near  the  equinox,  where  declination  changes  rapidly,  the  moon,  ai 
the  swifter  moving  body,  may  come  to  bavc  twice,  in  T&pid  succession, 
the  same  declination  with  the  sun,  and  upon  the -opposite  sides  of  the 
equator.  Near  the  solstice,  on  the  other  hand,  where  the  ecliptic  and 
equator  are  nearly  parallel,  the  moon — if  she  happens  to  be  nearer  the 
equator  than  the  sun  is,  owing  to  her  latitude— may  pass  the  region  in 
which  the  aspect  would  otherwise  l>c  liable  to  occur,  without  having  had 
a declination  equal  in  amount  to  that  of  the  sun. 

20.  If  the  sum  of  the  longitudes  of  the  sun  and  moon,  in  min- 
utes, on  being  divided  by  the  portion  (bhoga)  of  an  asterism 
(bha\  yields  a quotient  between  sixteen  and  seventeen,  there  is 
another,  a third,  vyatipdla . 

This  i6  simply  a special  application  of  the  rule  formerly  given  (ii.  66), 
for  finding,  for  any  given  time,  the  current  period  named  yoga.  The  sev- 
enteenth of  the  series,  as  is  shown  by  the  list  there  given,  has  the  same 
name,  vyattp&ta,  with  one  of  the  aspects  treated  of  in  this  chapter: 
judging  from  verse  22,  below,  it  is,  also  regarded  as  possessing  a like  por- 
tentous and  malignant  character. 

21.  Of  the  asterisms  (dhishnya)  Anleslui  ( sdrpa)}  Jycshtha  (din- 
dr  a),  and  Revati  ( jmushnyu),  the  last  quarters  are  junctions  of 
the  asterisms  (< bhasandhi ) ; the  first  quarter  in  the  astiti&ms  fol- 
lowing these  respectively  is  styled  ganddnta . 

22.  In  all  works,  one  must  avoid  the  terrible  trio  of  vyitip&tasf 
as  also  the  trio  of  ganddntas,  and  this  trio  of  junctions  of  js- 
terisms. 

The  division  of  the  ecliptic  into  twenty-sevenths,  or  asterisms,  coin- 
cides with  its  division  into  twelfths,  or  signs,  at  the  ends  of  the  ninth, 
eighteenth,  and  twenty-seventh  asterisms,  which  are  also  those  of  the 
fonrth,  eighth,  and  twelfth  signs  respectively.  To  this  innocent  circum- 
stance it  seems  to  bo  owing  that  those  points,  and  the  quarters  of  por- 
tions, or  arcs  of  200',  on  either  side  of  them,  are  regarded  and  stigma- 
tised as  unlucky  and  ominous.  Hence  the  tide  bhasandhi;  sandhi  is 
literally  “ putting  together,  joint,”  and  bha  is,  a.  has  been  noticed  else- 
where (note  to  iii.  9-12),  a name  both  of  the  asterisms  and  of  the  signs. 
In  which  of  its  various  senses  the  word  panda  is  used  in  the  compound 
ganddnta,  we  do  not  know. 

23.  Thus  hath  bfen  related, that  supreme,  pure,  excellent,  mys- 

terious, ahd  grand  system  of  the  heavenly  bodies : what  else  dost 
thou  desire  to  know  ? * 


In  this  verse  re-appeara  the  personality  of  the  revealer  of  the  treatise, 
the  incarnation  of  a portion  of  the  sun,  which  has  been  lost  sight  of 
since  near  the  beginning;  of  the  -work  (i.  7).  The  questiopa  addressed 
to  him,  in  answer  to  this  appeal,  by  Maya,  the  recipient  of  the  revela- 
tion, introduce  the  next  chapter,  which,  with  the  two  that  follow  it,  con- 
' tains  the  additional  explanations  and  instructions  vouchsafed  in  reply. 
The  last  three  chapters  confessedly  constitute  a separate  portion  of  the 
work,  which'  is  here  divided  into  a p&rva  khanda  and  an  uttara  kkanda, 
or  ii  “former  Part”  apd  a “latter  Part”  It  is  by  no  means  impossible 
that  the  whole  second.  Tart  is  an  appendix  to  thetext  of  the  Siadhhnta 
as  originally  constituted. 

Tho  title. of  the  next  following  chapter  is  bh&golddhyAya,  “chapter  of 
the  earth-globe” : in  the  wecond  part  of  the  treatise  the  chapters  are 
styled  adhy&ya,  “ lection,”  instead  of^  as  hitherto,  adhik&ra,  “ heading.” 


CHAPTER  XII. 

COSMOGONY,  GEOGRAPHY,  DIMENSIONS  OF  TIIE  CREATION. 

Conrans : — 1-9,  inquiries ; 10-28,  development  of  the  creative  agencies,  of  the  ele- 
ments, and  of  the  existing  creation ; 29-31,  form  and  disposition  of  the  atelier 
and  planetary  systems ; 82-44,  situation,  form,  structure,  and  divisions  of  tho 
earth;  45-72,  varying  phenomena  of  night  and  day  in  different  latitudes  and 
aones;  78-77,  revolutions  of  the  stars  end  planets ; 78-79,  regents  of  the  differ 
ent  divisions  of  time ; 80-90,  dimensions  of  the  planetary,  stellar,  and  ethereal 
orhifei 

1.  Then  the  demon  Maya,  ^prostrating  himself  with  hands  sup- 
pliantly  joined  before  him  wno  derived  his  being  from  the  part 
4>f  the  Sun,  and  revering  him  with  exceeding  devotion,  inquired 
99  follows: 

2.  O blessed  one!  of  what  measure  is  the  earth?  of  what 
form?  how  supported?  how  divided?  and  how  are  there  in  it 

' seven  interterranean  ( pdtdlq ) earths  ? 

8.  And  how  does  the  sun  cause  the  varying  distinction  of  day' 
and  night?  how  does  he  revolve  about  the  earth,  enlightening’ 
all  creatures? 

4.  For  what  reason  are  the  day  and  night  of  the  gods  and  of 
the  demons  opposed  to  one  another?  or  how  does  that  take  place 

' by  means  of  the  sun’s  completion  of  his  revolution  ? 

5.  Why  does  the  day  of  the  Fathers  consist  of  a month,  but 
that  of  mortals  of  sixty  nfidfa?  for  what  reason  is  not  this  latter 
everywhere  the  case  ? 

6.  Whence  is  it  that  the  regents  of  the  days,  years,  months,  - 
’ and  hours  (hard)  are  not  the  same  ?•  JJow  40®8  the  circle  of  as- 

tensms  (bhagana)  revolve?  what  istBe  suppprt  of  it  with  the 
planetar 


acii.  If.]  Tffuntle^n  and  Notes.  248 

7.  The' .orbits  of ’the  planets  and  stars,  uplifted  from  the  earth 
one  above  another — what  are  their  heights?  what  their  inter- 
vals ? what  their  diihensions  ? and  what  the  order  in  which  they 
are  fixed?  * 

8.  Why  are  the  rays  of  the  sun  hot  in  the  summer,  and  not 

so  in  the  winter?  how  far  do  his  rays  penetrate?  How  many 
modes  of  measuring  time  (mdna)  are  there  ? and  how  are  they 
employed?  • * 

9.  Resolve  these  my  difficulties,  0 blessed  one,  creator  of  crea- 
tures ! for  there  is  not  found  besides  thee  another  resolver,  who 
beholdcth  all  things. 


The  proper  answers  to  these  inquiries  commence  at  about  the  twenty- 
seventh  verse  of  the  chapter,  the  preceding  philosophical  history  of  tho 
development  of  the  existing  creation  being  apparently  volunteered  by 
tire  revelator.  All  the  questions  then  find  their  answers  in  this  chapter, 
excepting  that  as  to  the  methods  of  measuring  time,  which  is  disposed 
of  in  the  fourteenth  and  concluding  chnpter.  The  subject  of  the  thir- 
teenth chapter  also  sccins  not  to  be  coutcmplatcd  in  the  laying  ouj,  in 
this  passage,  of  the  scheme  of  subjects  to  be  treated  of  In  the  remain- 
der of  the  treatise. 


10.  Having  heard  the  words  thus  uttered  with  devotion  by 

Maya,  he  then  again  promulgated  this  mystoious  and  supreme 
Book  (adhydya) : ■ 

11.  Listen  with  concentrated  attention . I will  proclaim  the 
secret  doctrine  called  the  transcendental  (adhydtma):  there  is 
nothing  which  may  not  be  bestowed  on  those  who  arc  exceed- 
ingly devoted  to  me. 

12.  Yasudeva,  the  supreme  principle  of  divinity  (brahman), 
whose  form  is  all  that  is  (tat),  the  supreme  Person  ( purusha ),  un- 
manifestedj  free  from  qualities,  superior  to  the  twenty-five  prin- 
ciples, imperishable, 

13.  Contained  within  matter  (prakrti),  divine,  pervading  every- 
thing, without  and  within,  the  attractor — he,  having  in  the  first 
place  ereated  the  waters,  deposited  in  them  energy. 

14.  That  became  a golden  egg,  on  all  sides  enveloped  in  dark- 
ness: in  ft  first  became  manifested  the  unrestrained,  the  everlast- 
ing one. 

13.  He  in  the  scripture  ( chandas ) is  denominated  the  golden- 
woinbed  (hiranyagai-bha), <ne  blessed;  as  b sing  the  first  (deli)  ex- 
istence, ho  is  called  Aditya;  as  being  generator,  the  sun. 

16.  This*  sun,  likewise  named  S^vitar,  the  supreme  source  of 
light  ( jyotis ) upon  the  border  of  darkness— he  revolves,  bringing 
beings  into  being,  the  creator  of  creatures. 

17.  He  is  extolled  as  natural  illuminator,  destroyer  of  dark- 
ness, great.  The  Hymns  (raw)  are  his  disk,  the  Songs  (sdmdm) 
his  beams,  the  Liturgy  (yajQnsht)  his  form. 


244  SArya-Sidd^nlQg.  [***■ 18- 

18.  He,  the  blessed  one,  is  composed  of  the  trio  of  sacred 
scriptures,  the  soul  of  time,  the  producer  of  time,  mighty,  the 
soufof  the  universe,  all-penetrating,  subtle:  in  him  is  the  uni- 
verse established. 

19.  Having  made  for  his  chariot,  which  is  ‘composed  of  the 
universe,  a wheel  consisting  of  the  year,  and  having  yoked  the 
seven  metres  as  his  Btceds,  lie  revolves  continually. 

20.  Three  quarters  ard  immortal,  secret ; this  one  quarter  hath 
become  manifest  In  order  to  the  production  of  the  animated 
creation,  he,  the  mighty  one,  produced  Brahma,  the  principle  of 
consciousness  (nhdnkura). 

21.  Bestowing  upon  him  .the  Scriptures  (veda)  as  gifts,  and  es- 
tablishing him  within  the  egg  as  grandfather  of  all  worlds,  he 
himself  then  revolves,  causing  existence. 

22.  Then  Brahma,  wearing  the  form  of  the  principle  of  con- 
sciousness (ahankdra),  produced  mind  in  the  creation : from  mind 
was  born  the  moon ; from  the  eyes,  the  sun,  the  repository  of 
light; 

23.  From  mind,  the  ether ; thence,  in  succession,  wind,  fire, 
waters,  earth — these  five  elements  ( mahdlMiUi ) were  produced 
by  the  successive  addition  of  one  quality. 

" 24.  Agni  and  Sqpia,  the  sun  and  moon  : then  Mars  etc.  were 
, produced,  in  succession,  from  light,  earth,  ether,  water,  wind. 

25.  Again,  dividing  himself  twelve-fold,  he,  the  mighty  one, 
produced  what  is  known  as  the  signs ; and  yet  farther,  what  has 
the  form  of  the  asterisms  { nakshatra ),  tweuty-scvcn-fold.  . 

26.  Then  he  wrought  out  the  whole  animate  and  inanimate 
creation,  from  this  gods  downward,  producing  forms  of  matter 
(prakrti)  from  the  upper,  middle,  and  lower  currents  (srotax). 

27.  Having  produced  them  in  succession,  as  stated,,  by  a dif- 
ference of  quality  and  function,,  he  fashioned  the  distinctive  char- 
acter of  each,  according  to  the  showing  of  the  Scripture  (veda) — 

28.  That  is,  of  the  planets,  asterisks,  and  stars,*  of  the  earth, 
and  of  the  universe,  he  the  mighty  one;  of  gods,  demons,  ana 
mortals,  and  of  the  Perfected  (. riddhd ),  in  their  order. 

We  do  not  regard  ourselves  as  called  upon  to  enter  into  My  detailed 
examination  of  this  metaphysical  scheme  of  development  cl  the  crea- 
tion, or  to  compare  it  critically  with  the  similar  schemes  presented  in 
other  Hindu  works,  as  Mann  (chap,  i),  the  Uir&nas  (see  Wilson’s  Vishnu 
Fur&na,  Book  I),  etc.  We  will  merely  explain  a few  of  its  expressions, 
and  of  the  allusions  it  contains.  Vftsudeva  is  an  ordinary  epithet  of 
Vishnu,  and  its  usoin.  the  signification  here  given  it  seemB  indicative  of 
Vai&hnava  tendencies  oh  the  part  of  the  author  of  the  scheme.  The 
twenty-five  principles  referred  to  inverse  12  arc  those  established  by 
the  Sfiukhya  philosophy.  The  reference  in  verse  15,  first  half,  is  to  Rig- 
Veda  x.  121.  In  the  second  half  of  the  earn*  verse  we  have  a couple  of 
false  etymologies : Mitya  comes,  not  fromWt,  “first,”  but  from  cufiti, 


246 


*ii.  32.]  and  Notes . 

“ eternity” ; and  to  derive  surya,  u sun  ” from  the  root  #4,  “ generate” 
(from  which  xavitar  actually  cornea),  is  beyond  the  usual  measure  of 
Hindu  thcologico-philosophical  etymologizing.  The  Hymns,  Songs,  and 
Liturgy  are  the  three  bodies  of  scripture  commonly  known  as  the  Rig- 
Vcda,  S&ma-Vcda,  and  Yajnr-Vcda.  The  “seven  metres”  (v.  .19)  are 
those  which  are  most  often  employed  in  the  construction  of  the  Vedic 
hymns : in  parts  of  the  Veda  itself  they  arc  personified,  and  marvellous 
qualities  and  powers  are  ascribed  to  them.  The  obscure,  statement  con- 
tained in  the  first  half  of  verse  20  conics  from  verses  3 and  4 of  the 
purusha-hymn  (Rig- Veda  x.  90’:  the  hymn  is  also  found  in  others  of 
the  Vedic  texts).  The  second  half  of  verse  22  also  nearly  coincides 
with  a passage  (v.  13)  in  the  same  hymn.  Of  the  five  elements  assumed 
by  the  Hindu  philosophers,  the  first,  ether,  is  said  to  be  endowed  only 
with  the  quality  of  audibleness ; the  second,  air,  has  that  of  tangibility 
also;  the  third,  fire,  has  liolli,  along  with  color  ; to  these  qualities  the 
fourth  element,  water,  adds  that  of  savor;  the  last,  earth,  possesses  audi- 
bility, tangibility,  color,  savor,  and  odor:  this  is  according  to  the  doc- 
trines of  the  S&nkhya  philosophy.  In  verses  24  and  25  we  have  speci- 
fications introduced  out  of  consideration  for  the  general  character  and 
object  of  this  treatise : as  .also,  in  the  part  assigned  to  the  sun  in  the 
history  of  development,  wc  may  perhaps  recognize  homage  paid  to  its 
asserted  author.  For  the.  beings  called  in  verse  28  the  “perfected”  {sid- 
ilka),  see  below,  verses  3 L and  40. 

29.  This  Brail  ma-egg  is  hollow : within  it  is  the  universe,  con- 
sisting of  earth,  sk}',  etc.;  it  lias  the  form  of. a sphere,  like  a 
receptacle  made  of  a pair  ol‘  caldrons. 

30.  A circle  within  the  Brahma-egg  is  styled  the  orbit  of  the 
ether  (vyomati):  within  that  is  the  revolution  of  the  asterisms 
{bha) ; and  likewise,  in  order,  ouo  below  the  other, 

31.  Revolve  Saturn,  Jupiter,  Mars,  the  sun,  Venus,  Mercury, 
and  the  moon;  below,  in  succession.-  the  Perfected  (siddha)^  the 
Possessors  of  Knowledge  ( yulyMhttrd ),  and  the  clouds. 

The  order  of  proximity  to  the  earth  in  which  the  seven . planets  arc 
here  arranged  is,  as  noticed  above  (i.  51-52),  that  upon  which  depends 
the  succession  of  their  regency  over  the  days  of  the  week,  and  so  also 
the  names  of  the  latter.  So  far  as  tlic  first  three  and  the  last  are  con- 
cerned, it  is  a naturally  suggested  arrangement,  which  could  hardly  fail 
to  be  hit  Upon  by  any  nation  having  sulficicnt  skill  to  form  an  order  of 
succession  at  all : the  order  in  which  tho  sun.  Mercury,  and  Venus  are 
made  to  follow  one  another  is^  on  tho  other  hand,  a mailer  of  more  ar- 
bitrary detenni nation,  and  might  have  been  w.  .h  equal  propriety,  for 
aught  we  can  see,  reversed  or  otherwise  varied.  Of  the  supernatural 
beings  called  the  “possessors  of  knowledge”  (vidyddhara)  we  read  only 
in  this  verse : the  “ perfected  ” we  find  again  below,  in  vers^40,  as  inhab- 
itants of  a oity  on  tlic  earth's  surface. 

82.  Quite  in  the  middle  of  the  egg,  the  earth-globe  (lihfigola) 
stands  in  the  ether,  bearing  the  supreme  might  of  Brahma,  which 
is  of  the  nature  of  self-supporting  force. 

32 


246 


S&rya-Siddfldnta)  • [»«•  *3- 

■ 88.  Seven  cavities  within  it,  the  abodes  of  serpents  (ndga)  and 
demons  (asura),  eqdowed  with  the  savor  of  heavenly 'plants,  de- 
lightful,  are  the  interterranean  ( pdtdld ) earths. 

84.  A collection  of  manifold  jewels,  a mountain  of  gold,  is 
Meru,  passing  through  the  middle  of  the  earth-globe,  and  pro- 
truding on  either  side. 

85.  At  its  upper  end  are  stationed,  along  with  India,  the  gods, 
and  the  Great  Sages  (maharshi) ; at  its  lower  end,  in  like  man- 
ner, the  demons  (asura)  have  tlu-ir  place — each  the  enemy  of  the 
other. 

36.  Surrounding  it  on  every  side  is  fixed  next  this  great  ocean, 
like  a girdle  about  the  earth,  dividing  the  two  hemispheres  of 
the  gods  and  of  the  demons. 

37.  And  on  all  sides  of  the  midst  of  Moru,  in  equal  divisions 
of  the  ocean,  upon  islands  (dvlpa),  in  the  different  directions,  are 
the  eastern  and  other  cities,  fashioned  bv  the  gods. 

38.  At  a quadrant  of  the  earth’s  circumference  eastward,  in 
the  clime  (varsha)  llhndraqva,  is  the  city  famed  as  Yamakoti, 
having  wajls  and  gateways  of  gold. 

39.  To  the  southward,  in  the  clime  Bharata,  is  in  like  manner 
the  great  city  Lanka : to  the  west,  in  the  clime  called  Kctumala, 
is  declared  to  be  the  city  named  Uoinaka. 

40.  Northward,  in  the.  clime  Kuril,  is  declared  to  be  the  city 
called  that  of  the  Perfected  (siddha) ; in  it  dwell  the  magnani- 
mous Perfected,  free  from  trouble. 

41.  These  are  situated  also  at  a distance  from  one  another  of 
a quadrant  of  the  earth's  circumference ; to  the  north  of  them, 
at  the  same  distance,  in  Mem,  the  abode  of  the  gods  (sum). 

42.  Above  them  goes  the  sun  when  situated  at  the  equinoxes ; 
they  have  neither  equinoctial  shadow  nor  elevation  of  the  pole 
(akshonnati). 

43.  In  both  directions  from  Meru  arc  two  pole-stars  (dhruva- 
idrS),  fixed  in  the  midst  of  the  sky:  to  those  who  arc  situated  in 
places  of  no  latitude  (niraksha),  both  these  have*  their  place  in 
the  horizon. 

44.  Hence  there  is  in  those  cities  no  elevation  of  the  pole,  the 
two  pole-stars  being  situated  in  their  horizon ; but  their  degrees 
of  co-latitude  ( lambalca ) are  ninety : at  Meru  the  degrees  of  latl 
tude  (aloha)  arc  of  the  same  number. . 

Ia  these  verses  we  have  so  much  of  geography  as  the  author  of  the 
chapter  haB  seen  fit  to  connect  with  his  astronomical  explanations.  For 
a Hindu  account  df  the  earth,  it  is  wonderfully  moderate,  and  free  from 
falsehood.  ’Hie  absurd  fictions  which  the  Pur&nas  put  forth  as  geogra- 
phy arc  here  for  the  most  part  ignored,  only  two  or  three  of  the  features 
of  their  descriptions  being  retained,  and  those  in  an  altered  form.  To 
tie  Pnr&nas  (see  especially  Wilson’s  Vishnu  Pur&na,  Hook  II.,  chap, 
ii-vi),  the  earth  is  a plain,  of  immense ' dimensions.  Precisely  in  die 


247 


‘«iM4a]  Translation  and  Notes.  > 

• 

middle  of  jt  rises  Mount  Mem,  itself  of  a size  compared  with  which  the 
'earth,  an  measured  by  the  astronomers/  is  as  nothing : it  is  said  to  be 
84,000  yojanas  high,  and  buried  at  the  base  16,000  yojanas ; it  has  die 
shape  of  an  inverted  cone,  being  32,000  yojanas  in  diameter  at  its  up* . 
per  extremity,  and  only  16,000  at  the  earth's  surface.  Out  of  this  moun- 
tain the  astronomical  system  makes  the  axis  of  the  earth,  protrading  at  ’ 
either  extremity,  indeed,  but  of  dimensions  wholly  undefined.  As  the 
Pur&nas  declare  the  summit  of  Mcru,  and  the  mountains  immediately 
supporting  it,  to  be  the  site  of  the  cities  inhabited  by  the  different  divin- 
ities, so  also  we  have  here  the  gods  placed  upon  the  northern  extremity 
of  the  earth's  axis,  while  their  foes,  the  spirits  of  darkness,  have  their 
scat  at  the  southern.  The  central  circular  continent,  more  than  100,000 
yojanas  in  diameter,  in  the  midst  of  which  Meru  lies,  is  named  Jambft- 
dvlpa,  “the  island  of  the  rose-apple  tree":  it  is  intersected  by  six  paral- 
lel ranges  of  mountains,  miming  east  and  west,  and  connected  together 
by  short  cross-ranges:  the  countries  lying  between  these  ranges  are 
styled  'varshas,  “chines,”  ami  an*  all  ftiliy  named  and  described  in  the 
Pur&nas,  as  are  the  mountain-ranges  themselves.  The  half-moon-shaped 
strips  lying  at  the  bases  of  the  mountains  on  the  eastern,  southern,  west- 
ern, and  northern  edges  of  the  continent,  are  called  by  the  same  names 
that  arc  given  by  our  text  to  the  four  insular  dimes  which  it  sets  up. 
Bh&rata  is  a real  historical  nanus,  appearing  variously  in  the  curly  Hindu 
traditions;  Kuru,  or  Uitara-Kuru,  is  a title  applied  in  Hindu  geography 
of  a less  fictitious  character  to  the  country  or  people  situated  beyond  tlie 
range  of  the  Himalaya ; the  other  two  names  appear  to  "be  altogether 
imaginary.  #The  Vuraiuis  say  nothing  of  cities  in  these  four  climes. 
Lank&,  as  noticed  al»o\e  (i.  02),  is  properly  an  appellation  of  the  island 
Ceylon  ; and  Komaka  undoubtedly  comes  from  the  name  of  the  great 
city  which  was  the  mistress  of  the  western  world  at  the  period  of  lively 
commercial  intercourse  between  India  and  tbe  Mediterranean:  the  other 
two  cities  are  pure  figments  of  the  imagination/  Our  treatise,  it  will  be 
observed,  ignores  the  system  of  continents,  or  dvtjms,  and  simply  sur- 
rounds the  earth  with  an  ocean  in  the  midst,  like  a girdle : the  Pur&nas 
encompass  Jambfidvipa  about  with  six  other  tlvlpas , or  insular  ring- 
shaped  continents,  each  twice  as  vast  as  that  which  it  encloses,  and  each 
separated  from  the  next  by  an  ocean  of  the  same  extent  with  itself.  Of 
these  seven  occatis,  the  first,  which  washes  the  shores  of  JambiVMpa,  is' 
naturally  enough  acknowledged  to  be  composed  of  salt  water : but  the 
second  is  of  syrup,  thg  third  of  wine,  the  fourth  of  clarified  butter,  the 
fifth  of  whey,' the  sixth  of  milk,  and  the  last  of  sweet  water.  Outside 
the  latter  is  an  uninhabited  land  of  gold,  and  on  its  border,  as  the  out- 
most verge  of  creation,  is  the  monstrous  wall  of  t le  LokAloka  mountains, 
beyond  which  is  only  nothiugness  and  darkness. 

The  author  of  the  SiddhAuta-firoinani,  more  submissive  than  the 
writer  of  our  chapter  to  the  authority  of  tradition,  accepts  (Gol&dhy., 
chap,  ii)  the  scries  of  concentric  continents  and  oceans.  but  gives  them 
all  a place  in  the  unknown  southern  hemisphere,  while  he  regards  Jnm- 
bfidvlpa  as1  occupying  the  whole  of  the  northern. 

The  pdt&las,  or  interterranean  cavities,  spoken  of  in  verse  33,  are,  also 
an  important  feature  of  the  Puranic  geography.  If  our  author  has  not 


248 


S&rya-Siddh&nta,  [*«.  44- 

had  the  good  sense  to  reject  them,  along  with  the  insular  continents,  he 
at  least  passes  them  by  with  the  briefest  possible  notice.  In  the  Purfknaa 
they*  are  declared  to  be  each  of  them  10,000  yojanas  in  depth,  and 
their  divisions,  inhabitants,  and  productions  are  described  with  the  same 
ridiculous  detail  os  those  of  the  continents  on  the  earth's  surface. 

It  will  be  observed  that  the  text,  although  exhibiting  in  verse  41  a 
distinct  apprehension  of  the  fact  that  the  pole  is  situated  to  the  north- 
ward of  alt  points  of  the  equator  alike,  yet,  in  describing  the  position 
of  the  four  great  cities,  speaks  as  if  there  were  a north  direction  from 
Aferu,  in  the  continuation  of  the  line  drawn  to  the  latter  from  Lankh, 
and  au  east  and  west  direction  at  right  angles  with  this. 

For  the  terrestrial  equator,  considered  ns  a line  or  circle  upon  the 
earth’s  surface,  there  is  no  distinctive  name;  it  is  referred  to  simply  as 
the  place  “ of  no  latitude  ” ( niraksha , vt/aksha). 

45.  In  the  half- revolution  beginning  with  Aries,  the  sun,  be- 
ing in  the  hemisphere  of  the,  gods,  is  visible  to  the  gods:  but 
while  in  that  beginning  with  Libra,  he  is  visible  to  the  demons, 
moving  in  their  hemisphere. 

46.  Hence,  owing  to  his  exceeding  nearness,  the  rays  of  the 
sun  are  hot  in  the  hemisphere  of  the  gods  in  summer,  but  in 
that  of  the  demons  in  winter : in  the  contrary  season,  they  are 
sluggish. 

47.  At  the  equinox,  both  gods  and  demons  see  the  sun  in  the 
horizon ; their  day'  and  niglil  are  mutually  opposed  to^ach  other. 

48.  The  sun,  rising  at  the  first  of  Aries,  while  moving  on 
1 northward  for  three  signs,  completes  the  former  half-day  of  the 

dwellers  upon  Meru ; 

49.  In  like  manner,  while  moving  through  the  three  signs  be- 
ginning with  Cancer,  lie  completes  the  latter  half  of  their  day : 
he  accomplishes  the  same  lor  the  enemies  of  the  gods  while 
moving  through  the  three  signs  beginning  with  Libra  and  the 
three  beginning  with  Capricorn,  respectively. 

50.  Hence  are  their  night  and  day  mutually  opposed  to  one 
another;  and  the  measure  of  the  day  and  night  is  by  the  com- 
pletion of  the  sun’s  revolution. 

51.  Their  mid-day  and  midnight,  which  are  opposed  to  one 
another,  are  at  the  end  of  each  half-revolution  from  solstice  to 
solstice  (qyana).  The  gods  and  demoas  each  suppose  themselves 
to  be  uppermost. 

52.  Others,  too,  who  are  situated  upon  the  same  diameter 
( samasulrastha ),  think  one  another  underneath — as  the  dwellers 
in  nhadruqva  and  in  Ketumula,  and  the  inhabitants  of  LankS 
and  of  the  city  of  the  Perfected,  respectively. 

53.  And  everywhere  upon  the  globe  of  the  earth,  men  think 
their  own  place  to  be  uppermost : but  since  it  is  a globe  in  the 
ether,  where  .should  there  be  an  upper,  or  where  an  under  side 
of  it? 


xii.  05.] 


Translation  and  Notes. 


249 


. 64.  Owing  to  the  littleness  of  their  own  bodies,  men,  looking 
in  every  direction  from  the  position  they  occupy,  behold  this 
earth,  although  it  is  globular,  as  having  the  form  of  a wheel. 

66.  To  the  gods,  this  sphere  of  astcrisms  revolves  toward  the 
right;  to  the  enemies  of  the  gods,  toward  the  left;  in  a situa- 
tion of  no  latitude,  directly  overhead— always  in  a westerly  di- 
rection. 

56.  lienee,  in  the  latter  situation,  the  day  is  of  thirty  nSdfa, 
and  the  night  likewise : in  the  two  hemispheres  of  the  gods  and 
demons  there  take  place  a deticiency  and  an  excess,  always  op- 
posed to  one  another. 

57.  During  the  half-revolution  beginning' with  Aries,  there  is 
always  an  excess  of  the  day  to  the  north,  in  the  hemisphere  of-  • 
the  gods — greater  according  to  distance  north — and  a correspond- 
ing deficiency  of  the  night ; in  the  hemisphere  of  the  demons, 
the  reverse. 

58.  In  the  half-revolution  beginning  witli  Libra,  both  the  de- 
ficiency and  excess  of  day  and  night  in  the  two  hemispheres  are 
the  opposite  of  this : the  method  of  determining  them,  which  is 
always  dependent  upon  situation  (dera)  and  declination,  has  been 
before  explained. 

69.  Multiply  the  earth’s  circumference  by  the  sun’s  declination 
in  degrees,  and  divide  by  the  number  of  degrees  in  a circle:  the 
result,  in  ypjanas,  is  the  distance  from  the  place  of  no  latitude 
where  the  sun  is  passing  overhead. 

60.  Subtract  from  a quarter  of  the  earth’s  circumference  the 
number  of  yojanas  thus  derived  from  the  greatest  declination : 
at  the  distance  of  the  remaining  number  of  yojanas 

61.  There  occurs  once,  at  the  end  of  the  sun’s  half-revolution 
from  solstice  to  solstice,  a day  of  sixty  nadis,  and  a night  of  the 
same  length,  mutually  opposed  to  one  another,  in  the  two  hemi- 
spheres of  the  -gods  and  of  the  demons: 

.62.  In  the  intermediate  region,  the  deficiency  and  excess  of' 
day  and  night  arc  within  the  limit  of  sixty  nadis ; beyond,  this 
sphere  of  astcrisms  (bha)  revolves  perversely. 

63.  Subtract  from  a quarter  of  the  earth’s  circumference  the 
number  of  ‘yojanas  derived  from  the  declination  found  by  the 
sine  of  two  signs : at  that  distance  from  the  equator  the  sun  is 
not  seen,  in  the  hemisphere  of  the  gods,  wb  m in  Sagittarius  and 
Capricorn ; 

64.  So  also,  in  the  hemisphere  of  the  demons,  when  in  Gemi- 
ni and  Cancer : in  the  quarter  of  the  earth’s  circumference  where 
her  shadow  is  lost,  the  sun  may  be  shown  to  be  visible. 

, 65.  Subtract  from  the  fourth  part  of  the  earth’s  periphery 
(kakaHid)  the  number  of  yojanas  derived  from  the  declination 
found  by  the  sine  of  one  Bign : at  the  distance  from  the  place  of 
no  latitude  of  the  remaining  number  of  yojanas,  , 


260  S&rya-Siddhdnla,  [xii.'8fl- 

■ ■ 

66.  The  sun,  when  situated  in  Sagittarius,  Capricorn,  Scorpio, 
and  Aquarius,  is  not  seen  in  the  hemisphere  of  the  gods  ; in 
that  of  the  demons,  on  the  other  hand,  wneu  in  the  four  signs 
commencing  with  Taurus. 

67.  At  Meru,  the  gods  behold  the  sun,  after  but  a. single  rising, 
during  the  half  of  his  revolution  beginning  with  Aries ; the  de- 
mons, in  like  manner,  during  that  beginning  with  Libra. 

68.  The  sun,  during  his  northern  and  southern  progresses 
{ayana)  revolves  directly  over  a fifteenth  part  of  the  earth’s  cir- 
cumference, on  the  side  both  of  the  sods  and  of  the  demons. 

69.  Between  those  limits,  the  shadow  is  cast  both  southward 
and  northward ; beyond  them,  it  falls  toward  the  Meru  of  either 
hemisphere  respectively. 

70.  When  passing  overhead  at  Bhadrayva,  the  sun  is  rising  in 
BhSrata ; it  is,  moreover,  at  that  time,  midnight  in  Ketumala, 
and  sunset  in  Kuru. 

71.  In  like  manner  also  lie  produces,  by  his  revolution,  in 
Bhfirata  and  the  other  climes,  noon,  sunrise,  midnight,  and  sun- 
set, reckoning  from  cast  to  west. 

72.  To  one  going  toward  Meru,  there  take  place  an  elevation 
of  the  pole  (dhruva)  and  a depression  of  the  circle  of  asterisms ; 
to  one  going  toward  the  place  of  no  latitude,  on  the  contrary,  a 
depression  of  the  former  and  an  elevation  of  the  latter. 

This  detailed  exposition  of  the  varying  relations  of  day  and  night  in 
different  parts  of  the  glohc  is  quite  creditable  to  the  ingenuity,  and  U19 
distinctness  of  apprehension,  of  those  by  whom  it  was  drawh  out.  It 
is  for  the  most  part  so  clearly  expressed  as  to  need  no  additional  expla- 
nations : we  shall  append  to  it  only  a few  brief  remarks. 

How  far,  in  verse  46,  a true  statement  is  given  of  the  cause  of  the 
heat  of  summer  and  the  cold  of  winter,  may  he  made  a matter  of  some 
question  : tlie  word  which  we  have  translated  11  nearness”  (dsannatd)  lias 
no  light  to  mean  “ directne*?,  perpendicularity.”  and  yet,  when  taken  in 
connection  with  the  preceding  verse,  it  may  perhaps  admit  that  signifi- 
cation. The  second  chapter  shows  that  the  Hindus  knew  very  well 
that  the  sun  is  actually  nearer  to  the  whole  earth  in  winter,  or  when 
near  his  perigee,  than  in  summer.  • 

The  expression  ayandnta,  “at  the  end  of  an  ayana”  employed  in 
verses  51  and  01,  and  which  we  have  rendered  by  a paraphrase,  inigli1 
perhaps  have  been  as  well  translated,  briefly  and  simply,  “at  either 
solstice.”  Prqbably  ayana , as  used  in  the  sense  of  “ solstice”  {see  above, 
end  of  note  to  iii.  0-12),  is  an  abbreviated  form  of  ayanAnta , like /yd  for 
jyArdha  (ii.  15-27),  aiid  aksha  for  akshonnati  (i.  60). 

In  verse  55,  wc  have  translated  by  “ toward  the  right”  and  “ toward 
the  left”  the  adverbs  savyam  and  apaaavyam,  which  mean  literally  “left- 
wise”  and  “ right-wise” ; that  is  to  say,  in  such  a manner  that  the  left 
side  or  the  right  side  respectively  of  the  thing  making  the  revolution  is 
turned  toward  that  about  which  the  revolution  is  made,  this  being  the 
Hindu  mode  of  describing  the  pacing  of  one  person  about  another  per- 


251 


xiifW.]  Translation  and  Notes. 

son  or  thing,  especially  in  respectful  salutation  and  in  religious  cere- 
monial. 

The  natural  measure  of  the  day  and  of  the  night  is  assumed  in  verse 
56  etc.  to  he  the  li^f  of  a whole  day,  or  thirty  n&dts,  and  any  deviation 
from  that  norm  is  regarded  as  an  excess  \dhana,  vrddhi)  or  a deficiency 
(rna,  h&ni,  kxhar/a).  The  former  processes  referred  to  at  the  end  of 
verse  58  are  those  taught  in  ii.  60-62. 

We  have  already  above  (note  to  i.  63-65)  called  attention  to  the  fact 
that  all  the  Hindu  measurements  of  longitude  and  latitude  npon  the 
earth's  surface  are  made  in  yojanas,  and  not  in  degrees. 

The  expression  “ perversely"  ( vlparita ) in  verse  62  is  explained  by 
the  commentator  to  mean  “ in  such  manner  that  the  rules  as  already 
given  cannot  be  applied";  since  the  sine  of  the  ascensional  difference 
(cam — see  ii.  61)  as  found  by  them  would  be  greater  than  radius. 

The  latter  half  of  verse  61  is  obscure : its  meaning  seems  to  be,  as 
explained  by  the  commentator,  that  over  a corresponding  portion  of  the 
earth’s  surface  in  the  contrary  hemisphere  the  sun  is  continuously  visible 
during  the  same  period,  the  shadow  of  the  cart)],  which  is  the  cause  of 
night,  not  covering  that  portion. 

73.  The  circle  of  as  ter  is  ms,  bound  at  the  two  poles,  impelled 
by  the  provector  (pravaha)  winds,  revolves  eternally:  attached 
to  that  are  the  orbits  of  the  planets,  in  their  order. 

74.  The  gods  and  demons  behold  the  sun,  after  it  is  once  risen, 
for  half  a year ; the  Fathers  (pi taros),  who  have  their  station  in 
the  moon,  for  a half-month  (pnksha) ; and  men  upon  the  earth, 
during  their  own  day. 

75.  The  orbit  (AafoAa)  of  one  that  is  situated  higher  up  is 
large ; that  of  one  situated  lower  down  is  small.  Upon  a great 
orbit  the  degrees  arc  great ; so  also,  upon  a small  one,  they  are 
small. 

76.  A planet  situated  upon  a small  circuit  (< bhraraana ) traverses 
the  circle  of  constellations (bhagana)  in  a little  time;  one  revolv- 
ing on  a large  circle  (mandala),  in  a long  time. 

77.  The  moon,  upon  a very  small  orbit,  makes  many  revolu- 
tions : Saturn,  moving  upon  a great  orbit,  makes,  as  compared 
with  .her,  a rnucli  less  number  of  revolutions. 

The  connection  and  orderly  succession  of  subjects  is  by  qo  means 
strictly  maintained  in  this  part  of  the  Miaptcr.  The  seventy-fourth  verse 
is  palpably  out  of  place,  and  is,  moreover,  in  great  part  superfluous;  for 
the  statement  contained  in  its  first  half  has  alrcai  v twice  been  made,  in 
verses  45  and  67,  and  in  the  latter  passage  in  nearly  the  same  teqns  as 
here:  its  last  specification,  too,  is  of  a matter  too  obvious  to  call  for 
notice.  Nevertheless,  the  verse  cannot  well  be  spared  from  the  chapter, 
since  it  contains  the  only  answer  which  is  vouchsafed  to  the  question  of 
verse  5,  above,  respecting  the  day  and  night  of  the  Fathers.  In  the 
assignment  of  the  different  divisions  of  time,  as  single  days,  to  different 
orders  of  beifigs,  the  month  has  been  given  to  the  pitards , 11  Fathers,"  or 
manes  of  the  departed,  and  they  are  accordingly  located  in  the  moon, 


252  S&rya-Siddhdnta,  [xii:  77- 

each  portion  of  whose  surface  enjoys  a recurrence  of  day  and  night 
once  in  each  lunar  month.  The  next  following  verses,  75  to  77,  are  a 
rather  unnecessary  amplification  of  the  idea  already  expressed  in  i.  26- 
27  ; but  they  answer  well  enough  here  as  special  introduction  to  the  de- 
tailed exhibition  of  the  measurements  of  the  planetary  orbits  which  is 
to  follow.  Before  that  is  brought  in,  however,  we  have  the  connection 
again  broken,  by  the  intrusion  of  the  two  following  verses,  respecting 
the  regents  of  years,  months,  days,  aiul  hours. 

78.  Counting  downward  from  Saturn,  the  fourth  successively 
is  regent  of  the  day ; and  tne  third,  in  like  manner,  is  declared 
to  be  the  regent  of  the  year; 

79.  Reckoning  upward  from  the  moon  are  found,  in  succession, 
the  regents  of  the  months ; the  regents  of  the  hours  (hard)i  also, 
occur  in  downward  order  from  Saturn. 

This  passage  appears  to  be  introduced  here  as  answer  to  the  inquiry 
propounded  in  verse  6,  above.  Instead,  however,  of  explaining  why  the 
different  divisions  of  time  are  placed  under  the  superintendence  and  pro- 
tection of  different  planets,  the  text  contents  itself  with  reiterating,  in  a 
different  form,  what  had  already  been  said  before.1  (i.  51-52)  respecting 
the  order  of  succession  of  the  regents  of  the  successive  periods ; but 
adding  also  the  important  and  significant  specification  respecting  the 
hours,  or  twenty-fourths  of  the  day.  AVc  have  sufficiently  illustrated 
the  subject,  in  connection  with  the  other  passage;  we  will  only  repeat 
here  that,  the  planets  being  regarded  sir  standing  in  the  order  in  which 
they  are  mentioned  in  verse  31,  above,  their  successive  regency  over  the 
hours  is  the  one  fundamental  fact  upon  which  all  the  rest  depend,  each 
planet  being  constituted  lord  also  of  the  day  whose  first  hour  is  placed 
under  his  charge,  and  so  likewise  of  the  month  and  of  the  year  over 
whose  first  hour  and  day  he  is  regent — neither  the  mouth  nor  the  year, 
any  more  than  the  hour  itself,  being  divisions  of  time  which  are  known 
to  the  Hindus  in  any  other  uses,  and  the  name  of  the  hour,  horA,  which 
is  the  Greek  *3 betraying  the  source  whence  the  whole  system  was 
introduced  into  India. 

80.  The  orbit  ( kakshu. :)  of  the  astermms  (Ma)  is  the  circuit 
( bhramana ) of  the  sun  multiplied  by  sixty  : by  so  many  yojanas 
docs  the  circle  of  the  astcrisrris  revolve  above  all. 

81.  If.  the  stated  number  of  revolutions  of  the  moon  in  an 
jEon  (Jcdlpa)  be  multiplied  by  "the  moon’s  orbit,  the  result  is  to 
be  known  as  the  orbit  of  the  ether : so  far  do  the  rays  of  the  sun 
penetrate. 

82. -  If  this  be  divided  by  the  number  of  revolutions  of  any 
planet  in  an  vTCon  ( lealpa ),  the  result  will  be  the  orbit  of  that 
•planet:  divide  this  by  the  number  of  terrestrial  days,  and  the 
result  is  the  daily  eastward  motion  of  them  all. 

83.  Multiply  this  number  of  yojanas  of  daily  motion  hv  the 
oibit  of  the  moon,  and  divide  by  a planet’s  own  orbit ; the  re- 
sult is,  when  divided  by  fifteen,  its  daily  motion  in  minutes. 


Translation  and  Notes. 


253 


xil.  $0.] 

84.  Any  orbit,  multiplied  by  the  earth's  diameter  arid  divjded 
by  the.  earth's  circumference,  gives  the  diameter  of  that  orbit; 
and  this,  being  diminished  by  the  earth’s  diameter  and  halved, 
gives  the  distance  of  the  planet. 

85.  The  orbit  of  the  moon  is  three  hundred  and  twenty-four ' 
thousand  yojnnas  : that  of  Megsury’s  conjunction  (pghra)  is  one 
million  and  forty-three  thousand,  two  hundred  and  nine: 

86.  That  of  Venus's  conjunction  {fighra)  is  two  million,  six 
hundred  and  sixty-four  thousand,  six  hundred  and  thirty-seven : 
next,  that  of  the  sun,  Mercury,  and  Venus  is  four  million,  three 
hundred  and  thirty-one  thousand,  five  hundred : 

87.  That  of  Mars,  too,  is  eight  million,  one  hundred  and  forty- 
six  thousand,  nine  hundred  and  nine ; that  of  the  moon's  apsis 
( ucca ) is  thirty-eight  million,  three  hundred  and  twenty-eight 
thousand,  Tour  hundred  ami  eighty-four : 

88.  That  of  Jupiter,  fifty- one  million,  three  hundred  and  sev- 
enty-five thousand,  seven  hundred  and  sixty-four : of  the  moon’s 
node,  eighty  million,  live  hundred  and  seventy-two  thousand, 
eight  hundred  and  sixty -four : 

89.  Next,  of  Saturn,  one  hundred  and  twenty-seven  million, 
six  hundred  and  sixty -eight  thousand,  two  hundred  and  fifty-five : 
of  the  asterisins,  two  hundred  and  fifty-nine  million,  eight  hun- 
dred ami  ninety  thousand,  and  twelve : 

90.  The  entire  circumference  of  the  sphere  of  the  Brahma-egg 
is  eighteen  quadrillion,  seven  hundred  and  twelve  trillion,  eighty 
billion,  eight  hundred  ami  sixty-fon^ million:  within  this  is  the 
pervasion  of  the  sun's  rays. 

Wc  present  below  the  numerical  data  given  in  these  verses,  in  a form 
easier  of  reference  and  of  comparison  with  the  like  data  of  other 
treatises : > 


Planrt  etc. 

Orbit,  in  jejnnu. 

Muon, 

3a4,ooo 

" apsis, 

38.3a8.484 

u node, 

80,572,864 

Mercury  (conjunction). 

1,043,309 

Venus  (conjunction), 

3,664.637 

Sun, 

4.33i,5oo 

Mars, 

8,146,909 

J upitcr,  9 

51,375-764 

Saturn, 

ia7.668.355 

'Astcirisins, 

a59.890.0r3r 

Universe, 

18,71 3,080,864,000,6^0 

We  have  already  more  than  once  (see  above,  notes  to  i.  25-27,  and# 
iv.  1)  Jiad  occasion  tt>  notice  upon  what  principles  the  orbits  of  the  plan- 
ets, an  hero  stated,  were  constructed  by  the  Hindus.  That  of  the  m^on 
(sec  note  to  iv.  1)  was  obtained  by  a true  process  of  calculation,  from 
genuine  data,  and  is  a tolerable  approximation  to  the  truth : all  the 
* 33 


254 


[mi.  if«- 


S&rya-Siddhdhta, 

otlif  rs.are  manufactured  out  of  this,  upon  the  arbitrary  and  false  assump- 
tion that  the  mean* motion  of  all  the  planets,  each  upon  its  own  orbit.  ?s 
of  equal  absolute  amount,  and  lienee,  that  its*  apparent  value  in  each 
case,  as  seen  by  us,  is  inversely  as  the  planet's  distance,  or  that  the  di- 
' mansions  of  the  orlut  are  directly  as  the  time  employed  in  traversing 
it,  or  as  the  period  of  sidereal  revolt^ ion.  These  dimensions,  then,  may 
be  found  by  various  methods:  upon  dividing  the  circumference  of  tin- 
moon's  orbit  by  her  time  of  sidereal  revolution,  we  obtain  as  the 
amount  of  her  daily  motion  in  yojanns  11,858.717  nearly  (more  exactly 
11,858.71(593  + );  and  multiplying  this  by  the.  time  of  sidereal  revolu- 
tion of  any  planet,  we  obtain  that  planet's  orbit.  This  is  equivalent  to 
making  the  proportion 

moon's  sid.  rev.:  planet's  rid.  rev. : : moon's  orbit:  planei/n  orbit 

And  since  the  tinier  of  sidereal  revolution  of  the  planets  arc  inversely 
as  the  number  of  revolutions  made  bv  them  in  any  given  period,  this 
proportion,  again,  is  equivalent  to 

planet's  no.  of  rev.  in  an  .Eon  : moon's  do. : : moon's  orbit : planet's  orbit 

This  is  the  form  of  the.  proportion  from'  which  is  derived  the.  rule  a* 
stated  in  the  text,  only  the  latter  designates  the  product  of  the  multi- 
plication of  the  moon's  orbit  by  her  number  of  revolutions  as  the  orbit 
of  the  ether  (dkdea),  or  the  circumference  of  the  Bjahrna-egg,  within 
which  the  whole  creation,  as  above  taught,  is  enclosed.  This  is  the  same 
thing  with  attributing  to  the  outermost  shell  of  the  universe  one  com- 
plete/evolution  in  an  Ah* u (talpn)M  of  4,320,000,000  years. 

There  is  one  feature  of  the  system  exposed  in  ibis  passage  which  to 
us  is  hitherto  quite  inexplicable:  it  is  the  assignment  to  the  asterMus 
■ of  an  orbit  sixty  times  as  greaf  as  that,  of  the  sun.  This,  according  to 
all  the  analogies  of  the  system,  should  imply  a revolution  of  the  aster- 
isms  eastw  ard  about  the  earth  once  in  each  period  of  sixty  sidereal  years. 
The  same  orbit  is  found  allotted  to  them  in  the  Siddhuuta-^iroinuni 
(Ganitadhy.,  iv.  ft),  and  it  is  to  be  looked  upon,  accordingly,  as  an  es- 
sential part  of  the  general  Hindu  astronomical  system.  We  do  not  sec 
iiow  it  is  to  be  brought  into  connection  with  tin?  other  doctrines  of  -the 
system,  or  what  can  be  its  origin  and  import — unless,  indeed,  it  be 
merely  an  application  to  the  asterisms,  in  an  entirely  arbitrary  way,  of 
the  general  law  that  everything  must  be  made  to  ruvolvc  about  the 
earth  as  a centre.  We  have  noticed  above  (bote  to  iii.  9-12)  its  incon- 
sistency with  the  doctrine  of  the  precession  adopted  in  this  treatise. 

The  dimensions  of  the  several  orbits  stated  in  the  text  are  for  the  iiiosl 
part  correct,  being  such  as  are  derived  by  the  processes  above  explained 
from  the  numbers  of  sidereal  revolutions  given  in  a former  passage  (i.  29 
-34).  There  is,  however,  one  exception:  the  orbit  of  Mercury,  as  so 
derived,  is  1,043,207.8,  and  the  number  adopted  by  the  text — which  re- 
jects fractions  throughout,  taking  the  nearest  whole  number — should  be, 
^accordingly,  —208,  and  not  —209.  If  wc  took  os  divisor  the  number  of 
Mercury's  revolutions  in  an  .dSon  as  corrected  by  the  bija  (see  note  to 
i.  £9-34),  wc  should  actually  obtain  for  his  orbit  the  value  given  it  by 
tLd  text;  the  exact  quotient  being  1,043,208.7.3.  But  as  none  of  the 
other  orbits  given  arc  such  as  would  be  found  by  admitting  the  several 


Translation  and  Notes . 


255 


xiii.  fcj 

corrections  of  the  hlja%  it  seems  preferable  to  assume  that  the  text  has  at 
this  point  become  corrupt,  or  else  that  the  author*of  the  chapter  made 
a blunder  in  one  of  his  calculations.4  „ 

The  value  of  a minute  of  arc  upon  the  moon's  orbit  being  fifteen  yo- 
janas  (sod  note  to  iv.  2<-3),  the  value,  in  minutes,  of  any  planet's  mean 
daily  motion  may  be  readily  found  from  its  orbit  by  the  proportion  of 
which  the  rule  given  in  verse  83  is  a T statement,  as  follows:  as  the  dis- 
tance, or  the  orbit,  of  the  planet  in  question  is  to  that  of  the  moon,  so 
is  the  moon’s  mean  motion  in  minutes,  or  11, *58.717  -J- 15,  to  that  of 
the  planet. 

In  verso  84  we  avc  taught  to  calculate  the  distance  of  any  planet  from 
the  earth's  surface  : in  order  to  this,  we  are  first  to  find  the  diameter  of 
the  planet's  orbit,  adopting,  as  the  ratio  of  the  diameter  to  the  circum- 
ference, that  of  the  diameter  to  the  circumference  «»f  the  earth — the  for- 
mer, of  course,  as  calculated  (i.  59)  by  the  false  ratio  of  1 : *J  JO.  ^ After 
being  guilty  of  so  gross  an  inaccuracy,  it  is  ijiftto  superfluous, aand  a mere 
affectation  of  exactness,  to  take  into  account  so  trivial  a quantity  as  the 
radius  of  the  earth,  in  estimating  the  planet's  distance  from  the  earth. 

In  the  doctrine  of  the  orbits  of  the  planets,  as  here  laid  down,  we 
have  once  more  a total  negation  of  the  reality  of  their  cpieyclical  mo- 
tions, and  of  their  consequently  varying  distances  from  the  earth  in  dif- 
ferent parts  of  their  revolutions. 


C IT  APT  Ml  XIII. 

OF  THE  AR  MILT.  All  Y SP1IKRE,  AN D OTHER  INSTRUMENTS. 

Contents:—  1-13,  construction  and  equipment  of  the  armillary  sphere;  13*15,  po- 
sition of  certain  points  ami  sines  upon  it;  ir#-lfl,  its  adjustment  and  revolution; 

17-25,  other  instruments,  especially  lor  iho  determination  of  time. 

1.  Then,  having  bathed  in  a secret  and  pure  place,  bdlng  pure, 
.adorned,  having  worshipped  with  devotion  the  sun,  the  planets, 
the  nstcrisms  (win),  and  the  elves  (gn/iyaka), 

2.  Let  the  teacher,  in  order  to  the  instruction  of  the  pupil — 
hitnself  beholding  everything  clearly,  in  accordance  with  the 
knowledge  handed  down  by  successive  communication,  and 
learned  from  the  mouth  of  the  master  (guru) — 

3.  Prepare  the  wonder-working  fabric  o'  the  terrestrial'  and 
stellar  sphere  ( bhubhagola ) ..... 


* The  last  six  verses  of  the  chapter,  which  contain  the  numerical  data,  may  very 
possibly  be  a later  addition  to  its  original  content : thu  Ayiu-Akbari  (as  translated 
by  (Hull win),  in  its  account  of  thu  astronomy  of  the  Hindus,  which  it  professedly 
buses  upon  the  Sflrya-Siddhfintn,  gives  these  orbits  (8vo.  edition,  London.  1SU0, 
ii.  806),  but  with  the  fractional  parts  of  yojnnas,  ns  if  independently  derived  from 
the  data  and  by  tho  rules  of  the  text:  the  orbit  of  Mercury  it  state*  correctly,  as 
1,043,207ft  yojanas. 


256 


. S&rya-Siddhdnta 


[xill  3 


We  have  already  remarked  above  (note  to  xii.  1-0)  that  the  subject 
of  this  chapter  is  one  respecting  which  no  inquiries  were  addressed  at 
the  beginning  of  the  preceding  chapter  by  the  recipient  to  the  commu- 
nicator of  the  revelation,  and  that  tne  chapter  accordingly  wears  in  some 
measure  the  aspect  of  an  interpolation.  It  comes  in  here  as  furnishing 
a means  of  illustrating  to  the  pupjl  the  mutual  relations  of  the  earth 
and  the  heavens -as  explained  in  tne  last  chapter — and  yet  not  precisely 
as  there  explained ; for  it  gives  a representation  only  of  the  earth  and 
of  the  one  starry  concave  upon  which  the  apparent  movements  of  all 
the  heavenly  bodies  are  to  be  traced,  and  not  of  the  concentric  spheres 
and  orbits  out  of  which  the  universe  has  been  declared  to  be  constructed. 
The  chapter  has  a peculiar  title,  unlike  that  of  any  other  iu  the  treatise  : 
it  is  styled  jyotuhopanuhadadhydya , “lection  of  the  astronomical  Upa- 
nUbad.”  Upanishad  is  the  name  ordinarily  given  to  such  brief  treatises, 
of  the  Jater  Vedic  period,  or  of  times  yet  more  modern,  as  are  regarded 
as  inspired 'sources  of  philbsophical  and  theological  knowledge,  and  arc 
looked  upon  with  peculiar  reverence  : its  application  to  this  chapter  is 
equivalent  to  an  assumption  for  it  of  especial  sanctity  and  authority.  It 
may  possibly  also  indicate  that  the  chapter  is  originally  an  independent 
treatise,  incorporated  into  the  text  of  the  SArva-Siddlianta. 

The  word  bha,  in  verse  1,  may  mean  either  the  asterisms  proper 
( nakshalra ),  or  the  signs  (rdyi),  and  is  explained  by  the  commentator  as 
intended  to  include  both.  The  yvbytdcan,  “secret  ones”  arc  a class  of 
demigods  who  attend  upon  Kuvcra,  tlie  god  of  wealth,  and  are  the 
keepers  of  his  treasures:  why  they  are  mentioned  here,  as  objects  of 
especial  reverence  to  the  astronomical  teacher,  is  not  obvious.  The  com- 
mentator explains  the  word  by  “ Yakshas  etc.,  lesser  divinities.”  In  cur 
translation  of  verse  3 we  have  followed  the  reading  of  the  published 
text,  which  Colebrooke  also  appears  to  have  had  before  him  : our  own 
manuscripts  -read,  instead  of  bhubhuyola , bhuiniyola  and  Hiumer  yolu , 
u sphere  of  the  earth”  simply. 

Colebrooke,  in  his  essay  On  the  Indian  and  Arabian  Divisions  of  the 
Zodiac  (As.  lies.,  ix.  323  etc.;  Assays,  ii.  321  etc.)  to  which  we  have 
already  sq  often  had  occasion  to  refer,  gives  a translation  of  part  of  this 
chapter,  from  the  beginning  of  the  third  <o  the  middle  of  the  thirteenth 
verse,  as  also  a brief  sketch  of  the  ariniliary  .sphere  of  which  the  con-  * 
struction  is  taught  in  the  Siddhanta-(/iromnid.  lie  farther  furnishes  a 
description,  and  a comparison  with  these,  of  the  somewhat  similar  in- 
struments employed  by  the  Greeks,  the  Arabs,  and  the  early  European 
, astronomers.  It  has  not  seemed  to  ns  worth  while  to  extract  these  de- 
scriptions and  comparisons,  or  to  draw  up  others  from  independent  aim 
original  sources:  tne  object  of  the  Hindu  instrument  is  altogether  differ- 
ent from  that  of  the  others,  since  it  is  intended  merely  as  an  ill ust nitiofi 
of  the  positions  and  motions  of  the  heavenly  bodies,  while  those  arc 
meant  to  subserve  the  purposes  of  astronomical  observation ; and  its 
relation  to  them  is  determined  by  this  circumstance : while  it,  of  course, 
possesses  some  of  the  circles  which  enter  into  the  construction  of  the 
others,  it  is,  upotf  the  whole,  a very  different  and  much  more  complicated 
and  cumbersome  structure.  There  is  nothing  in  the  way  of  supposing 
that  the  first  hint  of  its  construction  may  have  been  borrowed  from  the 


Translation  and  Notes . 


257 


*iii.  8.] 

instruments  of  western  nations : but,  on-  the  other  hand,  it  may  possi- 
bly admit  also  of  being  regarded  as  an  independent  Hindu  device.  ■ 

8.  . . . Having  fashioned  an  earth-globe  of  wood,  of  the  de- 
sired size, 

4.  Fix  a staff,  passing  through  the  midst  of  it  and  protruding 
at  either  side,  for  Mcru;  and  likewise  a couple  of  sustaining 
hoops  (i kaJcshdi :),  and  the  equinoctial  hoop ; 

5.  These  are  to  be  made  with  graduated  divisions  (angula)  of 
degrees  of  the  circle  (bhagana).  ... 

The  fixing  of  a solid  globe  of  wood,  representing  the  earth,  in  the 
midst  of  this  instrument,  is  of  itself  enough  to  remler  impracticable  its 
application  to  purposes  of  astronomical  observation.  For  Meru,  the 
axis  and  poles  of  the  earth,  see  verse  .34  of  the  preceding  chapter.  We 
arc  not  informed  of  what  rchtiive  size  the  globe  and  the  encompassing 
hoops  are  to  be  made. ; probably  their  relation  is  to  be  such  that  the 
globe  will  be  ft  small  one,  contained  within  an  ample  sphere.  The  two 
“ supporting  hoops,”  to  which  are  to  be  attached  all  the  numerous  par- 
allels of  declination  hereafter  described,  arc,  of  course,  to  be  fastened  to 
the  axis  at  right  angles  to  one  another,  and  to  represent  the  equinoctial 
and  solstitial  colures.  The  commentary  directly  prescribes  thi*,  and  the 
text  also  assumes  it  in  a later  passage  (v.  10). 

Colebrooko,  following  the  gu^nnee  of  the  commentators,  treats  the 
former  half  of  verse  r»  as  belonging  to  the  following  passage,  instead  of 
"the  preceding.  It  can,  howeier,  admit  of  no  reasonable  question  that 
the  connection  as  established  in  mir  translation  Is  the  true  one : it  is  de- 
manded by  the  natural  construction  of  the  verses,  and  also  yields  a de- 
cidedly preferable  sense. 

5.  . . . Further — by  menus  of  the  several  day-radii,  as  adapted 
to  the  scale  established  Ibr  those  other  circles, 

6.  And  by  means  of  the  degrees  of  declination  and  latitude 
( vi/eshepa ) marked  olf  upon  the  latter — at  their  own  respective 
distances  in  declination,  according  to  the  declination  of  Aries 
etc.,  three 

7.  lloops  are  to  bo  prepared  and  fastened  : these  answer  also 
inversely  for  Cancer  etc.  In  the  same  manner,  three  for  Libra 
etc.,  answering  also  inversely  for  Capricorn  etc., 

’ 8.  And  situated  in  the  southern  hemisphere,  are  to  be  made 
and  fastened  to  the  two  hoop-supporterS.  \ . . 

The  grammatical  construction  of  this  passage  ;s  excessively  cumbrous 
and  intricate;  and  we  can  hardly  hope  that  the  \ vision  which  we  have 
given  of  it  will  be  clearly  understood  without  farther  explanations.  Its 
meaning,  however,  is  free  from  ambiguity.  We  have  thus  far  only  three 
of  the  circles  out  of  which  our  instrument  is  to  he  constructed,  namely 
those  intended"  to  represent  the  two  colures  and  the  equators  wo  arc 
next  to  add  hoops  for  the  diurnal  circles  described  by  the  sun  when  at 
the  points  of  connection  between  the  different  signs  "of  the  zodiac.  Of 
these  tlie^e  will  be,  of  course,  threo  north  of  the  equator,  one  for  the 


258 


[xi».  8- 


SGrya  ■ Siddh&nta, 

nun  at  the  end  of  Aries  and  at  the  beginning  of  Virgo,  one  for  the  sun 
at  the  end  of  Taurus  and  at  the  beginning  of  Leo,  and  one  for  thq  aun 
at  the  end  of  (if  mini  and  the  beginning  of  Cancer,  or  at  the  solstice  : 
also,  in  the  southern  hemisphere,  three  others  corresponding  to  these. 
The  dimensions  of  which  they  must  be  made  are  to  be  determined  by 
their  several  radii  (which  arc  called  day-radii — see.  above,  ii.  00),  ns 
ascertained  by  calculation  and  reduced  to  the  same  scale  upon  which  the 
coltircs  and  equator  were  constructed.  They  arc  then  to  be  attached  to 
the  two  general  supporting  hoops,  or  colures,  each  at  its  proper  distance 
from  the  equator;  this  distance  is  ascertained  by  calculating  the  decli- 
nation of  the  sun  when  at  the  points  in  question,  and  is  ‘determined 
upon  the  instrument  by  the  graduation  of  the  two  supporting  hoops. 
This  graduation  is  in  the  text  called  that  for  declination  (Aninli)  and 
latitude  ( vikshepa ) : it  will  be  remembered  that,  according  to  Hindu 
usage,  tlic  latter  means  distance  from  the  ecliptic  as  measured  upon  a 
circle  of  declination. 

8.  . . . Those  likewise  of  the  astcrisms  (hha)  situated  in  the 
southern  and  northern  hemispheres,  of  Abhijit, 

9.  Of  the  Seven  Sages  (, saplamliuyas ),  of  Agastya,  of  Brahma 
etc.,  are  to  be  fixed  .... 

If  the  orders  given  hi  these  verses  arc  to  ho  strictly  followed,  our  instru- 
ment must  now  be  burdened  with  fortbtwo  additional  circles  of  diurnal 
revolution,  namely  those  of  the  tweiiW-soveii  junction-stars  fyoflatara) 
of  the  astcrisms  and  of  that  of  Abhijit — which  is  here  especially  men- 
tioned, as  not  being  always  ranked  among  the*  astcrisms  (sec  above, 
p.  208  etc.) — those  of  the  seven  other  fixed  stars  of  which  the  positions 
were  staled  m the  eighth  chapter  (vv.  10-12  and  20-21),  and  also  those 
of  the  Seven  Sages,  or  the  conspicuous  stars  in  Ursa  Major  (see  end  of 
the  last  note  to  the  eighth  chapter).  Such  impracticable  directions, 
however,  cannot  but  inspire  the  suspicion  that  the  instrument  may  never 
have  been  constructed  except  upon  paper. 

9.  . . . Just  in  the  midst  of  all,  the  equinoctial  (vdishuvati) 
hoop  is  fixed. 

10.  Above  the  points  of  intersection  of  that  and  the  support- 
ing hoops  are  the  two  solstices  (ayana)  and  the  two  equinoxes 
(vishuvat)  .... 

Wc  have  already  noticed  (note  to  iii.  C)  that  the  celestial  equator  de- 
rives its  name  from  the  equinoxes  through  which  it  passes.  It  seem.*  a 
little  strange  that  the  adjustment  of  the*  hoop  representing  it  to  the  two 
supporting  hoops,  which  we  sliould  naturally  regard  os  the  first  step  in 
the  construction  of  the  instrument,  is  here  assumed  to  be  deferred  until 
after  alKthe  other  circles  of  dcclipation  arc  fixed  in  their  places. 

. The  weird  translated  11  above”  (urdhvam)  in  verse  10  requires  to  be 
understood  in  two  very  different  senses,  as  is  pointed  out  by  the  com- 
mentator, to  make  the  .definitions  of  position  of  the  solstices  and  of.thc 
equinoxes  both  correct : the  latter  arc  situated  precisely  at  the  intersec- 
tion of  the  equinoctial  eolure  with  the  equator ; the  former  at  a distance 
of  24°  above  and  below  the  intersection  of  the  equator  with  the  other 


Translation  and  Notes. 


259 


sin.  ft*] 

colure*  or  at  the  intersection  of  the  colure  with  the  third  parallel  of  the 
sun’s  declination,  on  either  side  of  th#equator. 

Wc'arc  next  taught  how  to  fix  in  its  proper  position  the  hoop  which 
is  to  represent  the  ecliptic. 

10.  . . . From  the  place  of  the  equinox,  with  the  exact  num- 
ber of  degrees,  as  proportioned  to  the  whole  circle, 

11.  Fix,  by  oblique  chords,  the  spaces  (kshetra)  of  Aries  and 
the  rest;  and  so  likewise  another  hoop,  running  obliquely  from 
solstice  (ayana)  to  solstice, 

12.  And  called  the  circle  of  declination  (krdnti):  upon  that 
the  sun  constantly  revolves,  giving  light : the  moon  and  the  other 
planets  also,  by  their  own  nodes,  which  are  situated  in  the  eclip- 
tic (i apamamlald )f 

13.  Being  drawn  away  from  it,  are  beheld  aj;  the  limit  of  their 
removal  in  latitude  (vikshepa)  from  the  corresponding  point  of 
declination.  ... 

Instead  of  simply  directing  that  a circle  or  hoop,  of  the  same  dimen- 
sions as  those  of  the  equator  and  coin  res,  he  constructed  to  .represent  the 
ecliptic,  and  then  attached  to  the  others  at  the  equinoxes  and  solstices, 
tliq  text  regards  it  as  necessary  to  fix',  upon  the  six  diurnal  circles  of 
the  sun  of  which  the  construction  and  adjustment  were  taught  above, 
in  verses  jt-8,  the  points  of  division  of  all  the  twelve  signs,  before 
the  ecliptic  hoop  can  he  added  to  the  instrument.  In  the  compound 
tiryayjyd , in  verse  11,  which  we  have  rendered  u oblique  chords,”  we 
conceive  jyd  to  have  its  own  more  proper  meaning  of  “chord,”  instead  of 
that  of  “sine,”  which,  by  substitution  fur  j yard  ha  (see  note  to  ii.  15-27, 
near  the  end),  it  has  hitherto  uniformly  borne.  We  are  to  ascertain  by 
calculation  the  measure  of  the  chord  of  30°,  to  reduce  it  to  the  scale  of 
dimensions  adopted  for  the  other  great  circles  of  the  instrument,  and 
then,  commencing  from  either  equinox,  to  lay  it  otf,  in  an  oblique  dircc- 
tioif,  to  the  successive  diurnal  circles,  northward  and  southward,  thus 
fixing  the  positions  upon  them  of  the  initial  ami  final  points  of  the 
twelve  signs;  and  through  all  these  points  the  ecliptic  hoop  is  to  be 
made  to  pass. 

It  does  not  appear  that  separate  hoops  for  the  orbits  of  the  other 
planets,  attached  to  the  ecliptic  at  their  respective  nodes,  arc  to  be  ad- 
ded to  the  instrument. 

In  verse  12  we  have  a name  for  the  ecliptic,  ajximandala , which  does 
not  occur  elsewhere  in  the  treatise.  The  word  might  be  literally  trans- 
lated “ off-circle,”  and  regarded  as  designating  the  circle  which  deviates 
in  direction  from  the  neighboring  equator ; but  t is  more  probably  an 
abbreviation  for  apakramamandah , which  would  mean,  like  the  ordinary 
terms  kr&ntiinandala , kranlivrita , “ circle  of  decimation.” 

18.  . . . The  orient  ccliptic-point  (lagna)  is  that  at  the  orient 
horizon ; the  Occident  point  (astamgachat)  is  similarly  determined. 

14.  The  meridian  eel  iptic-poin  t (madhi/ama)  is  as  calculated  by 
the  equivalents  in  right  ascension  (tanhoday&s),  for  mid-heaven 
(i khamadhya )■  above.  The  sine  which  is  between  the  meridian 


260 


[xifi,  16- 


Surija-Siddhdnla , 

(madhya)  and  the  horizon . (Icshitija)  is  styled  the  day-ineasure 
(anttjd).  m 1 * 

15.  And  the  sine  of  the  suns  ascensional  difference  (caradala) 
is  to  be  recognized  as  tlic  interval  between  the  equator  (viahuvai) 
and  flic  horizon.  ... 

These  verses  contain  ail  unnecessary  and  fraginpntary,  as  also  a con- 
fused ami  blundering,  definition  of  the  positions  upon  the  sphere  of  a 
few  among  the  points  and  lines  which  have  been  used  in  the  calculations 
of  the  earlier  parts  of  thn  treatise.  Wc  are  unwilling  to  believe  that 
the  passage  is  anything  but  a late  interpolation,  made  by  nil  awkward 
hand.  For  the  point  of  tin  ecliptic  termed  lugna , or  that  one  whieh  is 
at  any  given  moment  passing  the  eastern  horizon,  or  rising,  see  iii.  40- 
48,  and  note  upon  that  passage.  The  like  point  at  tlie  western  horizon, 
which  the  commentator  here  rails  astafugna,  “ lagna  of  Retting,”  and 
which  the  text  directs  us  to  find  “ in  a corresponding  manner,”  has  never 
been  named  or  taken  into  account,  anywhere  in  the  treatise : we  have 
seen  above  (as  for  instance,  in  ix.  4-o)  thM  all  its  processes  into  which 
distance  in  ascension  enters  as  an  element  are  transferred  for  calculation 
from  the  Occident  to  the  orient  horizon.  For  madhyalagna , the  point 
of  the  ecliptic  situated  upon  the  meridian,  sec  above,  iii.  10  and  note. 
Although  wc^have  ordinarily  translated  the.  term  by  “meridian  ecliptic- 
point*”  this  being  a conviMiicMit.  and  exact  definition  of  the  point  actually 
referred  to,  we  do  riot  regard  the  word  madhya , occurring  iu^,  as  mean- 
ing “meridian”  in  the  sei.su  in  which  it  is  used  in  modern  astronomy, 
namely  the  groat  circle  passing  through  the  observer’s  zenith  and  the 
north  and  south  points  of  his  horizon.  For  it  deserves  to-be  noted  that 
the  text  has  no  distinctive  name  for  the  meridian,  and  nowhere  makes 
^ny  reference  to  it  as  a circle  on  tlui  sphere : it  will  he.  seen  just  below 
that,  while  the  position  of  the  horizon  is  defined,  the  meridian  is  not 
contemplated  as  a circle  of  sufficient  consequence  to  require  to  he  rep- 
resented upon  the  illustrative  arm  ilia  it  .sphere.  The  commentator  not 
very  infrequently  has  occasion  to  speak  of  flics  meridian^ and  styles  it 
y&myoUararrltctj  “south  and  north  circle,”  or  urdhvaydmyotfaravrtta , 
“uppermost  south  and  north  circle.”  In  the  latter  half  of  \ else  14, 
where  we  have  translated  madhya  bv  “ meridian,1 ” it  would  have  been 
more  exact  to  say  “mid-hcavon,”  or  “the  sun  at  the  middle  of  his  visi- 
ble revolution,”  or  “ the  sun  when  at  the  point  called  madhyalagna .” 
For  the  “ day-measure”  (anly/i),  see  above,  iii.  34-80.  Its  definition 
given  here  is  as  Imd  as  it  could  .well  be  : for,  passing  over  the  fact  that 
the  line  in  question  is  not  properly  a sine,  and  moreover  that  the  text 
does  not  tell  us  ill  which  of  the  numberless  possible  directions  it  is  to  be 
drawn  from  the  meridian  to  the  horizon,  the  line  which  it  is  attempted 
to  describe  is  not  the  one  which  the  treatise  regards  as  the  antyd , but 
the  correspondent  of  the  latter  in  the  small  circle  described  by  the  sun. 
That  is  to  say,  the  text  here  substitutes  thn  line  DA  in  Fig.  8,  above 
(p. .88),  for  the  line  EG.  A similar  blunder  is  made  in  defining  the 
sine  of  the  sun’s  ascensional  difference  (carajyd):  the  line  All  in  the 
*ame  figure,  which  is  the11  earth-sine”  (kujyd,  kshifijyd),  is  taken,  in- 
stead of  its  equivalent  ip  terms  of  a great  circle,  C G.  - Moreover,  the 


Translation  and  Notes. 


281 


xiii.  19»] 

•text  reads  “ equator”  (vishuvat — E C in  the  figtts)&here  for  u east  and 
vest  hoar-circle9*  ( unmandala — (JPjjpthe  commentator  restores  the 
latter,  and  excuses  the  substitution  by  a false  translation  of  the  latter 
half  of  iii.  6,  making  it  mean  “ the  east  and  west  hour-circle  is  likewise 
denominated  the  equinoctial  circle.” 

In  verse  14,  lunkodayfa  is  substituted  for  the  more  usual  term  lanko- 
daydsavas  (sec  above,  iii.  49,  and  note),  in  the  sense  of  “ equivalents  of 
the  signs  in  right  ascension,”  literally,  “ at  Lankft.” 

15.  . . . Having  turned  upward  one’s  own  place,  the  circle  of 
the  horizon  is  midway  of  the  sphere. 

1G.  As  covered  with  a casing  (vasLrct)  and  as  left  uncovered, 
it  is  the  sphere  surrounded  by  Lokaloka.  . . . 

The  simple  direction  to  turn  upward  one's  own  situation  upon  the 
central  wooden  globe  which  represents  the  earth  docs  not,  it  is  evident, 

1 contemplate  any  very  careful  or  exact  adjustment  of  the  instrument. 

Verse  10  is  very  elliptical  and  obscure  in  its  expressions,  but  their 
general  meaning  plain,  and  is  that  which  is  attributed  to  them  by  (he 
commentator.  The  proper  elevation  having  been- given  to  the  pole  of 
the  sphere,  a circle  is  bv  some  means  or  other  to  be  fixed  about  ita 
midst,  or  equally  distant  from  its  zenith  and  nadir,  to  represent  the 
horizon.  Then  the  part  below  is  to  be  encased  in  a cloth  covering,  the 
upper  hemisphere  alone  being  left  open.  As  thus  arranged,  the  sphere 
is,  as  it  wcae,  girt  about  by  the  Lokaloka  mountains.  Lokaloka  is,  as  we 
have  seen  above  (note  to  xii.  .il2-44),  the  name  of  the  giant  in oun tain- 
range  which,  in  the  ] ’uranic  geography,  is  made  the  boundary  of  the 
universe:  it  is  apparently  so  called  because  it  separates 'the  worM  {Idea) 
from  the.  non-world  (a  lota) ; ami  as  out  of  tin?  1/ uranic  Mmi  tne  new 
astronomical  geography  makes  the  axis  ami  poles  of  the  earth,  so  out  of 
these  mountains  it  makes  the  visible  horizon. 

The  “ wonder-working  fabric  of  the  terrestrial  and  stellar  sphere”  is 
now  fully  constructed,  and  only  requires  farther,  in  order  to  its  comple- 
tion as  an  edifying  and  instructive  illustration  of  the  relations  of  the 
heavens  to  the  earth,  to  be  set  in  motion  about  its  fixed  axis. 

16.  . . . By  the  application  of  water  is  made  ascertainment  of 
the  revolution  of  time. 

17.  One  may  construct  a*  sphere-instrument  combined  with 
quicksilver : this  is  a mystery ; if  plainly  described,  it  would  be 
generally  intelligible  in  the  world. 

18.  Therefore  let  the  supreme  sphere  be  constructed  according 
to  the  instruction  of  the  preceptor  (guru).  In  each  successive 
age  (yu(ja)y  this  construction,  having  become  .ost,  is,  by  the  Sun’s 

19.  Favor,  again  revealed  to  some  one  or  other,  at  his 
pleasure.  . . 

Here  we  have  another  silly  mystification  of  a simple  and  compara- 
tively insignificant  matter,  like  that  already  noticed  at  the  end  of  the 
sixth  chapter.  The  revolution  of  the  machine  of  which  the  construc- 
tion has  now  been  explained,  in  imitation  of  the  actual  motion  of  .the 
34 


262  SQrya-Siddhdnta,  [xiiL  19- 

t 

heavqps  about  the  earthy  is  something,  so  calculated^  strike  the  .minds 
of^the  uninitiated  with  wondeij^hat  the  means  by  which  it  is  to  be 
accomplished  must  not  be  fully  explained  even  in  this  treatise,  lest  they 
should  become  too  generally  known : they  must  vbe  learned  by  each 
pupil  directly  from  his  teacher,  as  the  latter  has  received  them  by  suc- 
cessive tradition,  from  the  original  and  superhuman  source  whence  they 
came.  It  is  perfectly  evident  that  such  a fabric  could  only  be  made  to 
revolve  in  a rude  and  imperfect  way ; that  it  should  have  marked  time, 
and  continued  for  any  period  to  correspond  in  position  with  the  actual 
sphere,  is  impossible. 

The  word  which,  upon  the  authority  of  the  commentator,  we 'have 
rendered  “water,”  in  verse  16,  is  amrtasr&va , literally  “having  an  im- 
mortal flow”:  perhaps  the  phrase  should  be  translated  rather,  “by 
managing  a constant  current  of  water.” 

19.  ...  So  also,  one  should  construct  instruments  (yantra)  in 
order  to  the  ascertainment  of  time. 

. 20.  When  quite  alone,  one  should  apply  quicksilver  to  the 
ironder-causing  instrument.  By  the  gnomon  (gairtku),  staff  ( yashti), 
arc  (dhanwt),  wheel  (cakra),  instruments  for  taking  the  shadow, 
of  various  kinds, 

21.  According  to  the  instruction  of  the  preceptor  (guru),  is  to 
be ’gained  a knowledge  of  time  by  the  diligent.  ... 

The  commentator  interprets  the  first  part  of  verse  20  in  correspond- 
ence with  the  sense  of  the  preceding  passage : the  application  of  mer- 
cury to  a revolving  machine,  in  order  to  give  it  the  appearance  of  auto- 
matic potion,  must  be  made  privately,  lest  people,  understanding  the 
method  toq  well,  should  cease  to  wonder  at  it.  The  instruments  men- 
tioned in  the  latter  half  of  the  same  verse  are  explained  in  the  com- 
mentary simply  by  citations  from*  the  yantr&dhy&ya, 11  chapter  of  instru- 
ments,” of  the  Siddh&ntar^iromani  (Gol&dhy.,  pp.  111-136,  published 
edition).  We  will  state,  as  briefly  as  may  be,  their  character : 

The  gnomon  (ganku)  needs  no  explanation : its  construction  and  the 
method  of  using  it  have  been  fully  exhibited  in  the  third  chapter  of  our 
treatise.  The  “ staff-instrument”  (yashiiyanira)  is  described  as  follows. 
A circle  is  described  upon  a level  surface  with  a radius  proportioned  to 
that  of  the  sphere,  or  to  tabular  radius*  Its  car^jnal  points  arc  ascer- 
tained, and  its  east  and  west  and  north  and  sonth  diameters  are  drawn. 
From  the  former,  at  either  extremity,  is  laid  off  the  sine. of  amplitude 
(agrd)  ascertained  by  calculation  for  the  given  day  : the  points  thus  de- 
termined upon  the  circumference  *of  the  circle  represent  the  points  on 
the  horizon  at  which  the  sun  rises  and  sets.  Another  circle,  with  a ra- 
dius proportioned  to  that  of  the  calculated  diurnal  circle  of  the  day 
(dyujyd),  is  also  described  about  the  centre  of  the  other,  and  is  divided 
into  sixty  equal  parts,  representing  the  division  of  the  sun’s  daily  revolu- 
tion into  sixty  n&dk-  Into  a depression  at  the  centre,,  the  foot  of  a 
staff  (yashti),  equal  in  length  to  the  radius  of  the  larger  circle,  is  loosely 
inerted.  When  it  k desired  to  ascertain  the  time  of  the  day,  this  staff 
fi  pointed,  directly  toward  the  sun,  or  in  stfch  manner  that  it  casta  no 
shadow;  its  extremity  then  represents  the  place  of  the  sun  at  the 


Translation  and  1 Votes. 


208 


xiii.  89.] 

'moment  upon  Jhe  Bphere.  Measure,  by  a stiek^  the  distance  of  that 
extremity  from  the  point  of  sunrise  Shf  sunset : this  will  be  the  chord 
of  tbet  part;  of  the  diurnal  circle  which  is  intercepted  between  the  sun’s 
actual  position  and  the  point  at  which  ho  rose,  or  will  set : the  value  of 
the  corresponding  arc  in  nftdls  may  be  ascertained  by  applying  the  stick  # 
to  the  leaser  graduated  circle.  The  result  is  the  time  since  sunrise,  or  * 
till  sunset 

The  "wheel”  (cabna)  is  a very  simple  instrument  for  obtaining,  by 
observation,  the  sun’s  altitude  and  zenith-distance. ' It  is  simply  a wheel, 
suspended  bj  a string,  graduated  to  degrees,  having  its  lowest  point 
and  the  extremities  of  its  horizontal  diameter  distinctly  marked,  and 
with  a projecting  peg  at  the  centre.  When  used,  its  edge  is  turned  to- 
ward tne  sun,  so  that  the  shadow  of  the  peg  falls  upon  the  graduated, 
periphery,  and  the  distances  of  the  point  where  it  meets  the  latter  from 
the  horizontal  and  lowest  points  of  the  wheel  respectively  are  the 
required  altitude  and  zenith-distance  of  the  sun.  From  these,  by  the 
methods  of  the  third  chapter  (iii.  37-39),  the  time  may  be  derived. 

The  "arc”  (dhanua)  is  the  lower  half  of  the  instrument  just  described 
— or,  we  may  also  suppose,  a quadrant  of  it ; since  only  a quadrant  is 
required  for  making  the  observations  for  which  tne  instrument  is  em-  - 
ployed. 

21.  By  water-instruments,  the  vessel  (kapdla)  etc.,  by  the  pea* 
cock,  man,  monkey,  and  by  stringed  sand-receptacles,  one  may 
determine  time  accurately. 

22.  Quicksilver-holes,  water,  and  cords,  ropes  ($ulba\  and  oil 
and  water,  mercury,  and  sand  arc  used  in  these : these  applica- 
tions, too,  are  difficult. 

The  instruments  and  methods  hinted  at  in  these  verses  are  only  par- 
tially and  obscurely  explained  by  the  commentator.  The  hapdla , u cup” 
or  11  hemisphere,”  is  doubtless  the  instrument  which  is  particularly 
described  below,  in  verse  23.  The  nara9  “ man,1’  is  also  spoken  of  be- 
low, in  verse  24,  and  is  simply  a gnomon  ; it  is  perhaps  one  of  a partic- 
ular construction  and  size,  and  so  named  from  having  abont  the  height 
of  a man.  The  peacock  and  monkey  am  obscure.  The  “sand-vemels” 
(renugnrbha),  which  are  “ provided  with  cords”  (sas&tra),  arc  probably 
suspended  instruments,  of  the  general  character  of  our  bout-glasses. 
The  commentator  connects  them  also  with  the  "peacock,”  as  if  the 
latter  were  a figure  of  the  bird  having  such  a vessel  in  his  interior,  and 
letting  the  sand  pour  out  of  his  mouth.  In  illustration  of  thw  “quick- 
silver-hoW’  (pdraddrd)  a passage  is  cited  from  the  Siddh&nta-Qironaam 
(as  above),  giving  the  description  of  an  instrument  in  which  they  are 
applied.  It  is  a wheel,  having  on  its  outer  edge  a number  of  holes,  of 
equal  size,  and  at  equal  distances  from  ono  another,  but  upon  a rigpzag 
line : these  holes  are  filled  half  full  of  mercury,  and  stopped  at  the  on* 
flfce  : and  iWis  claimed  that  the  wheel  will  then,  if  supported  upon  an 
axis  by  a couple  of  props,  revolve  of  itself  The  application  of  this 
method  may  well  enough  be  styled  “difficult” : if  a machine  so  con- 
structed would  work,  theVindus  would  be  entitled  to  the  credit  of 
having  solved  the  problem  of  perpetual  motion.  The  descriptions  of 


264 


[xilL  22- 


S&rya-Siddhdnta , 

« 

pne  or  two  other  somewhat  similar  machines  are  also  cited  in  the  com' 
mentaiy  from  the  Siddli&nta-(J!ir<®iRiu : the  only  new  feature  worthy  of 
notice  which  they  contain  is  the  application  of  the  siphon,  or  bent  tube, 
in  emptying  a vessel  of  the  water  it  contains. 

It  will  hfive  been  noticed  that,  throughout  the  whole  of  this  chapter, 

* the  different  parts  or  passages  end  in  .the  middle  of  a verse.  In  the 
twenty-first  verse  the  coincidence  between  the  end  of  a passage  and  the 
end  of  a verse  is  re-established,  but  it  » at  the  cost  of  such  an  irregular- 
ity as  is  nowhere  else  committed  in  the.  treatise : the  verse  is  made  to 
consist  of  three  half-^lokas,  instead  of  two,  the  whole  chapter  being 
thus  allowed  to  contain  an  uneven  number  of  lines.  Thefe  are  two  or 
three  very  superfluous  naif-verses  at  the  beginning  of  the  chapter,  the 
omission  of  any  one  of  which  would  scein  an  cosier  and  preferable 
method  of  restoring  the  regular  and  connected  construction  of  the  test 

23.  A copper  vessel,  with  a hole  in  the  bottom,  set  in  a basin 
of  pure  water,  sinks  sixty  times  in  a day  and  night,  and  is  an 
accurate  hemispherical  instrument. 

This  instrument  appears  to  have  been  the  one  most  generally  and  fre- 
quently in  use  among  the  Hindus  for  the  measurement  of  time  : it  is  the 
only  one  described  in  the  Ayin-Akbari.  (ii.  302).  One  of  the  common 
names  for  the  sixtieth  part  of  the  day,  pkati  or  gkatikti,  literally  M ves- 
sel,” is  evidently  derived  from  it : the  other,  narfi  or  nhdilcd. , “ reed,” 

!>robablv  designated  in  the  first  place,  and  more  properly,  a measure  of 
ength,  and  not  of  time.  A verse  cited  in  the  commentary  to  this  pas- 
sage gives  the  form  and  dimensions  of  the  vessel  used : it  is  to  be  often 
palmi  weight,  of  copper,  six  digits  (angula)  high,  and  of  twice  that  width 
at  the  mouth,  and  is  to  contain  sixty  palus  of  water:  the  hole  in  the 
bottom  through  which  it  is  to  fill  itself  is  to  be  such  as  will  just  admit 
a gold  pin  four  digits  long,  and  weighing  three  and  a third  m&sha*. 
The  description  of  the  Ayin-Akbari  does  not  precisely  agree  with  this; 
and  it  is,  indeed,  sufficiently  evident  that  an  instrument  intended  for 
such  a purpose  could  not  be  accurately  constructed  by  Hindu  workmen 
from  measurements  alone,  but  would  have  to  be  tested  by  comparison 
with  some  rccoggized  standard,  or  by  actual  use. 

24.  So  also,  the  man-instrument  (narayantra)  is  good  in  the 
day-time,  and  when  the  sun  is  clear.  The  bfcst  determination  of 
time  by  meaus  of  determinations  of  the  shadow  has  been  ex- 
plained? 

We  have  already  noticed  above,  under  verse  21,  that  the  nara  was  a 
simple  gnomon.  The  explanations  here  referred  to  are,  of  course,  those 
which  are  presented  in  the  third  chapter. 

The  concluding  verse  of  the  chapter  is  an  encouragement  held  out  to 

4he  astronomical  %tiident.  k 

• * 

25.  Tie  who  thoroughly  knows  the  system  of  the  planets'and 
asterisms,  and  'the  sphere,  attains  the  world  of  the  planets  in  the 
■accession  of  births,  his  own  possessor* 


xiv.  8.} 


Translation  and  Notea. 


265 


CHAPTER  XIV. 

OF  THE  DIFFERENT  MODES  OF  RECKONING  TIME.  . 

Contests:— 1-2,  enumeration  of  tbe  modes  of  measuring  time,  and  general  explan- 
ation of  their  uses;  8,  solar  time',  4-6,  of  the  periods  of  eighty-six  days ; 7-11, 
of  points  and  divisions  in  the  sun's  revolution ; 18-13,  lunar  time;  14,  time  of  the 
Fathers ; 16,  sidereal  time ; 16-16,  of  the  months  and  their  aaterisms ; 17,  of  the 
twelve-year  cycle  of  Jupiter;  18-19,  civil,  or  mean  solar,  time;  20-21,  time  of 
the  gods,  Prajflpati.  and  Brahma ; 22-26,  conclusion  of  the  work. 

1.  The  modes  of  measuring  time  ( mdna ) are  nine,  namely  those 
of  Brahma,  of  the  gods,  of  the  Fathers,  of  Praj&pati,  of  Jupiter, . 
and  solar  ( sdura ),  civil  (sdvana),  lunar,  and  sidereal  time. 

2.  Of  four  modes,  namely  solar,  lunar,  sidereal,  and  civil  time, 
practical  use  is  made  among  men ; by  that  of  Jupiter  is  to  be  de- 
termined the  year  of  the  cycle  of  sixty  years ; of  the  rest,  no 
use  is  ever  made. 

This  chapter  contains  the  reply  of  the  sun's  incarnation  to  the  last  of 
the  questions  addressed  to  him  hy  the  original  recipient  of  his  revela- 
tion (see  above,  xii.  8).  The  word  mdna,  which  gives  it  its  title  of  md- 
n&dhydya,  and  which  wo  have  translated  “ mode  of  measuring  or  reck- 
oning time,”  literally  means  simply  “ measure” : it  is  the  same  tem\ 
which  wc  have  already  (iv.  2-3)  seen  applied  to  designate  the  measured 
disks  of  the  sun  and  moon. 

3.  By  solar  (sdura)  time  are  determined  the  measure  of  the 
day  ana  night,  the  sfuidacitinuikhas,  the  solstice  (ay ana),  the  equi- 
nox ( vishuvat ),  and  the  propitious  period  of  the  sun’s  entrance 
into  a sign  (sankrdnti). 

a 

The  adjective  saura,  which  we  translate  “solar,”  is  a^ccondarv  de- 
rivative from  sArya,  “ sun.”  It  is  applied  to  those  divisions  of  time 
which  are  dependent  on  and  determined  hv  the  sun’s  actual  motion 
along  the  ecliptic.  The  “day  and  night”  measured  hy  it  arc  probably 
those  of  the  gods  and  demons  respectively ; see  above,  xii.  48-50.  ’ The 
solar  year,  as  already  noticed  (note  to  i.  12-1  a),  is  sidereal,  not  tropical ; 
it  commences  whenever  the  sun  enters  the  first  sign  of  the  immovable 
sidereal  zodiac,  or  when  he  is  10  minutes  cast  in  longitude  from  the 
star  t Pise  him.  The  solar  month  is  the  timo  during  which  he  continues 
in  each  successive  sign,  or  arc  of  30°,  reckonii.  ? from  that  point  The 
length  of  the  solar  year  and  month  is  subject  only  to  an  infinitesimal 
variation,  due  to  the  slow  motion,  of  1'  in  511  years,  assumed  for  the 
sun's  line  of  apsides  (see  above,  i.  41-44) ; but  it  is,  as  lias  been -shown 
above  (note  to  i.  20-34,  near  the  end),  somewhat  differently  estimated 
by  different  authorities.  The  precise  length  of  the  solar  months,  as 
reckoned  according  to  this  S toy a-Siddh&nta,  is  thus  stated  by  Warren 
(K&la  Sankalita,  p.  60) : 


266 


[xiv.3* 


Duration  of  the  several  Solar  Months. 


No.j  . Nome.  | 

Duration. 

Bom  of 

duration. 

1 

d 

n 

V 

i»i 

ii.  ■ 

d 

■ 

V 

Ml 

l ! Vni^khs, 

3o 

55 

3a 

39 

3o 

55 

3a 

a 

39 

a > JyAiahtha^ 

3i 

34 

la 

4i 

6a 

*9 

44 

5 

ao 

3 i A'hfidhft, 

3i 

36 

38 

<44 

93 

56 

aa 

8 

4 

4 j (Jr&vojja, 

3k 

a8 

la 

4a 

ia5 

a4 

34 

10 

46 

5 ; Bh&drapada, 

3i 

a 

IO 

4o 

1 56 

afi 

44 

i3 

a6 

6 j Alvina. 

3o 

»7“ 

aa 

38 

186- 

54 

6 

16 

4 

7 j KArttika, 

a9 

54 

7 

35 

ai6 

48 

i3 

18 

3, 

8 j MArgafirshn, 

a9 

3o 

a4 

33 

a46 

18 

.37 

ai 

aa 

9 j P&usha, 

a9 

ao 

53 

3i 

a75 

39 

3o 

a3 

43 

io  i Mftghn, 

a9 

a7 

16 

3a 

3oT» 

6 

46 

a6 

i5 

ii  PhAlguna, 

a9 

48 

24 

a 

33 

334 

55 

IO 

a8 

48 

la  : C&itra, 

j 3o 

20 

21 

a 

. 36 

365 

i5 

3i 

3i 

*4 

The  former  passage  (i.  12-13)  took' no  note  of  any  solar  day ; in  this 
chapter,  however,  such  a division  of  time  is  distinctly  contemplated  : it 
is  also  recognized  by  the  Siddliant.i-£iromnni  (Ganit&dhy.,  ii.  8),  and 
seems  to  be,  for  certain  uses,  generally  accepted.  The  solar  day  is  the 
time  during  which  the  sun  traverses  each  successive  degree  of  the  eclip- 
tic, with  his  true  motion,  and  its  length  accordingly  varies  with  the  rap- 
idity of  his  motion  : three  hundred  and  sixty  such  days  compose  the 
sidereal  year.  Tn  order  to  determine  the  solar  day  corresponding  to  any 
given  moment,  it  is,  of  course,  only  necessary  to  calculate,  by  the  meth- 
ods of  the  second  chapter,  the  sun's  true  longitude  for  that  moment. 
Hence  it  is  a matter  of  very  little  practical  account:-  all  the  periods  re- 
garded as  determined  by  it  may  be  as  well  derived  directly  from  the 
sun’s  longitude,  without  going  through  the  form  of  calling  its  degmes 
days.  It  is  thus  with  the  equinoxes,  solstices,  and  entrances  of  the  sun 
into  a sign  ( sankrdnti , “ entrance  upon  connection  with”) : for  the  latter, 
and  for  the  continuance  of  the  propitious  influences  which  are  believed 
to  attend  upon  it,  sec  below,  verse  11.  The  shadafilimukhas  form  the 
subject  of  thAext  following  passage. 

The  manuscript  without  commentary  inserts  l&cre  the  following  verse : 
“the  day  and  night  of  the  gods  and  demons,  which  is  determined  by 
the  sun’s  revolution  through  the  circle  of  asterisms  Ibhacakra),  and  the 
number  of  the  Golden  (krta)  and  other  Ages,  as  already  stated,  is  to 
be  known.” 

4.  Beginning  with  Libra,  the  shadagUimvJcha  is  at  the  end  of 
the  periods  of  eighty-six  (shadafiti)  days,  in  succession:  there  are 
four  of  them,  occurring  in  the  signs  of  double  character  ( dvisva - 
bhdva) ; 

5.  Namely,  at  the  twenty-sixth  degree  of  Sagittarius,  at  the 
twenty-second  of  Pisces,  at  the  eighteenth  degree  of  Gemini,  and 
at  the  fourteenth  of  Virgo. 

* 6.  From  the  latter  pointy  the  sixteen  days  of  Virgo  which  re- 
main are  suitable  for  sacrifices:  anything  given  to  the  Fathers 
(pitaras)  in  them  is  inexhaustible. 


xiy.  10.]  Translation  and  Notes.  267 

a We  hate  not  been  able  to  find  anywhere  any  explanation  of  this  ca- 
rious division  of  the  Bun's  path  into  arcs  of  86°,  commencing  from  the 
autnmflal  equinox,  and  leaving  an  odd  remnant  of  16°  at  tho  end  of 
Virgo.  The  commentary  offers  nothing  whatever  in  elucidation  of  their 
character  and  significance.  The  epithet  u of  double  character"  (dvisva- 
bhdva)  belongs  to  the  four  signs  mentioned  in  verse^ ; judging  from  the 
connection  in  which  it  is  applied  to  them  by  Varaha-Mihira  (Laghu- 
j&taka,  i.  6,  in  Weber's  Indische  Studien,  ii.  278),  it  designates  them  aa 
either  variable  (rare)  or  fixed  ( athira ),  in  some  astrological  sense.  The  ^ 
term  shadapitimukha  is  composed  of  shadapiti , 11  eighty-six,”  and  mukha%  * 
11  mouth,  face,  beginning.”  Wc  do  not  understand  the  meaning  of  the 
compound  well  enpugh  to  venture  to  translate  it. 

7.  In  the  midst  of  the  zodiac  (phacabrd)  are  the  two  equinoxes 
(vishuvat),  situated  upon  the  same  diameter  (samasCUraga)^  and 
likewise  the  two  solstices  (ayana) ; these  four  are  well  known. 

8.  Between  these  are,  in  each  case,  two  entrances  (sankranti); 
from  the  immediateness  of  the  entrance  are  to  be  known  the  two 
feet  of  Vishnu. 

9.  From  the  sun's  entrance  (sankr&nti)  into  Capricorn,  six 
months  are  his  northern ‘progress  (vttardyana) ; so  likewise,  from 
the  beginning  of  Cancer,  six  months  are  liis  southern  progress 
(i dakshvndyana ). 

10.,  Thence  also  are  reckoned  the  seasons  (rtu\  the  cool  season 
(fifird)  and  the  rest,  each  prevailing  through  two  signs.  These 
twelve,  commencing  with  Aries,  are  the  months;  of  them  is 
made  up  the^car. 

The  commentator  explains  samasutraga,  like  samas&trastha  above 
(xii..52),  to  mean  situated  at  opposite  extremities  of  the  same  diameter 
of  the  earth,  or  antipodal  to  one  another. 

The  technical  term  for  the  sun’s  entrance  into  a sign  of  the  zodiac  is, 
as  noticed  already,  sankr&nti  (the  commentary  also  presents  the  equiva- 
lent word  sankramana) ; of  these  there  take  place  two  ^tween  each 
equinox  and  the  preceding  or  following  solstice.  The  ratter  half  of 
verse  8 is  qiiite  obscure.  The  commentator  appears  to  understand  it  as 
signifying  that,  in  each  quadrant,  the  entrance  (sankr&nti)  immediately 
following  the  solstice  or  equinox  is  styled  “Vishnu’s  feet”  In  the  ear-  , 
liest  Hindu  mythology,  Vishnu  is  die  sun,  especially  considered  as  occu- 
pying successively  the  three  stations  of  the  orient  horizon,  the  meridian, 
and  the  Occident  horizon;  and  the  three  steps  by  which  he  strides 
through  the  sky  are  his  only  distinctive  characteristic.  These  three 
steps,  then,  appear  under  various  forms  in  the  l.'ter  V&iahnava  mythol- 
ogy, and  there  is  plainly  some  reference  to  them  in  this  designation  of 
the*  sun's  entrances  into  the  signs.  It  would  seem  easiest  and  most  nat- 
ural to  recognize  in  the  three  Bigns  intervening  between  each  equinox 
and  solstice  Vishnu’s  three  steps,  and  to  regard  the  two  intermediate 
entrances  as  the  marks  of  his  feet ; this  may  possibly  be  the  figure  in- 
tended to  be  conveyed  by  the  language  of  the  text  ' 

The  word  rtu  means  Qriginally  and  literally  any  determined  period  of 
time!  a 11  season”  in  the  most  general  sense  of  the  term;  but  it  has  also 


268 


S&rya'Siddh&iitO) . [xiv.  IQ- 

been  employed  from  very  early  times  to  designate  the  various  divisions 
of  the  year*  They  were  anciently  reckoned  as  three,  five,  six,  or  sevrt ; 
hat  the  prevailing  division,  and  the  only  one  in  use  in  later  timeses  that 
into  six  seasons,  named  yigira,  Vasantaj  Grishina,  Varslia,  Qarad,  and 
Hcmanta,  which  may  be  represented  by  cool  season,  Bpring,  summer, 
rainy  season,  nutunm,  and  winter,  Qigira  begins  with  th^month  M&gha, 
or  about  the  middle  of  January  (sec  note  to  i»  48-51,  and  the  table 
given  below,  under  vv.  15-16),  and  each  season  in  succession  includes 
two  solar  months. 

11.  Multiply  the  number  of  minutes  in  the  sun's  measure 
{mdna)  by  sixty,  and  divide  by  his  daily  motion : a time  equal 
to  half  the  result,  in  uadis,  is  propitious  before  the  sun's  entrance 
into  a sign  ( sankrdnti)}  and  likewise  after  it. 

The  propitious  influences  referred  to  above,  in  verse  3,  as  attending 
upon  the  sun's  entrance  into  a sign,  arc  regarded  as  enduring  so  long  as 
any  part  of  his  disk  is  upon  the  point  of  separation  between  the  two 
signs.  This  time  is  found  by  the  following  proportion  : as  the  sun’s  ac- 
tual daily  motion,  in  minutes,  is  to  a day,  or  sixty  n&dis,  so  is  the  meas- 
ure of  liis  disk,  in  minutes,  to  the  time  which  it  will  occupy  in  passing 
the  point  referred  to. 

12.  As  the  moon,  setting  out  from  the  sun,.mfives  from  day  to 
day  eastward,  that  is  the  lunar  method  of  reck6uiti<r  time  {mdna) : 
a lunar  day  {tithi)  is  to  be  regarded  as  corresponding  to  tlrelvo 
degrees  of  motion. 

13.  The  lunar  day  {lithi)}  the  karaija,  the  genertfl  ceremonies, 
marriage,  shaving,  and  the  performance  of  vows,  fastings,  and 
pilgrimages,  are  determined  by  lunar  time. 

14.  Of  thirty  lunar  days  is  composed  the  lunar  month,  which 
is  declared  to  be  a day  and  a night  of  the  Fathers : the  end  of 
the  month  and  of  the  half-month  ( paksha ) are  at  their  mid-day 
and  midnight  respectively. 

For  the  tithi,  or  lunar  day,  see  above,  ii.  6G : for  the  karana,  see 
ii.  67-60.  For  the  month  con  sit  1 creel  as  the  day  of  the  pitaras,  or  manes 
of  the  departed,  see  note  to  xii.  73-77.  Manu  (i.  66)  pronounces  the 
i day  of  the  Fathers  to  be  the  dark  'half-month,  or  the  fortnight  from  full 
moon  to  new  moon,  and  their  night  to  be  the  light  half-month,  or  the 
fortnight  from  new  moon  to  full  moon.  With  this  mode  of  division 
might  be  made  to  accord  that  stated  in  the  latter  part  of  verse  14,  by 
rendering  madhye  “ between,*'  instead  of  “at  the  middle  point  of”:  we 
have  translated  according  to  thc-dircctions  of  the  commentator. 

15.  The  constant  revolution  of  the  circle  of  asterisms  (bhaca* 
kra)  is  called  a sidereal  day.  The  months  are  to  be  known  by 
the  names  of  the  asterisms  (i nakshatra ),  according  to  the  conjunc- 

; tion  (yoga)  at  the  end  of  ajunar  period  ( parvari ), 

- J6.  To  the  mdtaths  Kfirttika  etc.  belong,  as  concerns  the  con- 
junction (j samayoga] ),  the  asterisms  Krttikfi etc.,  two  by  two:. but 


269 


xir.  16.]'  Translation  and  Notes. 

p 

three  months,  namely  the  last/  the  next  to  the  last,  and  the  fifth, 

hare  triple  asterisms. 

• • 

The  subjeot  of  sidereal  time,  .although  one  of  prominent  importance 
in  the  present  treatise,  since  the  Subdivision  of  the  day  is  regulated 
entirely  by  it,  is  here  very  summarily  dismissed  with  half  a verse,  while 
w c find  appended  to  it  in  the  same  passage  matters  with  which  it  has 
nothing  properly  to  do. 

We  have  already  (note  to  i.  48-51)  had  occasion  to  notice  that  the 
months  are  regarded  as  having  received  their  names  from  the  asterisms 
(i nakshatra ) in  which  the  moon  became  full  during  their  continuance. 
According  to  Sir  William  Jones  (As.  lies.,  ii.  2$G),  it  is  asserted  by  the 
Hindus  “that,  when  their  lunar  year  wds  arranged  by  former  astrono- 
mers, the  moon  was  at  the  full  in  each  month  on  the  very  day  whan  it 
entered  the  nnkskalra , from  which  that  month  is  denominated.”  Wheth- 
er this  assertion  is  strictly  true  admits  of  much  doubt.  Our  text  docs 
not  imply  any  sucli  claim  : it.  only  declares  that  -the  month  is  to  be 
called  by  the  name  of  that  ascertain  with  which  the  moon  is  in  conjunc- 
tion ( yoga ) at  the  end  of  the  parcan : this  latter  word  might  mean  cither 
half  of  a lunar  month,  but  is  evidently  to  be  understood  here,  as  ex- 
plained by  the  commentary,  of  the  light  half  (rukla  paksha)  alone,  so 
that  the  end  of  the  parvan  (purrdufa)  is  equivalent  to  the  end  of 
the  day  of  full  moon  (ptirnimanta),  or  to  the  moment  of  opposition  in 
longitude.  Now  it  is  evident  that,  owing  to  the  incommensurability  of 
the  times  of  revolution  of  the  sun  and  moon,  as  also  to  the  revolution 
of  the  moon's  line  of  apsides,  full  muon  is  liabl*'  to  occur  in  succession 
iu  all  the  asterisms.  and  at  all  points  of  the  zodiac ; so  that  although, 
at  the  time  when  t lie  system  of  names  for  the  mouths  originated  and 
(^tabli.shed  itself,  they  were  doubtless  strictly  applicable,  they  would  not* 
long  continue  to  be  so.  Instead,  however,  of  being  compelled  to  alter 
continually  the  nomenclature  of  the  year,  w'e  arc  allowed,  by  verse  16, 
to  rail  a month  K&rttika  in  which  the*  lull  of  the  moon  takes  place  cithei: 
in  KrttikiVor  in  Rohinl,  and  soon;  the  twenty-seven  asterisms  being 
distributed  among  the  twelve  months  as  evenly  ns  the  nature  of  the  case 
admits.  9 

At  what  period  these  names  were  first  introduced  iuto  use  is  unknown. 
It  must  have  been,  of  course,  posterior  to  the  establishment  of  the  sys- 
tem of  asterisms,  but  it  was  probably  not  much  later,  as  the  names  are 
found  iu  some  of  the  earlier  texts  which  contaiu  those  of  the  hakshatras 
themselves.  We  can  hardly  suppose  that  they  were  not  originally  ap- 

tilicd  independently  to  the  lunar  months ; and  certainly,  no  more  suita- 
>le  derivation  could  be  found  for  the  name  of  a lmarpciiod  than  from 
the  a&lcrisin  in  which  the  moon  attained  during  hi  coutiuuance  her  full 
beauty  and  perfection.  In  later  times,  as  we  Lave  already  seen-  (note  to 
i.  48-4>l),  the  true  lunar  months  are  entirely  dependent  for  tlicir  nomen- 
clature upon  the  solar  months,  according  to  t.lic  determination  of  the 
latter,  as  regards  their  commencement  and  deration,  by  the  data  and 
methods  of  the  modern  astronomical  science.  There  has  been  handed 
down  another  system  of  names  for  the  months  (see  Colobrooke  in  As. 
Res.,  vii.  284 ; Essays,  i.  201),  which  have  nothing  to  do  with  the  aster- 
isms : whether  they  are  to  be  regarded  as  more  ancient  than  the  others 
35 


270 


Sforya-SiMMnta,  ‘ 


[xiv.  10- 


we  do  not  know.  They  are — commencing  with  the  first  month  of  the 
season  Vasanlo,  or  with  that  ono.  which  in  the  other  system  is  called 
CAitra — as  follows : Madliu,  MAdhava,  Qukra,  Quei,  Nablias,  Nabhasya, 
Islia,  Crja,  Sahas,  Sahasya,  Tapas,  Tapasya. 

For  the  sake  of  a clearer  understanding  of  the  relations  of  the  aster- 
isms,  months,  and  seasons,  we  present  their  correspondences  below  in  a 
tabular  form : 


Season. 

farad. 


Hemuita. 


Month 

i KArttika. 

V.(OcL  -Nov.) 

{MArgnyiraha. 
(Nov. -Dee.) 

Pfmslin. 

(Doc.- J oo.) 

rMAglia. 

: (Jan.-Veb.) 

FhAlguna. 

^ (Feb.-  Mur.) 


Aitcrimii  in  which 
full  moon  iiiny  occur. 

j Krttikl 
\ Rohini. 


j Pumirvaflu. 

( Fustiya. 

( Agleshft. 

( MngliA. 

P.-Plmlguni. 

U.-PhalgunS. 

Hasta. 


Vasanta. 


Orishma. 


Vanha. 


(Cftitrn. 
(Mir. -Apr.) 

VArikha. 

(Apr.  Muy.) 

rJy  Achilla. 
(May-June.) 

Asli&dha. 

b (June- July.) 


SrAvnna. 
luly  Aug.) 


BhAdrap&da. 
. (Aug.-Scpt.)J 


' ^viiia. 

farad.  (Sept. -Oct.) 


( CitrA. 

{ Svfiti. 

( ViyAkUL 

j AuurAdhA. 

j JvenhthA. 

1 Miila. 


j P.-AshAiM. 
J U.-Ath4flb£L 

J Cruvana 
( f ruviehtliA, 


( f ataMiishaj. 

< P.-Bhudrap&dA. 
( U.-BhadrapadA. 

JRevati. 

A 9 viiii. 

BharanL 


Dans  (As.  Res.,  iii.  218)  notices  that  some'  of  the  ancient  astrono- 
•xners  have  divided  the  astcrisms  somewhat  differently,  giving  to  frAvana 
the  three  beginning  with  fravana^to  BhAdrapada  the  -three  beginning 
with  Pfirva-BhAdrap&dA,  and  to  Alvina  only  Asvilii  and  Bharani.  It 
seems,  indeed,  that  the  selection  of  the  three  months  to  which  thrne 
asterisms,  instead  of  two,  were  assigned,  must  have  been  made  somewhat 
arbitrarily. 

It  will  be  noticed  that  in  this  passage  KArttika  is  treated  as  the  firsts 
of  the  series  of  months,  while  above  (v.  10)  f iqira  was  mentioned  as  the 
first  season,  and  while  in  practice  (see  note  to  i.  48-51)  VAi^Akha  is 
9 treated  as  the  first  of  the  solar  months,  and  CAitra  of  the  lunar.  Another 
name  for  MArgaglrsha,  also,  is  AgrahAyana,  which  appears  to  mean 
“commencement  of  the  year.”  How  much  significance  these  varia- 
tions of  usage  may  have,  and  what  is  their  reason,  is  not  known  to  us. 


Translation  and  Notes:* 


271 


liv.  17.] 

Ab  regards  V&i;&kha  and  C&itra,  indeed,  the  case  is  clear,  and  we  may 
also  regard  the  rani?  assigned  to  K&rttika  as  due  to  the  ancftnt  position 
of  Krttikfc,  as  first  among  the  lunar  mansions. 

17.  In  V&iguklia  etc.,  a conjunction  (yoga)  in  the  dark  half- 
month  (i Jcrshna ),  on  the  fifteenth  lunar  day  (tithi\  detenmnes  in 
like  manner  the  years  Karttika  etc.  of  Jupiter,  from  his  heliacal 
setting  (asta)  ana  rising  (uclaya). 

We  have  already,  in  an  early  part  of  the  treatise  (i.  55),  made  acquaint- 
ance with  a cycle  of  the  planet  Jupiter,  composed  of  sixty  years;  in 
this  verse  wc  have  introi lured  to  our  notice  a second  one,  containing 
twelve  years,  or  corresponding  to  .a  single  sidereal  revolution  of  the 
planet.  The  principle  upon  whig h its  nomenclature  is  based  is  very  evi- 
dent. Jupiter’s  revolution  is  treated  as  if,  like  that  of  the  sun,  it  deter- 
mined a year,  and  the  twelve  parts,  each  quite  nearly  equalling  a solar 
year  (see  note  to  i.  55),  into  which  it  is  divided,  are,  by  the  same  anal- 
ogy,  accounted  as  months,  and  accordingly  receive  the  names  of  the 
solar  months.  The  appellations  thus  applied  to  the  year?-,  in  their  order, 
wc  are  directed  to  determine  by  the  a^terisiu  (nalxhatra)  in  which  the 
planet,  is  found  to  hr  at  the  time  of  its  disappearance  in  the  sun's  rays, 
and  its  disengagement  from  them : for  it  would,  of  course,  set  and  rise 
licliaeally  twelve  limes  in  each  resolution,  and  each  time  about,  a month 
later  than  before.  The  name  of  tin*  year,  however,  will  not  agree  with 
that  of  the  month  in  which  the  rising  and  setting  occur,  blit  will  be  the 
opposite  of  it,  or  six  mouths  farther  forward  rn:  backward,  since  the 
month  is  named  from  Ihe  aslcrism  with  which  the  sun  is  in  opposition, 
but  the  year  of  the  cycle  from  that  with  which  he  is  in  conjunction. 
The  terms  in  which  the  rule  of  the  text  is  stated  are  not  altogether  un- 
ambiguous : there  is  no  expressed  grammatical  connection  between  the 
two  halves  of  the  verse,  and  we  are  compelled  to  add  in  our  translation 
the  important  word  u determines, 11  which  links  them  together.  "The 
meaning,  however,  wc  take  to  be  as  follows : if,  in  any  given  year,  the 
heliacal  slitting  of  Jupiter  takes  place  in  the  month  Yaieakha,  then  the 
astcrisni  with  which  the  moon  is  found  to  be  in  conjunction  at  the  end 
of  that  month — which  will  be,  of  course,  the  asterism  in  which  the  sun 
is  at  the  same  time  situated — will  determine  the  name  of  the  year,  which 
will  bo  Karttika:  and  soon,  from  year  to  year.  The  expression  “in 
like  manlier/’  in  the  second  half  of  the  verse,  is  interpreted  as  implying  i 
that,  to  the  years  of  this  cycle  is  made  the  same  distribution  of  the  as- 
terisms  as  .to  the  months  in  the  preceding  passage : the  second  and  third 
columns  of  the  last  tabic,  Mum,  will  apply  to  tuc  cycle,  if  w£  alter  their 
headings  respectively,  from  “ month"  to  “ year  c ? the  cycle,”  and  from 
“astcrisms  in  which  full  moon  may  occur”  to  “usteriaius  in  which  Ju- 
piter's heliacal  setting  and  rising  may  occur.” 

m There  is  one  untoward  circumstance  connected  with  this  arrangement 
wdiicli  is  not  taken  into  acconnt  by  the  text,  and  which  appeal's  to  op- 

Sose  a practical  difficulty  to  the  application  of  its  rule.  The  amount  of 
upiters  motion  during^a  solar  year  is  not  precisely  one  sign,  but  per- 
ceptibly more  than  that,  so  that  the  mean  interval  between  two  succes- 
sive heliacal  settings  is  a little  more  than  a solar  month ; and  this  dif- 


272 


• SAryarSiddhdnta , [*»v.  17- 

• 

fefence  accumulator  so  rapidly  that  the  thirteentli  setting  would  take 
place  abonttfour  degrees  farther  eastward  than  the  first,  so  that,  without 
some  system  of  periodical  omissions  of  a mouth,  the  correspondence 
between  the  names  of  the  years,  if  applied  in  regular  succession,  and 
the  astgpsms  in  which  the  planet  disappeared  would,  after  a few  revolu- 
tions, be  altogether  dislocated  and  broken  up.  Tf  the  cycle  were  of 
more  practical  consequence,  or  if -it  were  contemplated  as  one  of  the 
proper  subjects  of  this  treatise,  we  might  expect  to  find  some  method 
of  obviating  this  difficulty  prescribed.  Warren,  however,  ’in  his  brief 
account,  of  the  cycle  of  twelve  years  (K&la  Sankalita,  p.  21*2  etc.),  states 
that  he  knows  of  no  nation  or  tribe  making  any  use  of  it,  but  only  finds 
it  mentioned  in  the  books.  According  to  both  him  and  Davis  (As.  Res., 
iii.  217  etc.),  the  cycle  of  twelve  yeah  is  subordinate  to  that  of  sixty, 
the.  latter  being  divided  into  five  such  Cycles,  to  which  special  names  are 
applied,  and  of  each  of  which  the  successive  years  receive  in  order  the 
titles  of  the  solar  months.  The  appellations  of  the  cycles  themselves 
are  those  which  properly  belong  to  the  years  of  the  lustrum  (yuga),  or 
cycle  of  five  years,  by  which,  as  already  noticed  (note  to  i.  56-58),  the 
Hindus  appear  first  to  have  regulated  time,  and  effected  by  intercala- 
tion the  coincidence  of  the  solar  and  lunar  years : they  are  Samvatsara, 
Parivatsara,  Idavatsara,  Idvalsara,  (or  Anuvatsara),  and  Valsara  (or 
Idvatsara,  or  Udravatsara).  It  would  appear,  then,  cither  that  the  cycle 
of  sixty  years  was  derived  from  ami  founded  upon  the  ancient  lustrum, 
being  an  imitation  of  its  construction  in  time  of  the  planet  Jupiter, 
of  which  a month  equals  a solar  year,  or  else  that  the  already  existing 
cycle  had  been  later  fancifully  compared  with  the  lustrum,  and  subdivi- 
ded after  its  model  into  sub-cvclcs  for  years,  and  years  for  months:  of 
these  two  suppositions  wo  arc  inclined  to  regard  the  latter  as  decidedly 
the  more  probable. 

18.  From  rising  to  rising  of  the  sun,  that  is  called  civil  (sthrtna) 
reckoning.  By  that  arc  determined  the  civil  days  (sdvana)}  ami 

■ by  these  is  the  regulation  of  the  time  of  sacrifice; 

19.  Likewise  the  removal  of  unclcanncss  frofn  child-hearing 
etc.,  and  the  regents  of  days,  months,  and  years : the  mean  mo- 
tion of  the  planets,  too,  is  comput,ed4>y  civil  time. 

The  term  sAvanu  we  have  translated  u civil,”  as  being  a convenient 
way  of  distinguishing  this  from  the  other  kinds  of  time,  and  as  being 
very  properly  applicable  to  the  day  as  reckoned  in  practical  use  from 
, sunrise  to  sunrise  : in  the  more  general  sense,  as  denoting  the  me.  le  of 
reckoning,  the  mean  motions  of  the  planets,  and  the  regency  of  succes- 
sive periods,  savana  corresponds  to  what  we  call  “ mean  solar”  time. 
The  word  itself  seems  to  be  a derivative  from  savana , “ libation,”  llio 
three  daily  savanas , or  the  sunrise,  noon,  and  sunset  libations,  bcincL 
determined  by  this  reckoning. 

20.  The  mutually  opposed  day  and  night  of  the  gods  (sura) 
and  demons  (asura),  wnictf  has  been  already  explained,  is  time 
of  the  gods,  being  measured  by  the * completion  of  the  sun's 
revolution. 


Translation  and  Notes. 


278 


xiv.  27.] 

21.  The  space  of  a Patriarchate  (manvanlara)  is  styled  time 
of  Prajapati : in  it  is  no  distinction  of  day  fi;om  night.*  An  Moxi 
(kalpa)  is  called  time  of  Brahma. 

It  may  well  be  said  that  the  mode  of  .reckoning  by  time  of  the  gods 
has  been  already  explained:  the  length  of  a day  of  the  gods,  Vith  the 
method  of  its  determination,  has  been  stated  and  dwelt  upon,  in  almost 
identical  language,  over  ami  over  again  fscc  i.  13-14 ; xii.  45-50,  67, 
74 ; and  the  interpolated  verse  after  xiv.  3),  almost  as  if  it  were  so  new 
and  striking  an  idea  as  to  demand  and  bear  repeated  inculcation.  For 
the  Patriarchate  (manvantara),  or  period  of  308,448,000  years,  see 
above,  i.  18 : this  is  the  only  allusion  to  it  as  a unit  of  time  which  the 
. treatise  contains.  For  thc\Eon  (kalpa),  of  4,320,000,000  years,  as 
constituting  a day  of  Brahma,  see  above,  i.  20. 

The  remaining  verses  arc  simply  the  conclusion  of  the  treatise. 

22.  Thus  hath  been  told  thee  that  supreme  mystery,  lofty  and 
wonderful,  that  sacred  knowledge  {brahman),  most  exalted,  pure, 
all  guilt  destroying ; 

23.  And  the  highest  knowledge  of  the  heaven,  the  stars,  and 
the  planets  hath  been  exhibited:  he  who  knoweth  it  thoroughly 
obtaineth  in  the  worlds  of  the  sun  etc.  ail  everlasting  place. 

24.  With  these  words,  taking  leave  of  Maya,  and  being’  suit- 
ably worshipped  by  him,  the  part  of  the  sun  ascended  to  heaven, 
ana  entered  lus  own  disk. 

25.  So  then  Maya,  having  personally  learned  from  the  sun 
that  divine  knowledge,  regarded  himself  as  having  attained  his 
desire,  and  as  purified  from  sin. 

26.  Then,  too,  the  sages  ( rshr\  learning  that  Maya  had  received 
from  the  sun  this  gift,  drew  near  and  surrounded  him,  and  rev- 
erently asked  the  knowledge. 

27.  And  he  graciously  bestowed  upon  them  the  grand  system 
of  the  planets,  of  mysteries  in  the  world  the  most  wonderful, 
.and  equal  to  the  Scripturtf  (brahman). 

The  Surya-Siddhftnta,  in  t$c  form  in  which  it  is  here  presented,  as  ac- 
cepted by  lianganatha  and  fixed  by  his  commentary,  contains  exactly 
five  hundred  verses.  This  number,  of  course,  cannot  plausibly  be  looked 
upon  as  altogether  accidental : no  one  will  question  that  the  treatise  has 
been  intentionally  wrought  into  its  present  compass.  We  have  often 
found  occasion  above  to  point  out  indications,  more  or  less  distinct  and 
unequivocal,  of  alterations  and  interpolations ; and  although  in  some 
cases  our  suspicions  may  not  prove  well-founded,  there  can  he  no  rcason- 
4 able  doubt  that  the  text  of  the  treatise  has  undergone  silica  its  origin 
not  unimportant  extension  and  modification.  Any  farther  consideration 
of  this  point  we  reserve  for  the  general  historical  summary  to  be  pre- 
sented at  the  end  of  the  Appendix.  • 


274 


Mrya-Siddhdnta, 


[introd. 


APPENDIX: 

CONTAIN  I Xli  ADDITIONAL  NOTES  AND  TABLES,  CALCULATIONS  OF 
ECLIPSES,  A STELLAR  MAP,  Etc. 


1.  p.  ii.  a The  name  siddhdnta , by  which  the  astronomical  text- 
books are  generally 'called,  has,  by  derivation  and  original  meaning, 
nothing  to  do  with  astronomy,  but  signifies  simply  “established  conclu- 
sion and  it  is  variously  applied  to  other  uses  in  the  Sanskrit  literature. 

It  may  not  be  uninteresting  to  present  here  a summary  view  of  the 
existing  astronomical -literature  of  the  Hindus,  as  derived  from  such 
sources  of  information  upon  the  subject  as  are  accessible  to  us,  even 
though  such  a view  must  necessarily  be  imperfect  and  incomplete.  We 
commence  by  giving  n list  of  works  furnished  to  the  translator,  at  his 
request,  by  the  native  Professor  of  Mathematics  in  the  Sanskrit  College 
at  Pfina,  and  which  may  be  taken  as  representing  the  knowledge  pos- 
sessed, and  the  opinions  held,  by  the  learned  of- Western  India  at  the 
present  time.  Along  with.it  is  offered  the  list  of  nine  treatises  given  in 
the  modern  Sanskrit  Encyclopedia,  the  (,-abdakaIpadrumu,  as  entitled  to 
the  name  of  Siddh&nta.  The  longer  list  was  intended  to  be  arranged 
chronologically ; the  remarks  appended  to  the  names  of  treatises  arc 
those  of  its  compiler. 


i.  Brahma-Siddh&nta. 

7 . Surya-SiddhAnta. 

3.  Soma-SiddhAnta. 

4.  Vftsishtha-Siddh&nia. 
Romaka-SiddliAnta. 
P&ulastyarSiddhfuita. 
Brhaapati-Siddhaota. 
Garga-Siddhanta. 
VyAsa-SiddhAnta. 


5. 

6. 
7- 

-8. 

9- 

io. 


z.  Brahraa-SiddhAnta. 

7.  Surya-Siddhanta. 

3.  Soma- Siddhdnta. 

4-  Brhaspali-SiddhAnta. 

5.  Garga-SiddhAn La. 

6.  NAraria-SirfJhAnta. 

7-  PArAptru-Siddhanta. 

8-  PAidustya-SiddhAnta. 

9-  Vasiahtlia-SiddhAnta. 


PArAgara-SiddhAnta. 
ii.  Bhoja-Siddhanti;  earlier  than  the  yiromanj. 
i a.  VarAha-SiddhAnta ; earlier  than  the  (jfromani. 

1 3.  Brahmagupta-SiddhAota ; earlier  than  the  ^iromaqii. 
t4-  SiddhAnta-^iromani ; fake  1072  [A.D.  1 160 j. 

1 5.  Sundara-SiddhAnta;  about  400  years  ago.  [years  ngo 

1 6.  Tattva-Viveka-Siddh&nta  ; in  the  time  of  the  reign  of  Jaya  Sinha,  about  260 

17.  SArvabhAuma-Siddhfinta ; in  the  time  of  the  reign  of  Jaya  Sinha. 

18.  Laghu-Aiya-SiddhAnta ) 

19.  Brhad-A^arBiddliintn  t ^ th“  th° 


It  is  obvious  that  these  lists  are  uncritically  constructed,  and  that 
neither  of  themes  of  a nature  to  yield,  valuable  information  without  ad- 
ditional explanations.  The  one  is  most  unreasonably  curt,  and  seems 
founded  on  the  principle  of  allowing  the  title  of  Siddhdnta  to  no  work 


275 


note.]  Additiondl%6tes,  etc. 

which  ift  the  acknowledged  composition  of  a merely  human  author, 
'while  the  other  contains  treatises  of  very  heterogeneous  character  and 
value:  and  neither  list  distinguishes  works  how  actually  in  existence  from 
those  which  have  become  lost,  and  those  of  which  the  existence  at  any 
period  is  questionable.  A more  -satisfactory  account  of  tlie  Siddh&nta 
literature  may  be  drawn  up  from  the  notices  contained  in  the  writings  of 
Western  scholars,  and  especially  from  the  various  essays  of  Colobrooke. 
Vor  what  we  shall  here  offer,  he  is  our  main  authority. 

In  the  present  imperfect  state  of  our  knowledge  of  the  subject,  there 
is  perhaps  no  better  method  of  classifying  the  Hindu  astronomical  trear 
tises  than  by  dividing  them  into  four  classes,, as  follows:  first*. those 
which  profess  to  be  a revelation  on  the  part  of  some  superhuman  being ; 
second,  those  which  are  attributed  to  ancient  and  renowned  sages,  or  to 
other  supposititious  or  impersonal  authors ; third,  those  regarded  as  the 
works  of  actual  authors,  astronomers  of  an  early  and  uncertain  period ; 
fourth,  later  texts,  of  known  date  and  authorship,  and  mostly  of  a less 
independent  and  original  character.  • 

I.  The  first  class  comprises  the  Brahma"  S&rva,  Sonia,  Brhaspati,  and 
N&rada  Siddh&nta*. 

1.  Brahma-Siddkanta . The  earliest  treatise  bearing  this  name  is 
said  to  have  formed  a part  of  the  Yishnudlmrmottara  Purana,  a work 
which  seems  to  be  long  since  lost,,  and  scarcely  remembered  except  in 
connection  with  the  Siddh&nta.  The?  latter,  too,  is  only  known  by  a few 
citations  in  astronomical  writings,  and  by  the  treatise  of  Brahmagupta 
(see  below,  third  class)  founded  upon  it.  Another  work’ laying  claim  to 
the  same  title  is  that  which  we  have  nianv  times  cited  above  as  the 
(r'&kalya-Sanhit&.  Sanhita,  “text,  comprehensive  wtfrk,”  is  a Mm  em- 
ployed to  denote  a complete  course  of  astronomy,  astrology,  horoscopy, 
etc. : this  treatise,  according  to  the  manuscript  in  our  possession,  forms 
tlie  second  division  (prapna)  of  such  a course.  It  professes  to  be  re- 
■ vealed  by  Brahma  to  the  semi-divine  personage  N&rada.  Of  its  relation 
to  the  Surj  a-Siddh&nta  we  have  spoken  above  (note  to  vii^  10-12).  It 
docs  not  appear  to  be  referred  to  as  an  independent  work  in  either  of 
the  native  lists  we  have  given. 

2-.  S&rya- Siddh&nta.  This  is  the  treatise  of  which  the  translation 
has  been  given  above,  and  of  which,  accordingly,  we  do  not  need  to 
speak  here  more  particularly. 

3.  Soma- Siddh&nta.  Judging  from  its  title,  this  work  must  profess 
to  derive  its  origiu  from  the  moon  (soma),  as  the  preceding  from  the 
sun  (surya).  Bentley  speaks  of  it  aS  following  in  the  main  the  system 
of  the  S&rj’n-Siddh&ntn.  There  is  a manuscript  of  it  in  the  Berlin 
Library  (Webers  Catalogue,  No.  840),  and  C*  lebrooku  seems  also  to 
have  had  ijL  in  liis  bauds. 

4.  Jirhaspatm S iddh&nta.  Bjhaspati  is  the  r.  ime  of  a divine  person- 
age, priest  and  teacher  of  the  gods,  as  also  of  the  planet  Jupiter.  No 
work  bearing  this  name  is  mentioned,  so  far  as  we  can  ascertain,  by  any 
European  scholar,  although  Byliaspati  is  not  infrequently  referred  to  in 
native  writings  as  an  authority  in  astronomical  matters. 

5.  NAradi  Siddh&nta.  A N&radi-SanhitA,  or  course  of  astrology,  in 
tlie  Berlin  Library  (Weber,  No:  862),  and  an  occasional  reference  to 


276 


S&rya-J^uldhdniaj  [introd. 

Nkrada,  Among  other  divine  or  mythical  personages,  a*  an  astronomical  . 
authority,  are  all  the  indications  we  find  justifying  the  introduction  of 
this  name  into  the  list  of  the  (^abdakalpadnima. 

11.  In  the  second  class  wc  include  the  Gkrga,  Vyksa,  Pkragara,  Pku- 
li<ja,  I'anlastya,  and  Vasishtha  Sirhlhkntas.  Garga,  Par&carn,  Vyksa, 
Pulastya,  and  Vasishtha  arc  prominent  among  the  sages  of  the  ancient 
period  of  Hindu  history  : the  two  latter  arc  ot  the  number  of  those  who 
give  name  to  the  stars  in  Ursa  Major  (they  are.  (t  and  £ respectively). 
They  cannot  possibly  have  been  the  veritable  authors  of  Siddh&ntas,  or 
works  presenting  the  modern  astronomical  system  of  the  Hindus : hut — 
and  this  seems  to  be  especially  the  ease  with  regard  to  .Garga  and  Park- 
^ara — one  and  another  of  them  may  have  distinguished  themselves  in 
connection  with  the  older  science,  and  so  have  furnished  some  ground 
for  the  part  attributed  to  them  by  the  later  tradition,  and  for  th$  father- 
ing of  astronomical  works  upon  them. 

1.  Qarga-SiildMnta . Astronomical  treatises  and  commentaries  upon 
them  occasiofially  offer  citations  from  Garga  (sec,  for  instance,  Colc- 

. brooke’s  Essays,  ii.  356 ; Sir  William  Jones  in  As.  lies.,  ii.  397),  but  of 
a Siddbanla,  or  text-book  of  astronomy,  bearing  his  name,  we  find 
nowhere  any  mention  excepting  in  these  lists. 

2.  Vyusa-Siddhduta . This  name,  too,  is  known  to  us  only  from  the 
list  above  giwir. 

3.  Par&fara-SiddMnla.  According  to  Heutlov,  the  second  chapter 
of  the  Arya-Siddhknta  contains  :ui  extract  from'  this  work,  in  which  are 
stated  the  elements  of  the  mean  motions  of  the  planets  adopted  by  it. 
Thu  work  ii  self  appears  to  be  lost;  unless,  indeed,  it  may  have  been 
contained,  in  a manuscript  of  the  Mackenzie  Collection,  which  in  Wil- 
son’s Catalogue  (i.  120)  is  called  Yriddlia-Parasara,  mid  said  to  be  M a 
system  of  astrology,  attributed  to  Purusara,  the  father  of  Vyksa.” 

4.  Pauli ca-Siddhduta . The  planetary  elements  of  this  treatise  also 

are  preserved  in  later  commentaries,  and  are  stated  by  Huntley  and 
Col e b rook e.  have  noticed  above  (note  to  i.  4-6)  that  al-Iili'iun  at- 

tributes it  to  Pan  I us  the  Greek  ; whence  Wobei  (Iml.  Lit.,  p.  226)  con- 
jectures that  it  was  founded'iipoii  the  A7cru;'iv/»j  of  Puulus1  Alexandrinus. 
If  this  account  of  its  origin  be  correct.  *lie  Pul icpi  tp  uhomthc  later 
Hindus  attribute  it  is  a fictitious  personage,  whom1  iiainc  js  manufactured 
out  of  Pku1i<;a.  The  work,  it  \\  ill  be  seen,  is  not  mentioned  in  either  of 
the  lists  wc  have  given,  its  place  appearing  to  be  taken  by  the.  Pulastya- 
Siddli&nta.  According  to  the  Hindu  tradition,  the  school  represented 
by  the  Paulica-Siddlmnta  was  the  uval  of  that  of  Aryahhntta. 

5.  Pulastya- Siddh&nta.  Of  this  Siddhanta  we  find  mention  only  in 
such  native  lists  as  omit  the  preceding,  lienee  we  arc  led  to  conjecture 
that  the  two  names  may  indicate  the  same  work;  an  attempt,  founded 
upon  the  similarity  of  tiic  names,  having  been  made  by  sdhic  to  attribute* 
the  PauliQa-Siddhknta  to  a known  and  acknowledged  Hindu  sage. 

6.  Vasishtha- Siddhdn  fa, . This  work  is  spoken  of  as  actually  in  ex- 
istence by  .both  Colcbrooke  and  Hentley,  and  the  latter  states  its  sys- 
tem to  correspond  with  that  of  the  H&rya-Siddhknta.  More  than  one 
treatise  bearing  the  name  is  referred  to,  the  older  one  being  of  unknown 
authorship,  and  the  other  a later  compilation  founded  upon  this,  by 


\ islmu-camlra,  who  is  said  also  to  have.  derived  his  material  in  part  from 
Aryabhatta.  A copy  of  a Vrthlha-V  asishtha-Siddh&nta  formed  a part  of 
the  Mackenzie  Collection  (Wilson’s  Catalogue,  i.  121). 

III.  To  the  third  class  may  lie  assigned  the  Siddhantas  of  Aryabliat- 
ta,  Varklia-iuiliira,  and  Brahmagupta,  and  the  Rom  aka-Si  ddh&nta,  as 
well  as  the  later  version,  of  the  Vasislitha-Siddh&uta,  last  spoken  of. 
The  first  three  names  arc  those  of  greatest  prominence  and  highest  im- 
portance in  the  history  of- Hindu  astronomical  science,  and  there  is 
every  reason  to  belic\c  that  the  sages  who  bore  them  lived  about  £he 
time  when  the  modern  system  may  ho  supposed  to  have  .received  its 
final  and  fully  developed  form,  or  during  the  fifth  and  sixth  centuries  of 
our  era. 

1.  A rya-Siddhu  at  a.  The  two  principal  works  of  Aryabhatta  appear 
to  have  been  originally  entitled  the  Ary&shtai;at.*i,  “ work  of -eight  hun- 
dred verses,”  and  I >ac;agitik&,  tm  work  of  ten  cantos.”  Colebrooke  knew 
neithcrof  them  excepting  by  citations  in  other  a.-trouomical  text-books 
ami  commentaries.  Bentley  had  in  hi-  hand* two  1 realises  which  he 
calls  Ihe  Arya-Siddlmnta  ami  the  Laghii-Arya-Siddhanta,  which  arc  pos- 
sibly identical  with  those  above  named.*  Tins  Berlin  Library  aNo  con- 
tains (Weber,  ?fo.  b.'J4)  a work  which  professes  to  he  a commentary  on 
the  Dacagitika. 

2.  Var&ha- SUhlhanUt.  The  only  dL'.iue'.Ri'ly  astronomical  work  of 
Yurnhi'L-mihirn  appears  to  have  liei-u  his  Bain  a -si« Mhantika,- or  Compen- 
dium of  Five  Astronomies,  «.»f  which  we  lime  already  spoken  (note  to 
i.  2 and  which  was  founded  upon  tin*  Brahma,  Surya,  Fftulica,  Va- 
si.-Jitha,  ami  Komaku  Siddhantas.  It  U Mippi»M.*d  to  bo  in>  longer  in 
existence,  although  the  a>lrniogic:d  work-  of  the  Mime  author  have  been 

"carefully  piVMTvod,  and  arc  uiihoiil  diliieulty  accessible.  * 

d.  tiruhiiia-Sidilhuiihi.  The  projier  title  of  the  work  composed  by 
Brahmagupta,  upon  the  foundation  ««f  an  earlier  tr.-ati^e  hearing  this 
name,  is  Bralimu-sphula-Siddhniilu,  il  convclcd  Brail nia-Siddhiiuyi,1"  but 
the  word  gphjiM,  “ correct ctl,”  is  lrci|iiciilly  omitted  in  citing  it*  as  lias 
her n our  own  usage  iu  the  notes  to  the  Surya:Siddhan1;i.  Colebrooke 
possessed  an  imperfect  copy  of  it,  and  it  was  also  in  Bentley's  posses- 
sion. 1!pou  it  in  as  professed ly  founded,  in  the-  main,  the  Siddhauta-t^i- 
roiiiani  of  Bhuskura.  ' . * 

4.  JtoHiaLttSiddluivhr.  Of  the  name  of  this  treatise,  the  qply  one 
we.  haw  thus  far  met  with  which  is  not  demrd  from  a real  or  supposed 
author,  we.  have  spoken  in  the  note  to  i.  4-0.  It  is  said  by  Colebrooke 
to  he  by  Frishcna,  and  to  have  been  founded  in  part  upon  the  original 
1 Yasibhtha-Siddliiluta : its  early  date  is  proved  by  its  being  one  of  those 
treated  as  authorities  l»y  Ysinilumiihira.  No  opv  of  Jt  seems  to  have 
have  been  discolored  in  later  times. 

jUur  list  also  mentions  a Bhoja-Siddlianta.  probably  referring  to  some 
nstronomieol  work  published  during  the  reign,  and  under  the  patronage, 
of  Raja  Blioja  Deva,  of  bhiir&y'in  the  tenth  or  clevcmh  century  , of 
our  era. 


* Sue.  nn  article  by  Fits-Edward  Hall,  Esq.,  On  the  Arya  Shhlhfinta,  in  the  Jour- 
nal of  Lite  American  Oriental  Society,  vol.  vi,  1S0U. 

:*i 


278 


| introd.  note- 


SHrya-Siddhdnia , 

IV#  Our  fourth  class  is  headed  xl>y  the  fiiddh&nta-Qiromani,  written  in 
the  twelfth  century  bv  lih ask ura  Aefcrya,  and  founded  upon  the  Bralnna- 
Siddlianta  of  Brahmagupta.  Our  juiracrou^rcfcrencea  to  it  and  cita- 
tions from  it  indicate  the  promincut  and  important  position  which  it 
occupies  in  the. modern  astronomical  literature  of  India.  For  a dcscrip-. 
tiou  of  the  numerous  commentaries  upon  it,  see  Colobrooke’s  Hindu 
Algebra,  note  A (Rssays,  ii.  460  etc.). 

The  longer  of  the  lists  given  above  mentions  two  or  three  other 
works  «»f  "yet  later  date.  Among  them  the  Siddhhnta-Smulara  is  the 
most  ancient,  having  Jieen  composed  by  Jnuua-r&ja  at  the  beginning  of 
the  sixteenth  century.  The  Graha-IAghava  is  a treatise  of  the  same 
class,  and  is  highly  considered  and  much  used  throughout  India,  idthough 
omitted  from  the  Pflna  list.  It  )s  of  nearly  the  same  date  with  the 
work  last  spoken  of,  being  the  composition  of  lianei/a,  and  dated  fake 
1442  (A.D.  1520).  The  Siddh&nta  Tattva-Viveka,  more  usually  styled 
the  Tattva-Viveka  simply,  is  a century  later : it  was  written  by  Kama- 
lakara,  about  A.  L).  1020.  The  KiddhaiJta-S&rvabli&uma  dates  from  very 
nearly  the  same  period,  and  is  the  work  of  Muui<;varaj  who  is  also  the 
author  of  a cmnmcntun  on  ilic  (^inunani.  and  the  son  of  llangan&tliu, 
the  commentator  on  the  SAna-Siddhuiilu.  * 

Tlii^  class  of  astronomical  writing*  might,  be  almost  indefinitely  ex- 
tend eJ,  but  the  works  whii-li  haio  been  mentioned  appear  to  bo  the 
uio«il  authoritative  and  important. 

Of  all  the  treatises  whose  nunie>  wo  have  cited,  we  know  of  but  three 
which  hate  a>  via  been  published — the  Surya-Siddhanta,  the  Siddlmnta- 
^'iromani.  and  the  (jraha-Lugh.'uu  ; the  two  latter  under  the  auspices  of 
the  School-ISook  Society  of  ( alcnUa.  1W.  Hall's  edition  of  the  Shi  va 
KiddJiunta,  to  w hich  reference  is  made  in  our  Introductory  Note,  Las’ 
been  completed  by  tlie  addition  of  a fourth  Fasciculus  since  our  own 
publication  wn-»  commenced,  so  1 bat  we  have  been  able  to  avail  ourselves 
of  its  valuable  assistance  throughout. 

2.  i>.  ii.  Jlangauatha,  in  the  verses  with  which  he  closes  his  com- 
mentary, states  it  to  have  been  completed  on  the  same  day  with  the 
birth  of  liis  son  Muni  (/vara,  in  tlie  pttkn  year  1525,  or  A.  1).  1603.  For 

#1h9  relationship  to  other  well-known  a'.thors  or  commentators  of  astro- 
nomical trcali.-es,  see  * 'ulobruokeV  I'Nsiys  ii.  452  etc.  Other  commenta- 
tors on  rile  Surya-Siddh/mtn  mentioned  by  < 'olebrookc  are  N rail  ilia,  who 
wrote  but  a few  years  later  than  Kangunulha,  and  Bhfidhara  and  IKUlfi, 
Bliai,  whose  age  is  not  stated.  The  Mackenzie  collection  (see  Wilson’s 
Catalogue,  p.  118  etc.)  contained  commentaries  on  the  whole  or  parts  of 
the  same  text  by  Mallikarjiinu,  Yellaya,  an  Aryaldiatta,.  Mammabhatta, 
and  Taminaya. 

3.  j».  iii.  As  no  especially  suitable  opportunity  lia^liithcrto  offered 
itself  for  giving  in  our  notes  the  synonymy  of  the  names  of  the  planets, 
we  present  here  all  the  appellations  by  which  they  are  known  in  the  text 
of  the  Siirya-Siddhanta. 

The  sun  is  called  by  the  following  names  derived  from  roots  signify- 
ing “ to  shine’ : urka,  bk&nu,  ravi , vivasvant,  s&rya;  also  savitar,  liter- 
•ally  “ enlivciicr,  generator” ; bh$9kara>  “ light-maker” ; dinakara  and 


*■  Additional  Notes,  etc.  *•279' 

* 

divAkara , “ day-maker” ; and  tigmAncu  ami  ttkskn&nru.  “having "hot  or 
piling  rays”  1 8 - 

1 lie  moon,  besides  her  ordinary  names  ivufrr,  candra , vidhuy  is  styled 
nipAkura,  11  night-maker” ; nipapati.  “ lord  of  night”;  anushnagu , pita-  . 
.<7*b  y?'Anp«,  ritndidkxtiy  himaraprai , himYtnpu , himudulhiti , “having cool 
rays”  ; and  pr/rm  and  papAnka,  “marked  with  a hare”  : the  Hindu  fancy 
sees  itho  figure  of  this  animal  in  the  spots  on  the  moon’s  disk.  The 
name  soma  nowhere  directly  occurs,  but  it  is  implied  in  the  title  s&utnya 
given  to  Mercury. 

Mercury  is  styled  jfia  and  bud  ha,  “ wise,  knowing” ; also  pafija  and 
sAumya,  “ son  of  the  moon/’  The  reason  of  neither  appellation  is  ob- 
vious. ft  will  lie  seen  below  lhat  tho  in  non,  the  sun,  and  the  earth  have 
each  of  them  one  of  the  lesser  planets  assigned  to  it  as  its  son : why 
Mercury,  Saturn,  and  Mars  were*  selected,  and  on  what  grounds  their 
respective  parentage  was  given  them,  is  hitherto  entirely  unknown. 

Venus  has  one  name,  pvkra,  “ brilliant,”  which  i<  derived  from  lier  ■ 
actual  character:  she  is  also  known  as  bhrgu , which  is  the  name  of  one 
of  the"  most  noted  of  the  ancient  sages,  or  as  bhrguja  or  bhArgava, 

“ son  of  Bhrgu.” 

Man  has  likewise  a single  appellation,  angurnku,  ■■  i;oal/’  which  is 
given  him  on  arronnf  of  hi-*  tiny  horning  light  : all  his  other  titles, 
namely  kuja,  bhaputra , bhuwiputra,  bhuxnta,  him  tuna,  mark  him  as  “son 
of  the  earth.” 

Jupiter  is  known  as  brhaspati , which  b,  as  already  more  than  once 
noticed,  tlie  name  of  a divine  personage,  priest  and  teacher  among  tlift 
gods ; #the  word  means  originally  “ l«»rd  «»f  worship.”  #The  planet  also 
receives  some  of  his  title*,  namely  guru,  “ preceptor/'  and  amarejya , 
“teacher  of  the  immortals/’  The  only  other  name  given  to  it,  jlva9 
“ living,”  is  of  doubtful  origin. 

Saturn  has  two  appellations,  each  represented  by  several  forms; 
namely  “sun  of  the.  aun/’  or  arkart , <‘nki,  shryalauaya ; aucl  “the  slow- 
moving,1 " or  mqtida,  pani,  rtinaiprara. 

All  these  names,  it  will  be  noticed,  arc  of  native  Hindu  origin,  and 
have  nothing,  to  do  with  the  appellations  given  by  other  nations  to  the 
planets.  Tn  the  Hindu  astrological  writings  however,  even  those  of  a 
very  early  period  (see  Weber's  Iml.  Stud.,  ii.  -Mil),  appear,  along  with 
these,  other  titles  which  are  evidently  derived  from  those  of  the 
(i  reeks. 

•ft.  p.  2.  Wo  have  everywhere  cited  Bentley's  work  on  Hindu  as- 
tronomy according'  to  tho  London  edition  of  it  (8vo.,  1825),  the  only 
one  to  which  we  have  had  access.  • 

In  ft  few  instances,  where  we  have  not  speeiii  *1  the  part  of  Bh&skara’s 
Siddhknt^-Viroinani  to  which  we  #rcfer,  the  Gaiiitiulliy&ya,  or  properly 
astronomical  portion  of  it,  is  iutended. 

5.  p.  17.  For  the  convenience  of  any  who  may  desire  to  make  a 
more  detailed  examination  of  the  elements  of  the  mean  motions  of  the 
planets  adopted  in  this  treatise,  and  to  work  out  the  results  dedlicible 
from  them,  we  present  them  in  the  following  table  in  a more  exact  form. 
We  give  the  mean  time  of  sidereal  revolution,  in  mean  solar  days,  and 

• 


280  S&rya-Siddhdnta.  . {}• 

the  amount  of  mean  motion,  in  seconds,  during  a day,  and  also  (lurin', 
a Julian  year,  of  ;105£  mean  solar  days. 


Mean  Motions  of  the  Planets. 


Planrt. 

Time  of  “ 
fliilcrnnl  re  ’iilutiqn. 

Moan  daily  motion. 

Moan  yearly  motion 

Sun, 

il 

365.25875048 

1 » 

3,548.16956 

li 

1,295,968.931 

Mercury, 

87.96970228 

14,732.34496 

5,380,988.996 

Venus, 

224.69856755 

5,767.72702 

2,106,662.295 

Mars, 

686.99749  394 

1 ,886.46976 

689,033.081 

Jupiter, 

4,332.32065235 

299.14683 

109,263.381 

Saturn, 

Moon, 

1 o,7G5. 77307.10 1 

x ao.38  i5i 
i 

43,969.346  ; 

- eider,  rev., 

27.3a1fi7.f16 

: 47,434.86773  “ 

I7,3a5,585.437 

synod,  rev., 

29.5305879.5 

1 43,886.69817 

16,029,616.507 

apsis, 

3,232.0936-41? 

l 400.97848 

146.457.389 

node, 

6,794.39983 1 a 1 

[ 190.74532 

(■>9,669.730 

6.  p.  17.  The  system  of  the  Kurya-Siddluliita,  so  far  as  concerns 
the  mean  motions  of  the  planets,  the  date  of  the  last  general  conjunc- 
tion, and  the  frequency  of  its  recurrence,  i*  also  •that,  of  the  £&kalya- 
Sanhita.  It  is  likewise,  presented,  according  to  1 lent  lev  (Hind.  Astr„  p. 
110),  hy  the  Soma  and  Vasishtlia  Siddhantas.  So  far  as  can  he  gath- 
ered Iruiii  the  elements  of  the  Paiilicu  and  Laglm-Arva  ttiddlmntus,  as 
reported  by  Cohibrookc  ar.d  Bentley,  these  treatises,  too,  followed  a simi- 
lar system  ; the  revolutions  of  tin*  planets  in  an  Age,  as  stated  l>y  them, 
where  they  differ  from  those  of  the  SArva-Siddhfinta,  always  ditfer  hy  a 
number  which  is  a multiple  of  four.  Some  of  the.  astronomical  text- 
books, however,  have  constructed  their  systems  in  a somewhat  different 
manner.  Thus  the  Siddhanta-t/iromaui,  following  the  authority  of 
Brahmagupta  and- of  the  earlier  Bralmia-Siddliauta,  makes  the  planets 
commence  their  motions’ together  at  the  star  E l'iscjnni  at  the.  very  com- 
mencement of  the  ./Kon,  and  return  to  ,*  general  conjunction  at  the  same 
pointfonly  after  the  lapse  of  the  whole  oeric<l  of  4,-120,000,000  yeprs. 
The  same  is  the  ease  with  the  Arvn  and  l>urfir;ar;i.  Siddh&ntgs : they  too, 
as  reported  by  Bentley  (Hind.  Asfr.,  pj».  MR,  150), state* the  revolutions 
of  the  planets  for  the  whole  only,  and  in  numbers  which  have  no 
common  divisor,  so  that  they  assume  ho  briefer  cycle  of  conjunction. 
But  they  all,  at  the  same  time,  take  special  notice  of  the  commence- 
ment of  the  Iron  Age,  which  they  make  to  begin  at  the  moment  of  mean 
sunrise  at  Lank£t,  and  jmanage  to  effect  very  nearly  a general  conjunc- 
tion at  the  time  of  its  occurrence,  as  is  shown  by  the  table  at  the  end 
of  thjs  note,  in  which  arc  presented  the  positions  of  all  the  planets,  and 
of  the  moon’s  apsis  and  node,  as  stated  by  them  for  that  moment. 

We  insert  these  data  hftre,  because  they  seem  to  us  to  furnish  ground 
for  important  conclusions*  respecting  tb<;  comparative  antiquity  of  the 
two  systems.  The  commencement  of  the  Iren  Age,  which  to  the  one 
is  of  cardinal  importance  as  an  astronomical  epoch,  is  to  the  other 
himply  a chronological  tta,  having  no  astronomical  significance.  Now 
if,  as  has  been  shown  in  our  notes  to  be  altogether  probable,  that  epoch 


i.  34.]  Additional  Notes , etc.  281 


is  in  fact,  of  astronomical  origin,  being  arrived  at  by  retrospective  calcu- 
lation of  tlic  planetary  motions,  wo  can  liardly  avoid  the  conclusion  that 
the  system  wbjch  presents  it  in  its  true  character  is  the  more  ancient 
and  original.*  This  conclusion  is  strengthened  by  the  notice  taken  of 
the  epoch  by  the  Siddh&nta-^iromani  and  its' kindred  treatises.  We  do 
not  see  how  tlicir  treatment  of  it,is  to  be  explained,  excepting  upon  .the^ 
supposition  that  a general  conjunction  at  that  time  was  already  so  firmly 
established  as  a fundamental  dogma  of  tlic  Hindu  astronomy,  that  they 
were  compelled,  even  while  rejecting  tlic  theory  of  brief  cycles  and  re- 
curring conjunctions,  to  pay  it  homage  by  so  constructing  their  elements 
that  these  should  exhibit,  at  least  a very  near  approach  to  a conjunction 
at  the  moment.  Wc  arc  clearly  of  opinion,  therefore,  tliatj  apart  from 
all  consideration  of  the  relative  age  of  the  separate  treatises,  the  systeiA 
represented  by  the  Surva-Siddliaiita  is  the  more  ancient. 

Mean  Places  of  the  Planets , 0 dc  A . M.  at  Ujjayinl , Feb . 1 8th,  B.  C.  3 1 02. 


Planet.  i Siddh&nta^/iromnni. ! Arya-Siddliflnta.  PArA^ara-SiddkAnta. \ 


1 

H 

. 

n 

0 

v 

V 

11 

4 

/ 

<■'"! 

Son,  i 

O 

o 

o 

O 

u 

0 

0 

0 

O 

0 

0 

0 1 

Mercury, 

1 L 

>7 

■M 

1 1 

31 

3-1 

36 

• M 

31 

17 

!7  ! 

Venus, 

1 1 

?H 

■b 

Id 

. TI 

27 

7 

13 

IX 

26 

58 

34  ! 

Mars,  > 

I E 

’9 

3 

5* 

O 

O 

o' 

O 

II 

39 

i4 

38 

Jupiter,  ' 

1 1 

7 9 

’7 

36 

11 

37 

n 

13 

27 

2 

53 

Saturn,  1 

II 

38 

4<> 

34 

0 

O 

n 

O 

II 

28 

57 

22 

Moon, 

o 

»» 

1) 

i) 

0 

O 

0 

(i 

O 

0 

10 

48 

'•  ap?K  | 

4 

5 

39 

46 

4 

3 

5u 

34 

4 

5 

12 

39 

• “ node,  | 

5 

3 

13 

58 

5 

3 

38 

34 

5 

2 

49 

12 

7*  p.  20.  We  present  in  tlic  annexed  table,  in  die  same  form  as 
above  (note  6),  the  elements  of  tlic  mean  motions  of  the  planets  as  cor- 
rected by  the  bija. 


Mean  Motions  of  the  Planets,  as  corrected  hy  the  bija. 


* Plan*. 

Tiffin  of 

vidnrcnl  revolution.  | 

1 1 " " ~ 1 

^Vli'on  daily  motion. 

Mercury, 

d 

1 4,732-33 182 

Venus, 

224.69895ir)2 

5,767.-71717 

Jupiter, 

4,332.41581277 

29^;.  14036 

Saturn, 

10,764.891 71 ->83 

120.39136 

Muon's  apsis, 

3,23?. 1 2«i  5592 

,40097:119  , 

“ node, 
t ! — 

i 6.79428280845 

190.7/861  ; 

Mau  yearly  motion. 


5,380,984.196  '■ 
2, 106,658.695 
109,360.981 
43.972-946 
!46,456.l4j9  ti| 
69,670.^36  . 


8.  p.  22.  At  the  time  when  wc  wrote  our  note,  we,liad  not  omgVjM 
that  lJentlcy  himself  explains,  in  a foot-note  to  page  117  of  his-iyork, 
this  apparent  error.  In  the  ease  of  Mercury,  since  the  number  of  revo- 
lutions as  stated  by  tbe  text  of  our  treatise  did  not  yield  him  the  result 
which  he  desired,  Jic  has  quietly  taken  the  liberty  of  altering  it  from 
17,937,000  to  17,937,024,  assuming,  as  his  justification,  an  error  of  the 
copyists  which  has  not  the  slightest  plausibility,  and  ignoring  the  tact 


282  * SCirya-Smhdnta , [i.  84. 

that  the  correctness  of  the  former  number  is  avouched  by  its  occurrence 
in  other  treatises.  It  is  highly  characteristic  of  Bci)tley,  that  he  has 
thus  arbitrarily  amended  one  of  the  data  upon.wlych  he  rests  the  most 
. important  of  his  general  conclusions,  a conclusion  which,  but  for  such 
emendation,  would  be  not  a little  weakened  or  modified.  Any  one  can 
see  for  himself,  upon  referring  to  our  table  given  on  page  44,  with  how 
much  plausibility  Bentley  is  able  to  deduce,  from  the  dates  of  its  fourth 
column,  the  year  A.D.  1091  as  that  of  the  composition  of  the  Sfirya- 
Siddh&nta.  We  have  been  solicitous  to  allow  Bentley  all  the  credit  we 
- possibly  could  for.his  labors  upon  the  Hindu  astronomy,  but  we  cannot 
avoid  expressing  here  onr  settled  conviction  that,  as  an  authority  upon 
the  subject,  he  is  hardly  more  to  be  trusted  than  Bailly  himself,  that  his 
. work  must  bo  used  with  the  cxtrcincst  caution,  and  that  his  determina- 
t lion  of  the  successive  epochs  in  the  history  of  astronomical  science  in 
India  is  from  beginning  to  end  utterly  worthless. 

9.  p.  23.  We  have  not  fulfilled  our  promise  to  recur  in  the  eighth 
chapter  to  the  subject  of  the  sun’s  error  of  position,  because  we  felt  our- 
selves incompetent  to  cast  at  present  any  valuable  light  upon  it.  Noth- 
ing but  a careful  and  thorough  sifting  and  comparison  of  all  the  earliest 
treatises,  together  with  the  traditions  preserved  by  the  commentators, 
and  the  practical  methods  of  construction  of  the  calendar,  is  likely  to 
settle  the  question  as  to  the  maimer  in  which  the  elements  of  the  plan- 
etary orbits  were  originally  made  up. 

, 10.  p.  24.  Tn  making  out  our  comparative  table  of  sidereal  revolu- 

tions, we  have  calculated  the  column  for  Ptolemy  as  we  conceive  that 
he  would  himself  have  calculated  it,  had  he  been  called  upon  to  do  so. 
M.  Biot,  having  jn  view  an  object  different  from  ours,  has  carefully  re- 
viled Ptolemy’s  -processes  (see  his  Trait6  Elemental  re  d’ Astronomic 
Physique,  tfn,u  ed„  v.  37-71),  and  has  deduced  from  the  latter’s  original 
data  what  lie  regards  as  the  true  times  of  sidereal  revolution  of  the  pri- 
mary planets  furnished  by  them ; his  periods  are  accordingly  slightly 
different  from  those  presented  in  our  table. 

Colebrooke  (As.  lies.,  xii.  240  ; Essays  ii.  41?)  has  also  given  a com- 
parative table  of.  the  daily  motions  of  the  plaflcts,  but  has  committed  in 
it  the  gross  error  of  setting  sido  by  •de  the  sidereal  rates  of  moLion  of 
the  Hindu  text-books  and  the  tropical  rates  of  Ptolemy  and  Lalandc. 
Of  course,  his  data  being  incommensurable,  the  conclusions  he  draws 
from  their  comparison  arc  erroneous. 

11.  p.  27.  We  add,  in  the  following  table,  a comparison  of  the  po- 
sitions of  the  apsides  and  nodes  of  the  planets  as  stated  in  our  treatise — 
being  those  which  arc  adopted,  with  unimportant  variations,  bj^all  the 
schools  of  Hindu  astronomy — with  those  laid  down  by  Ptolemy  in  his 
Syntaxis.  The  latter  we  giife  as  stated  by  Ptolemy  for  his  own  period, 
without  reducing  them  to  tffeir  value  in  distances' from  the  initial  point 
of  the  Hindu  sphere.  The  actual  distance  of  that  point,  or  of  the 
vernal  equinox  of  A.1).  560,  from  the  vernal  equinox  of  Ptolemy’s  time, 
is  about  5£°.  We  should  remark  also  that  Ptolemy  does  not  state 
. expressly  and  distinctly  the  positions  of  the  nodes : we  derive  them  from 
* the  rules  given  by  him,  in  the  Bixth  chapter  of  his  thirteenth  Book^  for 


i.  48.]  Additional  Notes , etc.  283 

w 

calculating  the  latitude  of  the  planets : not  being,  however,  altogether 
confident  of  our  correct  understanding  and  interpretation  of  tlioqp  rules. 

Positions  of  the  Apsides  and  Nodes  of  the  Planet*. 


Planet. 

I Sftryo- 
iSultlllfilltA. 

Ptolemy. 

j Difference. 

a. 

Apsides : 

■i  ° 

t 

■» 

1 

i • 

■ ! 

Sun, 

77 

i5 

65 

3o 

; + 11 

45  j 

Mercury, 

j 220 

2G 

190 

0 

i + 3o 

26  | 

Venus, 

i 79 

49 

55 

0 

. .+  a 4 

49 

Mars, 

. )3<> 

j 

1 1 5 

3o 

; +14 

3i 

Jupiter, 

■ 171 

16 

161 

0 

: + 10 

16 

Saturn, 

38 

233 

0 

' + 3 

38* 

Nodes: 

Mercury, 

! 

20 

44 

10 

0 

' + 10 

44 

V onus. 

45 

' .55 

.0 

+ 4 

45 

Mars, 

4<> 

4 

25 

3o 

. + i4 

34 

Jupiter, 

: 79 

4i 

5k 

0 

1 f 28 

4i 

Saturn,  - 

- 10a 

25 

i83 

0 

-82 

35 

It  will  be  perceivtMl  that  the  differences  hero  are  not  so  great  as  to  ex- 
clude llie  supposition  of  a connected  origin.  We  do  not.  ourschcs  be- 
lieve that  the  Hindus  were  ever  suilieicritly  skilled  in  observation,  or  in 
the  discussion  of  the  results  of  observation,  to  be  able  to  derive  such 
data  for  themselves,  or  even  intelligently  to  modify  and  improve  them, 
when  obtained  from  other  sources.  In  order,  however,  fully  to  under- 
stand the  relation  of  the  Hindu  to  the  Greek  science  in  this  part,  we  re- 
quire to  know,  first,  wlnit-  were  the  positions  assigned  to  the  apsides  and 
nodes  by  Greek  astronomers  prior  to  Ptolemy,  and  secondly,  what  were 
their  actual  positions  at  the  periods  in  question.  Upon  the  first  point 
no  information  appears  to  have  been  handed  down  to  our  times ; and  as 
regards  the  other,  we  have  not  found  any  modern  determination  of  the 
desired  data,  and  are  not  ourselves  at  present  in  a situation  to  uudertake 
so  intricate  and  laborious  a calculation. 

12.  p.  29.  The  era  oT  the  kali  yuffa,  or  Iron  Age,  is  not  in  prac- 
tical use  among  the  Hindus  of  tlic*prcscnt  day:  two  others,  of  a less 
remote,  date,  arc  ordinarily  employed  by  them  in  the.  giving  of  dates. 
These  arc  styled  the  eras  of  Calivfthana  and  of  V’ikrain&ditya  respect- 
ively, from  two  sovereigns  so  named  : their  origin  and  historical  signifi- 
cance are  matters  of  much  doubt  and  controversy.  The  years  of  the 
era  of  ^i&Iiv&liuna  are,  according  to  Warren  (Ksila  Sankalita,  p.  381  and' 
elsewhere),  solar  years:  their  reckoning  comncnccs  after  the  lapse  pf 
3179  qpnpletn  years  of  the  Iron  Age,  or  carl)  in  April,  A.D.  78:  the 
1782nd; year,  accordingly,  coinciding  with  the  4901st  of  the  Iron  Age, 
commenced,  as  is  shown  by  the  table  ou  p.  30,  April  12th,  1859,  and 
ended  April  lltli,  18G0.  The  years  of  this  era  arc  generally  cited  os 
gaka  or  gdka  years.  In  the  other  era,  the  luui-solar  reckoning  is  followed 
(Warren,  as  above,  p.  391  and  elsewhere) ; and  its  first  year  began  with 
the  3045th  of  the  Iron  Age,  or  early  in  58  B.  0. : its  1962nd  year,  coin- 
ciding with  tiie  4961st  of  the  remoter  era, 'commenced  (see  table  on  p;* 


284 


Surya-Siddh&nta,  [i-  48- 

• 

30)  April  4 tli,  1859,  and  ended  March  22nd,  1860.  Tho  ycyirs  of  this 
era  are. called  and  quoted  as  sumvatsara  years,  or,  by  abbreviation,  sim- 
ply samvat. 

13.  p.  39.  M.  Vivien  dc  St.  Martin  (in  Julian's  Memoires dc  lliouen-  ^ 
Thsaug,  ii.  258)  supposes  the  \iilue  of  the  li  iu  use  in  China  during  the 
seventh  century  to  have  been  alumt  329  metres,  or  1080  English  feet. 
This  would  make  the  values  of  the  three  kinds  of  yojana  mentioned  by 
the  Buddhist  traveller  to  be  8,1,  0^,  and  3J-  English  miles  respectively. 

14.  p.  4-1.  In  the  first  table  upon  this  page,  wo  ^jivc,  by  an  ovor- 
sight.,' given  the  earth's  heliocentric  longitude,  instead  of  the  sun’s  geo- 
centric longitude.  To  the  sun's  place  as  stated,  accordingly,  should  be 
added,  180°.  • 

15-  p.  52.  M.  Biot  (Journal  des  Savants,  1H59,  p.  409)  suggests  that 
the  Hindus,  like  Albatcgniu-s  obtained  their  sines  directly  from  the 
chords  of  Hipparchus  or  Ptolemy.  This  may  not  be  an  altogether  im- 
possible suppopition,  but  it  is  at  loa^t  an  unnecessary  one,  for  they  cer- 
tainly liad  geometry  enough,  at  the  time,  of  the  elaboration  of  tlmii- 
astronomical  system,  to  construct  their  table  independently.  ^)ur  notes 
have  presented  tfclambre's  view  of  tin1  method  of  its  rniistrir'tion  and 
the  reason  of  its  limitation  to  ares  which  are  multiples  of  3°  15'.  W'u 
canuot  but  feel,  however,  upon  liiaturer  consideration,  that  the  enrrceL- 
nfiss  of  that  view  is  very  qin*stionable ; that  the.  lliudus  eould  probably 
have  made  out  a more  complete  table,  if  they  had  chosen  to  do  so;  anil 
that  a sufficient  reason  is  found  for  their  selection  of  the  arc.  of  3°  If/ 
in  the  fact  that  it  is  a natural  subdivision  of  a recognized  unit,  tin*  are  of 
30°,  while  thi;  .-uric*  of  twenty-four  sines  was  sulliricnlly  full  and  accu- 
rate for  their  uses.  We  have  been  at  the  pains  to  calculate  the  complete 
series  of  Hindu  sines  from  Ptolemy's  table  of  chords,  assuming  the  value 
of  radius  t.o  be  313sff  in  order  to  test  the  question  whether  there  wore 
any  correspondence  of  errors  between  them  which  should  prove  the  oik* 
to  l.e  derived  from  the  other  : our  results  are  as  follows.  In  fixe  of  the 
instances  (the  J 4th,  15th,  191  li,  22nd,  and  23rd  sines  of  the  table)  in 
which  the  value  of  the  Hindu  sine  exceeds  the  truth,  Ptolemy  supports 
the  error;  in  the  other  three  eas qp  (tin.  1 0th,  17th,  and  18th  'dues), 
Ptolejiiy  alfords  the  correct  \sihie;  to  the  0th  sine,  also,  which  by  the 
• Hindus  is  made  too  small,  Ptolemy \*  fable  gives  its  true  \aluc,  but  the 
next  following  sine  lie  makes  to*>  great,  (namely  1520.5!),  which  would 
give  1521,  instead  of  1520);  this  is  his  only  independent  error.  Thu 
evidence  yielded  by  the  comparison  may  be  regarded  as  not  altogether 
unequivocal. 

For  the  benefit  of  any  who  may  desire  to  make  practical  use  of  the 
Hindu  sines,  in  calculations  conducted  according  to  the  processor  of  the 
Shrya-Siddhauta,  we  give,  updh  the  opposite  page,  a more  detailed  tablg 
of  them  than  has  been  presented  hitherto,  with  such  sets  of  differences 
annexed  as  will  enable  the  calculator  readily  to  find  the  sine  of  any 
given  arc,  or  the  reverse,  without  resorting  to  the  laborious  proportion* 
by  which  the  text  contemplates  thnt  they  should  In  each  ease  be  deter- 
mined. Such  a table  vc  have  ourselves  found  highly  useful,  and  even 
almost  indispensable,  in  connection  with  our  own  calculations. 


286 


Sfoya-Siddhdnta, 


[ii  27- 


In  explaining  hew  the  Hindus  may  hare  arrived  at  their,  empirical 
rule,  as  laid  down  in  verses  15  and  16,  for  the  development  of  the  series 
of  sines,  we  have  also,  as  mentioned  in  our  note,  followed  the  guidance 
of  Dclainbrc.  Prof.  Newton,  however,  is  of  opinion  that  the  rule  m 
question  was  probably  obtained  by  direct  geometrical  demonstration,  in* 
sonic  such  method  as  the  following,  which  is  much  more  in  accordance 
with  the  mathematical  proceB&cs  exhibited  or  implied  in  other  parts  of 
the  Sftrya-Siddh&nta. 

Id  the  quadrant  AB  (Fig.  34),  let  B F,  BD,  and  BE  he  three  arcs,  of 

which  each  exceeds. its  predecessor 
lgm  by  the  equal  increment  D F or  D E ; 

■ and  let  F'm,  D l,  and  E it  be  their 

sines,  increasing  by  the  unequal  dif- 
ferences DA  and  Eg.  Now  as  E D 
and  D F are  small  arcs  (they  are 
shown  in  the  figure  of  three  times 
the  proportional  length  of  the  arcs 
of  difference  of  the  Hindu  table), 
BD g and  D F A may  be  regarded  as 
plane  triangles,  and  the  angles  made 
by  V,  I)  at  l)  as  right  angles : lienee 
the  angles  ED .7  and  CD/  are  equal, 
the  triangles  ED//  and  CDZurc 
similar,  and  E D : E// : : C D : C l ; or 
E//=E  D.G  Z-^C  D.  In  like  man- 
ner, DAz=E  D.C  C D.  There- 
fore DA— E^  = ED.Z  m-|-C  D ; and  E^,  which  is  the  amount  by 
which  E k exceeds  DZ,  equals  D A— (ED./m-^CD).  But,  by  simi- 
larity of  the  triangles  CDZ  and  DFA,  FA,  or  Zm,  equals  ED.D/-r 
CD;  and  lienee  ED.Zm-s-CD  = (ED2-^CD2)Di,  or  (ED-r 
C D)2  D L Now  when  E D equals  225'  and  C D 8438',  E D — C D = 
* "early  (or  exactly  and  (ED-J-C  D)2=y^  nearly  (more 

exactly,  ?Td.n)-  Hence  E A=DZ  + DA  — DZ,  which  is  equiva- 
lent to  the  Hindu  rule.  9 

m When  we  wrote  the  note  to  the  passage  of  the  text  relating  to  the* 
sines,  we  assumed  that  the  rule  as  there  stated  would  give  the  series  of 
sines,  having  found  upon  trial  that  it  held  good  for  the  first  few  terms  of 
the  series.'  But,  it  having  been  pointed  out  to  us  by  Prof.  Newton  that 
the  adoption  of  -fa  as  the  value  of  ED-^-CD  could  not  but  lead  to 
palpably  erroneous  results,  we  carried  our  calculations  farther,  and  fmnd 
that  only  five  of  the  sines  following  the  first  one  can  be  deduced  from 
it  by  the  processes  prescribed ; that  with  the  seventh  sinaobegins  a dis- 
cordance between  the  table  and  the  result  of 'Calculation  by  4he  rule, 
which  goes  on  increasing  to  the  end,  where  it  amounts  to  as  much  as 
70  in  the  value  obtained  for  radius. 

This  untoward  circumstance,  which  may  be  regarded  as  a trait  highly 
characteristic  of  a Hindu  astronomical  treatise,  seems  to  us  rather  to 
-&v6r  the  opinion  that  the  rule  is  the  result  of  construction  and  demon- 
stration, and  not  empirically  deduced  from  a consideration  of  the  actual . 
second  differences.  In  the  latter  case  we  should  more  naturally  suppose  * 


287 


u»  Additional  Notes , etg. 

that  it  would  have  been  tested  throughout  by  actual  trial;  while,  if  it 
had  been  arrived  at  in  the  manner  above  explained,  an  application  of  it 
* to  the  first  few  members  only  of  the  series  might  more  easily  have  been 
accepted  as  a sufficient  test  of  its  correctness. 

16.  p.  59.  .Wo  arc  not  sure  that  the  name  bhuja  may*Hbt  origin- 
ally and  properly  belong  rather  to  the  arc  than  to  its  chora  or  sine.  It 
conies  from  a root  hhuj , “bend,”  and  signifies  primarily  14  a bend,  curve, 11 
being  applied  also  to  designate  the  arm  on  account  of  the  latter’s  sup- 
pleness or  flexibility.  The  word  koti  also  most  frequently  means  4lthe 
end  or  horn  of  a bow.”  We  might.,  then,  look  upon  the  relations  of  the 
arc  ( dhanus , eApn,  k&rmuka)  and  its  parts  and  appurtenances  as  follows.' 
The  whole  arc  taken  into  account  is  (Fig.  2,  p.  59)  QRS:  of  thb/^RC 
is  the  bhuja,  curve  or  bow  proper,  while  B Q and  CS  are  its  t wtfcfofu 
or  horns : B C is  the  chord  or  bow-string  (jyd  etc.),  or,  more  dutfnet- 
ivcly,  the  bhujujifct ; which  name,  by  substitution  for  jydrihe \ is  alio  ap- 
plied to  either  of  its  halves,  BJI  or  HC:  BF  or  CL  ia  m like' manner 
the  kntijyd;  R 1 1,  finally,  the  versed  sine,  is  the  “arrow”  (para,  if Au)  f* 
by  this  name  it  is  often  known  in  other  treatises,  although  not  once  stt 
styled  in  this  Siddh&nta.  If  this  view  be  correct,  the  terms  bhuja  and 
knti  ns  applied  to  the  base  and  perpendicular  of  a right-angled  triangle, 
arc  given  them  on  account  of  their  relation,  to  one  another  ai^jjgijt  and 
cosine,  while  the  synonyms  of  thuja,  namely  bbhu  and  dosy  are employed 
on  account  only  of  their  agreement  with  it  in  the  signification  ^anA,” 
and  not  iy  that  which  gives  it  its  true  application.  For  koti  the  treatite 
affords  no  synonyms. 

12.  p.  6a.  M.  Delarnbrc,  in  his  History  of  Ancient  Astronomy  (i. 
462  etc).,  has  subjected  to  a detailed  examination  tlie  rules  of  the  Sfirya- 
iSiddhduta  for  the  calculation  of  the  equations  of  the  centre  for  the  sun 
and  moon,  Iuls  reduced  them  to  a single  formula,  and  has  calculated  for 
each  degree  of  a quadrant  the  values  of  the  equations,  comparing  them 
with  those  furnished  by  the  Hindu  tables,  as  reported  by  Davis  (As.  Res., 
ii.  255-256).  M.  Biot  has  more  recently,  in  the  Journal  dcs  Savants 
for  1859  (p.  384  etc.),  taken  up  the  same  subject  anew,  especially  point- 
' ing  out,  and  illustrating  by  figures  and  calculations,  the  error  of  the 
-Hindus  in  assuming  the  variation  of  the  equation  to  be  the  same  in  all 
the  four  quadrants  of  mean  revolution. 

a IN.  p&  76.  Neither  Delambre  nor  Biot  (both  as  above  cited),  nor 
any  other  western  savant  who  Inis  treated  of  the  Hindu  astronomy,  has 
found  any  means  of  accounting  for  the  variation  of  dimensions  of  the 
planetary  epicycles.  In  its  present  form  ami  extent,  indeed,  it  seema  to 
defy  explanation : we  can  only  conjecture  tha,  it  may  be  an  unintelli- 
gent and  reasonless  extension  to  all  the  planets,  and  to  both  classes  of 
epicycles,  of  a correction  originally  devised  and  applied  only  in  one  or 
two  special  cases.  According  to  Colebrookc  (As.  Res.,  xii.  235  etc. ; 
. Essays,  ii.  400  etc.),  there  ^discordance  among  the  different  Hindu  au- 
thorities upon  this  point.  Aryabhata  agrees  with  the  Sflrva-SiddhAnta 
throughout;  Brahmagupta  and  BhAskara  make  the  epicycles  ouijjof 
Venus  and  Man  variable ; MunS^vara,  in  the  Siddhfcnta-SArvabhhuma, 
regards  all  the  epicycles  as  invariable. 


288 


J&rya-SuJdh&nta, 


[fi.  65- 


19.  p.  02.  Our  suggestion  of  a possible  derivation  of  the  term  yoga 
from  tlic  “Bum”  of  the  longitudes  of  the  sun  and  moon  is  unquestion- 
ably erroneous.  That  tenn  is  to  be  understood  here-  in  the  sense  of 
“junction,  conjunction,”  and  the  conception  upon  which  is  founded  its 
application  to  the  periods  in  question  is  that  of  a conjunction  (yoga)  of 
the  moon  with  the  twenty-seven  astcrisms  (nakshatra)  in  their  order,  or 
her  successive  continuance  m their  respective  portions.  Only  the  sys- 
tem is  divorced  from  any  actual  connection  with  the  asterisms ; for  while 
the  latter  arc  stellar  groups,  having  fixed  positions  in  the  heavens,  they 
arc  here  treated  as  if  the  twcnty-scvcn-fold  division  of  the  ecliptic  found- 
ed upon  them  had  no  natural  limits,  but  was  to  be  reckoned  from  the 
actual  position  of  the  sun  at  any  given  moment. 

According  to  Warren  (K&la  Sankalita,  p.  74),  the  names  of  the  twenty- 
seven  yogas,  as  given  by  us  on  page  02,  arc  also  applied  by  the  Hin- 
dus to  the  junction-stars  ( yoga  tar  A ) of  tlic  astcrisms  (with  the  omission, 
of  course,  of  Abhijit)  : for  which  sec  the  notes  to  the.  eighth  chapter. 
This  fact  wc  do  not  find  noticed  elsewhere;  possibly  the  usage  is  a local 
one  only. 

Of  the  twenty-eight  yogas  of  the  other  system,  to  which  the  Sftrva- 
Siddh&nta  makes  no  reference,  the  names  arc  given  by  Colcbrooke  as 
follows : 


i.  Ananda. 

а.  KAIadwjda. 

3.  Dhflmra. 

4.  Fr&jfipati. 

5.  SAumya. 

б.  Dhvflnksbn. 

7. 'Dhvaja. 

8.  (^rivatsa. 

9-  Vajra. 


10.  Mudgara. 

11.  Chntira. 

12.  M:\itra.- 

13.  MAnasa. 

14.  Padma. 

1 5.  Lninbaka. 

1 6.  Ut'piita. 

17.  Mrtyu. 

18.  KAiia. 


19.  Sidrilii. 

20.  (iiljha. 

2T.  Amrta.  # 
22.  Musala. 
a3.  Gada. 

24.  Miltnnga. 

25.  Itfikshasa. 

26.  Cara. 

27.  Stliira. 

28.  Pravardha. 


Colebrookc  says  farther  : il  The  foregoing  list  is  extracted  from  the 
Batnam&lA  of  £ripati.  lie  adds  the  rule  by  which  the  yogas  are  reg- 
ulated. On  a Sunday,  the  naksltalras  answer  to  the  yogas  in  their 
natural  order;  viz.  Agvinl  to  Ananda,  Hharaiii  to  Kaladanda,  etc.  lint, 
on  a Monday,  the  first  yoga  (Ananda)  corresponds  to  Mygagiras,  the 
seednd  to  ArdrA,  and  so  forth.  On  a Tuesday,  the  nakshatra  which 
answers  to  the  first  yoga  is  A<;lesh&;  on  Wednesday,  Hast  a ; on  Thurs- 
day, AnurAdhA ; on  Friday,  Uttara-AshAdhA;  and  on  Saturday,  (’ata- 
bhisliaj  ” 

This  is  by  no  means  a clear  and  sufficient  explanation  of  the  charac- 
ter and  use  of  the  system,  yet  we  seem  to  sec  distinctly  from  it  that  this, 
no  less  than  the  other  system,  is  cut  off  from  any  actual  connection  with 
the  twenty-eight  astcrisms,  since  the  succession  of  the  yogas  is  made  to 
depend  upon  the  day  of  the  week,  while  the  week  stands  in  no  constant 
and  definable  relation  to  the  motion  of  the  moon. 


90*.  p.  102.  In  stating  that  the  S&rya-SiddhAnta  furnished  no  hint  of 
thl  precession  excepting  in  this  passage,  we  failed  to  notice  that  in  one 
other  place,  namely  in  connection  with  the ‘rales  for  finding  the  time 


289 


iv.]  Calculation  of  a Lunar  Eclipse. 

wlicn  the  declinations  of  the  sun  and  moon  are  equal  (xL  C),  the-  pre- 
cession is  distinctly  ordered  to  be  calculated,  and  in  terms  which  con-  - 
tain  an  evident  reference  to  those  in  which  the  fact  of  the  precession  is  > 
here  stated.  The  exception,  however,  is  one  which  goes  to  proven  rather 
than  overthrow,  the  general  rule  : the  process  in  which  we  are  for  once 
favored  with  explicit  directions  upon  the  point  in  question  is  the  one  of 
all  othcnNin  the  work  the  most  trivial,  ami  the  chapter  which  contains  it 
furnishes,  as  pointed  out  by  us  in  the  notes,  good  reason  to  suspect  late 
alteratftns  and  interpolations.  We  do  not,  then,  regard  the  statement 
made  in  our  note  a*  requiring  to  be  either  retracted  or  seriously  modi- 
fied. Nor  do  we,  although  fully  appreciating  the  difficulty  of  assuming 
that  the  original  elabomtors  of  the  general  Hindu  system  can  have  been 
ignorant  of,  or  ignored,  the  precession,  regret  the  force  and  distinctness 
with  w hich  we  have  stated  the  circumstances  which  appear  to  favor  that 
assumption.  Whether  it  be  true  or  false,  there  is  much  in  connection 
with  the  subject  which  is  strange,  and  demands  explanation:  and  that 
can  only  be  satisfactorily  given  when  there  shall  have  been  attained  a 
more  thorough  comprehension  of  the  early  history  and  the  varying  forms 
of  the  science  in  India. 

21.. p.  114.  The  commentary  frequently  styles  'the  sine  of  altitude 
mahuranku , “ great  guiuuon,"  to  distinguish  it  from  the  ranku , “gno- 
mon.” 

22.  p.  131.  Our  statement  that  the  Sun  a-Siddh&nta  employs  only 
the  term  tjrnhu  to  designate,  tlie  planets  requires  a riiglit  modification. 
In  one  instance  (ii.GO)  the\  are  called  khnearin , and  in  one  other  (ix.  9) 
kliacara , both  words  signilx  iug  “ moving  in  the.  other”  (*ee  xii.  23,  81). 

23.  p.  138.  This  use  of  the  \\*>rd  pri/cf,  *■  OP.*t,  east  point,'1  appears 
to  he  taken  from  the.  projections-  of  celipx-s,  as  directed  to  be  drawn  in 
the  sixth  chapter.  Thus,  in  the  figure  there  given  (Fig.  27,  p.  157), 
EM  and  v M represent  the  directions  of  the  equator  and  ecliptic  with 
reference  to  one  another  at  the  moment  of  first  contact,  ami  E and  v 
arc  the  east-points  (prftci)  of  those  lines  respectively:  the  arc  Er,  or 
the  “interval  of  the  two  east-points,”  is  the.  measure  of  tl\c  angle  which 
the  two  lilies  make  with  one  another  at  the  given  time. 

21.  p.  141.  As  promised  above,  we  present  here,  by  way  of  appen- 
dix to  the  fourth  chapter  of  our  translation  and  note*,  a 

Calculation,  according  to  tub  Data  and  Methods  of  the  SCrya- 
Siddjiaxta,  of  tiik  Linar  Ecuphk  of  Fkiirvary  JSth,  1800, 

FOll  TIIE  LATITUDE  AND  T.ONU1TUDE  OF  WAS  III  * ■ TON. 

TlaiHy,  in  his  work  on  the  Hindu  astronomy  (p.  355  etc.),  presents 
several  calculations  of  eclipses  by  Hindu  methods,  namely  of  the  lunar 
eclipse  of  July  29th,  1730,  of  the  lunar  eclipse  of  Juno  17th,  1704, and 
of  the  solar  eclipse  of  Nov.  29th,  1704.  Hut,  owing  to  his  imperfect 
comprehension  of  the  character  and  meaning  of  many  of  the  processes, 
and  owing  to  his  incessant  use  of  Hindu  terms  in  the  most  barbarous 
transcriptions,  without  explanations,  .his  iutended  illustrations  are  only 
with  difficulty  intelligible,  and  are  exceedingly  irksome  to  study.  Davis, 


290 


SArya-Siddhdntn  [iv. 

in  his  fi/st  Valuable  article  in  the  Asiatic  Researches  (ii.  2*73  etc.),  has 
also  furnished  a calculation  of  a lunar  eclipse,  as  made  by  native  astron- 
omers, comparing  their  results,  obtained  by  several  different  methods, 
with  the  actual  elements  of  the  eclipse,  as  given  by  the  Nautical  Alma- 
nac. As  it  seemed  desirable  to  give  a like  practical  illustration  of  the 
Hindu  methods  of  calculation,  in  connection  with  this  fuller  exposition 
of  their  foundation  and  meaning,  and  by  way  of  an  additional  test  of  the 
accuracy  of  the  results  which  the  system  is  in  condition  to  furnish,  we 
have  selected  for  the  purpose  the  partial  eclipse  of  the  moon  wfltcli  oc- 
curred on  the  evening  of  Feb.  Glh,  18G0.  Our  calculations  are  made 
according  to  tlie  elements  of  our  text  alone,  without  adding,  like  Davis, 
the  correction  of  thc'6(;'a,  since  our  object  is  to  illustrate  the  text,  itself, 
and  not  the  modem  system  as  altered  from  it.  The  course  of  the  suc- 
cessive steps  of  our  processes  may  not.  everywhere  strictly  accord  with 
that  which  would  be  pursued  by  a native  astronomer,  as  we  take  the 
rules  of  the  text  and  apply  them  according  to  our  own  conception  of 
their  connection. 

We  omit  the  preliminary  tentative  processes,  and  conceive  ourselves 
to  have  ascertained  that,  at  the  time  of  full  moon  in  the  month  Magha, 
I.  A.  49G1  (sec  page  30),  or  samvat  1917  (see  add.  note  12),  the  moon 
will  be  eclipsed. 

I.  To  find  the  sum  of  days  (uhargana,  dinarari)  for  mean  midnight 
next  preceding  full  moon.  9 

The  sixth  day  of  February,  1800,  being  tlio  day  of  full  moon  (punii 
md),  is  the  fifteenth  day  of  the  first,  or  liglil,  half  of  the  lunar  month 
Mfigha,  the  eleventh  month  of  the  year,  as  is  shown  by  the  table  on 
page  30.  The  time,  then,  for  which  we  are  to  find  the  sum  of  days,  is 
4960?  luh»  M*1,  reckoning  (i.  5G)  only  from  the  commencement  of  the 
Iron  Age.  For  this  period  the  sum  of  days,  as  found  by  the  processes 
already  sufficiently  illustrated  in  the  notes  to  i.  48-51,  is  i,8li,9Sl  days. 

II.  To  find  the  mean  longitude  of  the  sun  and  moon,  and  of  the 
moon’s  apsis. 

The  proportions  (i.  53) 

f . tau.ofin : /ix/yotbw  </*  a3°  17'  1" 
Ij^77.9*7»Ga8 : 1,81  *,981 : : -J  r 703,336  :6G,37orov  3*  90  44'  uy" 

( 488,203  ; ,•  ,3°  43'  1" 

give  us — rejecting  whole  revolutions,  and  deducting  3"  from  the  motion 
of  the  moon’s  apsis,  for  its  position  at  the  epoch  (see  note  to  i.  50-58) — 
the  mean  longitudes  required.  These  are  for  the  time  of  mean  midnight 
atUjjayinl:  to  find  them  .for  mean  midnight  at  Washington,  which  is 
distant  from  Ujjayint  lG7ly.28,  upon  a parallel  of  latitude  393G?.75  in 
circumference  (note  to  i.  63-65),  we  add  to  the  position  of  each 
or  .42453  of  its  mean  motion  during  a sidereal  day.  This  correction  is 
styled  the  def&nlaraphala . We  have,  then, 

Long.  ntUjjiiy.  Correction.  Long,  nl  Wiiili’n. 

San,  9*23°  17'  1"  + q.V  2"  = 9*  a3°  42'  3" 

Moon,  3«  90  44'  *9'  + 5°  34'  43"  = 3»  i5°  19'  2" 

Moon's  apais,  io*  i3°  43'  1"  + 2' 5o"  = io*i3°45'5i" 


fr’]  Calculation  of  a Lunar  Eclipse'.  291 

The  place  of  the  sun’s  apsis  remains  as  already  .found  for  Jan.  1st 
(note  to  ii.  39) : 

Longitude  of  sun's  apsis,  ar  17®  17'  a4" 

In  applying  here  the  correction  for  difference  of  meridian,. as  well  as 
in  all  other  processes  of  the  whole  calculation  into  which  tjie  amounts 
of  motion  of  the  planets  etc.  during  fractious  of  a day  enter  as  elements, 
w*  have  derived  those  amounts  from  the  motions  during  a sidereal  day, 
and  not,  as  in  the  illustrative  processes  of  our  notes,  during  a mean  ap- 
.lar  day.  The  divisions  of  the  day  given  in  the  text  (i.  11-12)  are  dis- 
tinctly stated  to  be  those  of  sidereal  time,  and  all  the  rules  of  the*  treat- 
ise are  constructed  accordingly  (see,  for  instance,  ii.  50).  It  is  evident, 
then,  that  in  making  any  proportion  in  which  is  involved  the  amount  of 
motion  during  60  n&dis,  that  amount  is  to  be  regarded  as  the  motion 
during  a sidereal  day  only.  In  overlooking  in  our  notes  the  difference 
between  the  two,  we  have  followed  the  example  of  all  the  illustrations  of 
Hindu  methods  of  calculation  known  to  us.  aThc  difference  is,  indeed, 
in  a Hindu  process,  of  very  small  account ; but  wc  have  preferred,  in 
making  this  calculation,  to  follow  what  wc  conceive  to  be  the  cxacter 
method.  The  mean  motions  during  a sidereal  day  of  .the  bodies  con- 
cerned in  a lunar  eclipse  arc  as  follows  : 


Sun, 

8'  58"  18"'  55"" 

Monn, 

8'  a5"  Ji'"  11"" 

Moon's  ap*isf 

fi'  39"  53'" 

Moon's  node,  ■ 

3'  10"  |3"'  28"" 

111.  To  lind  the  true  longitudes  and  motions  of  the  sun  and  moon 

1. 

To  find  the  sun's  true  longitude  (note  to  ii.  30) : 

Jjongitude  of  Mill's  npsi*>. 

a*  170  17'  24" 

deduct  sun's  monn  longitude  (ii.  29), 

9*  i3°  4»'  3" 

Sun's  mean  anomaly  ( kendrn ), 

41  23°  35'  21" 

Are  determining  the  sine  ((thuja — ii.  -10), 

36°  25' 

• 

Sine  of  sun's  mean  anomaly  'Utujvji/ii), 

20io' 

Corrected  epicycle  (ii.  38), 

1 3°  48' 

* 

Kquntioii  (bh  ujajytiphala — ii.  39),  • 

+ i°  18' 

add  to  sun's  mean  longitude, 

ps  a3°  42' 

Sun’s  true  longitude, 

p*  a5°  0' 

2. 

To  find  the  moon's  true  longitude  (note  to  ii.  30) : 

Longitude  of  moon's  apsis, 

1 Os  1 3°  45'  5l" 

deduct  moon's  mean  longitude, 

1 5°  ip'  a" 

Moons  mean  anomaly, 

6*  28°  26'  4p" 

Arc  determining  the  sine,  * 

a8°  27' 

Sine  of  moon's  mean  anomaly, 

1637' 

Corrected  epicycle, 

3r°  5o' 

Equation, 

— 20  a5' 

deduct  from  moon’s  mean  longitude,  . 

3i  s5°  ip' 

Moon’s  true  longitude, 

3*  ia°  54' 

292 


S(i  rya-Siddkdnta, 


'3.  To  find  the  sun's  true  rati*  of  motion  (ii.  48—49) : 

Sun’s  mean  motion  in  60  nadU,  58'  58" 

Sine  of  sun's  mean  anomaly,  ao4o' 

Difference  of  sines,  i83' 

Daily  increase  of  sine  of  anomaly,  47'  58" 

Equutlbn  of  motion,  - i'  5o" 

add  to  sun's  mean  motion,  58'  58" 

Sun's  true  motion,  , Go'  48" 

4.  To  find  the  moon's  trim  rate  of  motion  (ii.  47-40) 

Moon's  mean  motion  in  60  nadfc,  . 788'  aV' 

deduct  motion  of  apsis  (ii.*  47),  6'  4o" 

Daily  increase  of  moon's  mean  anomaly,  781 ' 45" 

Sine  of  moon’s  moan  anomaly,  1637' 

Difference  of  sines,  199' 

Daily  increase  of  sine  of  anomaly,  G91'  25" 

Equation  of  motion,  -f.  t>i'  8" 

add  to  moon's  mean  motion,  ' 788'  25" 

Moon's  true  motion,  849'  33" 


IV.  To  find  the  interval  between  Iho  given  instant  of  midnight  and 
the  end  of  the  half-month,  or  the  moment,  of  opposition  in  longitude  of 
the  sun  and  inoon,  which  is  the  middle  of  the  eclipse. 

At  the  instant  of  mean  midnight  pipccding  full  moon,  wc  have  found 
the  true  longitudes  of  the  sun  and  moon,  and  their  distance  in  longitude, 
to  be  as  follows : 


• Sun’s  true  longitude,  9*  2 5°  o' 

Moon’s  do.,  3“  i?°  54' 

- Distance  in  longitude,  6*  1 a°  6' 

Hence  wc  see  that  the  moon  has  still  12?  C V to  gain  upon  the  sun.  Wc 
have  also  found  their  true. rates  of  motion,  and.  the  difference  of  those 
rates,  to  be  as  follows : 


Moon’s  true  motion,  • 849'  33"* 

Sun's  do.,  Go'  48" 


Moon's  daily  gain,  ^ 788'  45" 

Now  wc  make  the  proportion  : if  the  moon,  in  60  n&dis  gains  upon 
the  sun  788'  45",  in  how  many  n&dls  will  she  gain  her  present  distance 
in  longitude  from  the  sun  ? or 

788'  45"  :6o«{:  726' : 55n  i3*  3P 


It  thus  appears  that  the  time  of  opposition  is  55n  13v  3P  after  mean 
midnight  of  Feb.  5-6.  This  result,  however,  requires  correction,  for 
the  moon’s  motion  has  become  sensibly  accelerated  during  so  long  an 
interval,  and  we  find,  upon  calculation,  that  she  is  then  S*  past  the  point 
of  opposition.  A repetition  of  the  same  process  shows  that  it  is  ncccs- 
- sary  to  deduct  10v  3p  from  the  time  stated.  Then,  at  55n  3V  idler  mean 
midnight,  we  have  as  follows : 


293 


ir.]  Calculation  of  a Lunar  Eclipse. 

Sun’s  mean  longitude. 

Equation  of  place, 


9>  a5° 

3b  27°  aa' 
io«  i3°  5a' 

- i®  a6' 

Mood’s  true  longitude,  3a  a 5°  56' 

By  the  same  process  as  before,  the  true  motions  of  the  two  planets 
at  the  moment  of  opposition  are  found  to  be  : 

Sun’s  true  motion,  6o'  48" 

Moon’s  do.  854'  36" 

It  would  have  been  better  to  adopt,  as  the  starting-point  of  our  cal- 
culations, the  mean  midnight  following,  instead  of  lliat  preceding,  the 
opposition  of  the  sun  and  moon,  because  in  that  case,  tho  interval  to 
the  inomcu£  of  opposition  being  so  much  less,  it  might  have  been  found 
by  a single  process,  not  requiring  farther  correction.  The  same  change 
would  have  enabled  us  to  follow^  strictly  the  ride  given  in  ii.  6(5  for  find- 
ing the  end  of  the  lunar  day ; which  rule  we  were  obliged  above  to  ap- 
ply in  a somewhat  modified  form,  because  a little  more  than  one  whole 
* luuar  day  was  found  to  intervene  between  the  given  midnight  and  the 
moment  of  opposition. 

V.  To  determine  the  instant  of  local  time  corresponding  to  the  mid- 
dle of  the  eclipse. 

What  we  have  thus  far  found  is  the  interval  between  mean  midnight 
and  the  moment,  of  opposition.  But  since  Hindu  time  is  practically 
reckoned  from  true  sunrise  to  true  sunrise,  we  have  now,  in  order  to  de- 
termine at  what  time  the  eclipse  will  take  place,  to  ascertain  the  inter- 
val bel  ween  mean  midnight  and  true  sunrise. 

In  order  to  this,  we  require  first  to  know  the  equation  of  time,  or  the 
difference  between  mean  midnight  and  true  or  apparent  midnight*  which 
is  the  moment,  jvhen  the  sun  actually  crosses  the  inferior  meridian.  As 
concerns  this  correction,  wo  have  deviated  somewhat  from  the  method 
contemplated  by  the  text.  It  is  there  prescribed  (ii.  40)  that,  so  sfpn 
as  the  sun’s  equation  of  the  centre  lias  been  determined,  there  should 
at  once  be  calculated  from  it,  and  applied  to  the  lopgitiule  of  the  two 
planets,  a correction  representing,  in  terms  of  their  motion,  the  equation 
of  time  ; so  that  the  distance  of  the  moment  of  opposition  from  mean 
midnight  docs  not.  directly  enter  into  account  at  all.  We  have  preferred 
to  follow  the  course  wc  have  taken,  in  order  to  bring  out  and  illustrate 
more  fully  the  utter  inadequacy  of  the  present  method  of  making  al- 
lowance for  the  equation  of  time,  to ‘which  wc  liavtf  already  briefly  re- 
ferred in  the  note  to  ii.  40.  The  method  in  question  is  virtually  as  fol- 
lows : the  sun  being  found  at  tlic  given  midnight  to  be  1°  18',  or  78', 
in  ad  vancc' of  his  mean  place,  the  equation  of  time  may  be  ascertained 
by  this  proportion:  -as  a whole  Circle  is  to  a sidereal  day,  so. is  the  sun’s 
equation  of  place  to  the  time  by  which  his  true  transit  will  precede  or 
follow  his  mean  transit ; or,  in  the  present  ease, 

31,600' : 6o» : : 78' : on  i3* 

38 


Sun  b true  longitude, 
Moon’s  mean  longitude, 
Longitude  of  apsis, 
Equation  of  moon’s  place. 


9>  *4° 

+ - i°  aof 


294  S&rya-Siddh&nta,  [iv. 

which  gives  ns  13  vin&dis,  or  5 minutes,  ns  the  valnc  of  the  equation. 
But  this  is  assuming  that  the  sun's  motion  takes  place  along  the  equator, 
instead  of  along  the  ecliptic,  which  is  so  grossly  and  palpably  erroneous 
that  wo.  wonder  how  the  Hindus  could  have  tolerated  a process  which 
implied  it.  Their  own  methods  furnish  the  means  of  making  a vastly 
more  correct  determination  of  the  equation  in  question.  The  mean  lon- 
gitude of  the  sun  at  the  given  midnight  is — after  adding  to  it  the  amount 
of  the  precession,  as  determined  farther  on — 10s  14°  7;:  hence,  if  the 
sun  were  10B  14°  7'  distant  upon  the  equator  from  the  vernal  equinox, 
or  if  lie  had  that  amount  of  right  ascension-moan  and  true  midnight 
would  coincide.  But  he  is  actually  at  10H  15°  25;  of  longitude.  If, 
then,  we  ascertain  what  point  oil  the  equator  will  pass  the  meridian  at 
the  same  time  with  that  point  of  the  ecliptic,  its  distance  from  the  sun's 
mean  place  in  right  ascension  will  he  the  equation  of* time  required. 
This  may  be  accomplished  as  follows.  The  sun  is  in  the  eleventh  sign, 
of  which  the  equivalent  in  right  ascension  (iii.  42-45)  is  1795P  : his 
distance  from  its  commencement  is  15°  25',  or  925'.  lienee  the  pro- 
portion (ii.  46) 

i8oo' : T795p  : : cpV  : 922P 

gives  us  022P  as  the  ascensional  equivalent  of  the  part  of  the  eleventh 
sign  traversed  by  the  sun  (bhuktasavas).'  Now  add  together  the 


Ascensional  equivalents  of  three  quadrants,  _ i6,aoop 

do.  of  the  tenth  sign,  i,9-35p 

do.  of  the  part  of  the  eleventh  sign  traversed,  9?2P 


their  sum  is  19,0^- -p 


which  is  equal  to  10"  17°  37' ; this,  then,  is  the  sun's  true  right  ascen- 
sion. The  difference  between  it  and  his  mean  rigljt  ascension,  10"  14°  7', 
is  3°  30',  of  which  the  equivalent  in  sidereal  time  is  2 1 OP  or  35v,  or  14 
minutes.  This,  which  is  more  than  two  and  a half  times  as  mucli  as 
the  value  formerly  found  for  the  equation,  is  quite  nearly  correct ; its 
actual  amount  for  Feb.  6th  being  given  by  the  Nautical  Almanac  as 
14m  20". 

There  is  not,  among  all  the  processes  taught  in  the  Sfirya-Siddh&nta, 
anAher  one  of  so  inexcusably  bungling  a character  as  this,  while  the 
means  lay  so  ready  at  hand  for  making  it  tolerably  exact- 

In  going  on  to  calculate  the  local  time  of  the  eclipse,  we  shall  adopt 
the  valuation  of  the  equation  of  time  given  by  the  Hindu  method,  or 
13v,  but  we  sliall  reserve  the  distance  of  the  phases  of  the  eclipse  from 
mid  night,*  free  from  this  constant  error  of  about  10m,  for  filial  compari- 
son with  the  like  data  given  by  our  modern  tables. 

To  find  the  local  time,  we  must  first  ascertain  (ii.  59)  the  length  of 
the  sun's  day,  from  midnight  to  midnight,  and  in  order  to  this  we  need 
to  know  in  what  sign  the  sun  is.  Hence  we  require 

1.  To  determine  the  amount  of  precession  for  the  given  date. 

By  iii.  9-12,  the  proportion  • 

1,577,917,828** : Goon*  : : 1,811,981,1 : on»  8«  8°  a'  i4".6 

gives  us  248°  2f  14". 6 as  the  part  of  a revolution  accomplished  by  the 


295 


iv.]  Calculation  of  a Lunar  Eclipse. 


movable  point.  Of  this,  the  port  determining  the  sine  is  68°  2# 14w.6. 
Then  the  farther  propo||;ion 

to:  3: : 68°  2'  i4"-6  : ao°  *4'  44" 


gives  us  20°  24'  44"  as  the  amount  of  the  precession.  Now,  then,  to 
tho 

Sun’s  trjie  longitude,  9*  a5°  56' 

add  the  precession,  a 5' 


Sun’s  distance  from  yernal  equinox,  io«  i6°  ai' 

This  quantity  is  often  called  say ana  stwya;  that  is  to  say, 11  the  sun’s 
longitude  with  the  precession  (aynna)  added.” 

The  sun  is  accordingly  in  the  eleventh  sign,  of  which  the  ascensional 
equivalent  is  1795P.  Ilis  daily  inutiun  lias  been  found  to  be  60'  48". 
Hence  the  proportion  (ii.  50) 


i8ou' : 1 7<yr)p  : : Go'  4S" : Gr-p.64 

gives  us  CIp,  or  10v  Ip,  as  the  excess  of  the  sun’s  day  over  a true  side- 
real day  ot  00  uadis : its  length  is  accordingly  GUn  10v  IP,  or  21,061P. 

Next  wc  desire  to  know  how  much  of  Ihi*  day  passed  between  mid- 
night and  sunrise,  and  for  this  purpose  wc  have 
2.  To  find  the  sun's  ascensional  difference  ( cara ). 

a.  To  ascertain  the  sun’s  declination,  and  its  sine  and  versed  sine. 


The  sun's  longitude,  with  precession  added  (jtiyaaa  sitrya), 
Arc  determining  the  sine  ( bhujd ), 

Sine,  , 


IO*  i6°  21? 

43*  39' 
a372' 


Now,  then,  the  proportion  (ii.  2$) 

VW  : 1 3yr'  : : ^72' : 964' 

gives  us  964'  as  the  sine  of  declination  ( kr&ntijyit ) ; the  corresponding 
arc  (ii.  33)  is  16°  17' S;  its  versed  sine  (ii.  31-32)  is  139'. 

b.  To  find  the  radius  of  the  sun  s diurnal  circle  (ii.  60). 


From  radius,  3438' 

deduct  versed  sine  of  declination,  i '</ 

Radius  of  diurnal  circle  ( dinavydsadah , dyujyn),  3299' 

c.  To  find  Iho  earth-sine  (ii.  61). 

The  measure  of  the  equinoctial  shadow  at  W ashington  is  (see  note  to 
ii.  G1-C3)  9d.03.  The  proportion,  then, 

iarl  :#9d.G8  : : 9G4' : : 7- S' 

shows  the  value  of  the  earth-sine  (kshitijya.  k 7 7/d)  to  be  778#. 

(1.  To  find  the  sun’s  ascensional  difference  yii.  61-62). 

The  proportion 

3299' : 3438' : : 77S' : Si  1' 

gives  the  sine  of  ascensional  difference  (cwra/yA),  which  is  811'.  The 
corresponding  arc,  or  the  sun’s  ascensional  dillcrcucc  (cura,  caradola),  is 
13°  39',  or  819P. 


296 


Sdrya-Siddhdntat 


[iv. 


3.  To  find  the  time  from  midnight  to  sunrise. 

The  sun’s  declination  being  south,  the  ascensional  difference  is  to  be 
added  (ii.  G2-G3)  to  the  quarter  of  the  sun’s  complete  day,  to  give  the 
length  of  the  half-night.  That  is  to  say, 


Quarter  or  sun's  complete  day  (ai.GGip-r  4),  5,4 1 5p 

Sun's  ascensional  difference,  819P 

Sun's  half-night,  G,a34p 

The  interval  between  true  midnight  and  true  sunrise  is  therefore 
6,234p,  or  I7n  19v.  That  from  Sunrise  till  noon  (a  quantity  required  in 
later  processes)  is  found  in  like  manner  by  subtracting  the  ascensional 
difference  from  the  quarter-day : it  is  459GP. 

Now  then,  finally, 


Time  of  opposition,  reckoned  from  mean  midnight,  55n  3* 

deduct  equation  of  lime,  1 3v 

do.  reckoned  from  true  midnjglit,  54"  5ov 

deduct  interval  till  sunrise,  1711  19? 

do.  reckoned  from  sunrise,  37«3i» 


The  time  at  which  the  opposition  of  the  sun  and  moon  in  longitude 
tabes  place,  or  the  middle  of  the  eclipse,  is  accordingly,  by  civil  reckon- 
ing at  Washington,  37 11  3iv. 

VI.  To  determine  the  diamelors  of  the  sun,  moon,  and  shadow. 

1.  To  find  the  sun’s  apparent  diameter. 

4 The  sun’s  mean  motion  hi  a sidereal  day  being  58'  08",  his  true  mo- 
tion at  the  time  of  the  eclipse  being  69*  48”,  and  his  mean  diameter 
6500  yojanas,  we  find,  by  the  proportion  (iv.  2) 


58'  58"  : Go'  48"  : : G5ooy  : 67027.81 


that  the  sun  covers  of  his  mean  orbit,  at  the  time  of  the  eclipse,  G702.81 
yojanas.  This  is  reduced  to  its  value  upon  the  moon’s  mean  orbit  by 
the  proportion  (iv.  2) 

57,7ri3,33G  : 4,32'>,ooo  : : 67021.81  : 5oty.37 

And  upon  dividing  the  result,  501.37  yojanas,  by  15  (iv.  3),  we  find  the 
sun’s  apparent  diameter  to  be  33'  ?j". 

2.  To  find  the  moon’s  apparent  diameter. 

In  like  manner  as  before,  the  proportion  (iv.  2) 

788'  aj"  : 854'  36  : : 4807  : 52oy.3 

shows  11s  that  the  moon’s  corrected  diameter  is  520.3  yojanas.  This  also, 
divided  by  15  (iv.  3),  gives  the  value  of  the  moon’s  apparent  diameter  in 
arc : it  is  34'  41". 

3.  To  find  the  diameter  of  the  earth’s  shadow. 

The  following  proportion  (iv.  4), 

788'  a5"  : 854'  36"  : : iGooy  : i734y.3 

determines  the  value  of  the  earth’s  corrected  diameter  («6rt)  to  bo  1734.3 
yojanas. 


297 


ir.]  Calculation  of  a Lunar  Eclipse . * 

Again,  from  the 

Sun's  corrected  diameter,  67027.81 

deduct  the  earth’s  diameter  (iv.  4),  1600 

remains  5ioaj.8i 

and  this  remainder,  when  reduced  by  the  following  proportion  (iy.  5), 
G5ooy  : 4807  : : 5ioay.8i  : 3767.8 

gives  ns  the  ezeesa  of  the  earth’s  corrected  diameter  (sfcf)  over  the  di- 
ameter of  the  Bhadow  on  the  moon’s  mean  orbit.  Hence,  from  the 


Earth’s  corrected  diameter,  i?34y.3 

deduct  last  result,  ■ 3767.8' 

Diameter  of  shadow,  » 1 3577.5 

divide  by  i5 

Diameter  of  shadow  in  arc,  90'  3o" 


VII.  To  determine  tlie  moon’s  latitude  at  the  middlo  of  the  eclipse, 
and  the  amount  of  greatest  obscuration. 

The  proportion  (i.  53) 

I»577,9i  7,828  : 232,238  : : 1,811,981  : 2GG«iv  8*  70  28'  25" 

gives  us  the  amount  of  retrograde  motion  of  the  moon’s  node  since  the 
commencement  of  the  Iron  Age.  Deducting  from  this  6B,  for  the  posi- 
tion of  the  node  at  that  time  (note  to  i.  56-58),  and  taking  the  pomple- 
ment  to  a whole  circle,  we  have 

Longitude  of  moon’s  node,  mean  midnight,  at  Ujj., 
deduct  for  difference  of  meridian, 

Longitude  of  moon’s  node,  mean  midnight,  at  Wash'n, 
deduct  motion  during  55“  3V, 

Longitude  of  moon's  node  at  moment  of  opposition, 
subtract  from  moon’s  longitude  (ii.  67), 

Moon’s  distance  from  node, 

Arc  determining  the  sine  (1 bhuja ), 

Sine, 

Hence  the  proportion 

3438/ : 270' : : 209' : 16'  25" 
gives  us,  as  the  moon’s  latitude  at  the  moment  of  opposition,  16'  25"  S. 


Now,  then,  by  iv.  10-11, 

Semi-diameter  of  eclipsed  body  (34'  41  "-r  2),  17'  22" 

do.  of  eclipsing  body  (90'  80"-r  2),  45'  i5"  • 

{heir  sum,  ' 62'  37" 

deduct  moon's  latitude,  16'  25" 

Amount  of  greatest  obscuration  (yrdia),  46'  12" 


and  sinco  this  amount  is  greater  than  the  diameter  of  the  eclipsed  body, 
it  is  evident  that  the  eclipse  is  a total  one. 


220  3i#  35" 
i 9 21" 

91  22°  3o'  l4" 
2'  55" 

22°  27'  19" 
3-  25°  56' 

6*  3°  29' 

3°  29' 

209' 


298 


S&rya-Siddhdnta , 


[iv. 


This  is  a most  unfortunate  result  for  the  Hindu  calculation  to  yield  ; 
for,  in -point  of  fact,  the  eclipse  in  question  is  only  a partial  one,  obscur- 
ing about  four-fifths  of  the  diameter  of  the  moon’s  disk.  The  source  of 
the  error  lies  mainly  in  the  misplacement,  relatively  to  the  sun  and  moon, 
of  the  moon’s  node,  and  the  consequent  false  value  found  for  the  moon’s 
latitude.  The  latter  quantity  actually  amounts,  at  the  time  of  opposi- 
tion, to  35'  42",  or  more  than  twice  the  value  given  it  by  the  .Hindu 
processes.  And  it  will  be  seen,  on  referring  to  the  table  on  p.  44,  that 
the  relative  error  in  the  place  of  the  moon’s  node,  having  been  accumu- 
lating for  seven  centuries,  is  now  about  3-|-°,  and  so  reduces,  by  more 
than  half,  the  true  distance  of  the  moon  from  her  node.  We  have  tried 
whether  the  admission  of  the  correction  of  the  btja  would  better  thq  re- 
sult, but  that  is  not  jthe  case. : the  error  of  position  is  still  (see  the  table) 
nearly  2°,  and  the  inqon’s  latitude  is  increased  only  to  24'  11",  so  that 
the  eclipse  still  appears  to  be  total.  It  is  evidently  high  time  that  a new 
correction  of  btja  be  applied  bv  the  Hindu  astronomers  to  their  elements, 
at  least  to  such  as  enter  into  the  calculation  of  eclipses. 

VIII.  To  find  tlic  duration  of  the  eclipse,  and  of  total  obscuration, 
and  the  times  of  contact,  immersion,  emergence,  and  separation. 


Diameter  of  the  eclipsing  body,  the  shadow, 
do.  eclipsed  body,  the  moon, 


90'  3o"  90'  3o" 
34' 4i"  34'  4i" 


Sum  and  difference,  12V  1 1"  5:V  4y" 

Half-sum  and  half-difference  (C  M and  C N,  Fig.  21  y p.  133),  6s'  35"  27'  55" 

Squares  of  do.,  3919'  724' 

• deduct  square  of  latitude,  269'  269' 


remain, 

Square  roots  of  remainders  (G  A and  C B), 


365o'  AW 

Go'  25"  21'  19" 


In  order  to  reduce  these  quantities  to  time,  wc  need  first  to  ascertain 
the  difference  of  the  true  daily  motions  of  the  suu  and  /noon  at  the 
given  moment : 


Moon’s  true  daily  motion,  854'  30" 

Sun’s  do.,  60'  48" 

Moon’s  gain  in  a day,  793'  48" 

Hence  the  proportions  (iv.  13) 


793'  48"  : Co« : : | 


60'  25" 
ai#  19" 


4n  34v 
i"  36?  4? 


give  us  the  half-duration  of  the  eclipse  as  411  34v,  and  the  half-time  of 
total  obscuration  as  1?1  3GV  -Ip,  supposing  the  moon’s  latitude  to  remain 
constant  through  the  whole  continuance  of  the  eclipse.  Wc  now  pro- 
ceed to  correct  these  results  for  the  moon’s  motion  in  latitude.  Aud 
first,  as  regards  the  half-duration.  Wc  calculate  the  amount  of  motion 
of  the  moon  and  of  her  node  during  the  mean  half-duration  by  the  fol- 
lowing proportions  (iv.  14) : 

6on : 854'  36"  : : 4“  34v : i°  5'  2" 

600  ; 3'  10" : : 4“  34* : i4" 


Farther, 


To  and  from  moon’s  long,  at  opposition,  3*  a5°  56' 

3-  25°  » 

add  and  subtract  motion  during  half-duration, 

i°  5* 

i°  5' 

Moon’s  long,  at  end  and  beginning  of  eclipse,  3* 

270  r 

3»  *4°  5r 

From  and  to  long,  of  node  at  opposition,  9s 

22°  2l" 

9»  aa°  vf  ai" 

subtract  and  ad#  motion  during  half-duration, 

1 4" 

if 

Long,  of  node  at  end  and  beginning  of  eclipse,  9a 

aa8  vf 

,■  aa8  aB' 

Moon's  distance  from  node,  6a 

4°  34' 

6*  a°a3' 

Arc  determining  sine, 

4°  34' 

a8  a3' 

Bine, 

»74' 

1 43' 

Moon's  latitude  at  end  and  beginning  of  eclipse, 

a r’  3i'' 

s.  uJ  i4"  a. 

• 

From  these  valuations  of  the  latitude  we 

now  proceed  to  calculate 

anew,  in  the  same  manner  as  before,  the  half-durations,  as  follows : 

- Square  of  half-sum  of  diameters, 

39,9' 

39^ 

deduct  squares  of  latitude, 

463' 

iafl* 

remain, 

1t93' 

Square  roots  of  remainders, 

58' 47".  61’  35" 

And  tlic  proportions 

793'  48"  : fxjn ; ; | 

m ' 


58*  47" : 4n  afiv  3p 
6i'  35"  : 4®  39^  aP 


give  ns  the  corrected  values  of  tlic  intervals  between  opposition  and  con- 
tact and  separation  respectively,  or  the  former  and  latter  half-durations, 
as  4 11  39v  2P  and  4»  So*  3P. 


The  text  contemplates  the  repetition  of  this  corrective  process,  if  still 
greater  accuracy  be  required  in  the  results  attained  : we  have  not  thought 
it  worth  while  to  carry  the  calculation  any  farther,  as  a second  correc- 
tion would  be  of  altogether  insignificant  amount. 

By  a like  process,  the  former  and  latter  half-times  of  total  obscura- 
tion, and  the  moon's  latitude  at  immersion  and  emergence,  arc  found  to 
be  as  follows : 


. Moon's  latitude  at  immersion  anil  emergence,  i4'  36"  18'  i3" 

Halftimes  of  total  obscuration,  am  42 v 3p  m 39V  4p 

By  adding  the  two  halves  wc  obtain 

Duration  of  the  eclipse  ( nthiti ),  9"  5V  5p 

do.  of  total  obscuration  (vimarda),  3n  iav  ip 

And  by  subtracting  and  adding  the  half-times  of  duration  and  of 
total  obscuration  from  and  to  tlic  time  of  o]  position  (iv.  16-17),  we 
obtain  the  following  scheme  for  the  successive  phases  of  the  eclipse : 


PllOSC. 

First  contact* 
Immersion, 
Middle  of  eclipse, 
Emergence, 

Last  contact, 


Time  of  occurrence  : 
after  mean  mill  night,  ofier  sunrise. 
5o»  a3v  49  3m  5i*  4? 

53u  jut  3p  35n  4B»  3p 

55n  3v  op  3711  3i*  op 

56d  3a*  4p  3pu  o*  Jp. 

59a  39V  3p  4i“  57v  3p 


800  S&rya-Siddhdnta , [iv. 

The  proper  calculation  of  the  eclipse  is  now  completed.  If,  however, 
we  desire  to  project  it,  we  have  still  to  determine  the  valana , or  deflec- 
tion of  the  ecliptic  from  an  east  and  west  line,  for  its  different  phases, 
as  also  the  scale  of  projection.  We  will  therefore  proceed  to  calculate 
them,  deferring  to  the  end  of  the  whole  process  any  comparison  of  the 
results  wc  have  obtained  with  those  given  by  moc^rn  astronomical 
science. 

IX.  To  calculate  the  deflection  of  tlie  ecliptic  from  an  east  and  west 
line  ( valana ) for  the  middle,  beginning,  and  end  of  the  eclipse. 

1.  For  the  middle  of  the  eclipse. 

a.  To  find  tlie  length  of  the  moon’s  day  and  night  respectively  at  the 


given  time. 

Moon’s  longitude  at  opposition. 

3*  25°  56’ 

Precession, 

20°  25' 

Moon's  distance  from  vernal  equinox, 

4»  160  ai' 

Arc  determining  sine, 

43°  31/ 

Sine, 

‘..37a' 

The  moon’s  declination  is  then  found  by  the  following  proportion 
(ii.  28) : 

3438' : 1397' : : 2372' : 964'= sin  160  17' 

Now,  from 

Moon's  declination,  • . 

1 6°  17'  N.' 

deduct  her  latitude  (ii.  58), 

16' S. 

Moon’s  true  declination, 

1 6°  I'M. 

Sine  of  do., 

948' 

Versed  sine  of  do., 

1 35' 

deduct  from  radius  (ii.  60), 

3438' 

Moon’s  day -radius,  33o3' 


Again,  to  find  the  earth-sine,  wc  say  (ii.  61), 

i ad  : 9d.68  : : 948' : 76^  ==  earth-sine, 
and  to  find  the  ascensional  difference  (ii.  61-62), 

33o3' : 3438'. : : 705' : 796'  “sin  i3°  24'  or  8o4'. 

The  excess  of  the  moon’s  complete  revolution  over  a sidereal  day  is  found 
by  the  proportion  (ii.  59) 

1800'  ■ 1795P  : : 849'  33"  : 848P 

Adding  this  to  a sidereal  day,  or  21,GC0p,  we  find  that,  the  moon’s  day 
is  of  22,448p,  of  which  one  quarter  is  5G12P.  Increase  and  diminish 
B this  by  the  moon’s  ascensional  difference  (ii.  62),  and  the  half-day  and 
half-night  are  found  to  be  6416p  and  4808p  respectively. 

All  this  laborious  process  of  ascertaining  the  length  of  the  moon’s 
half-day,  or  tlie  time  which,  with  the  given  declination,  she  would  oc- 
cupy in  rising  from  the  horizon  to  the  meridian,  is  rendered  necessary 
by  the  correction  which  the  commentary  applies  to  the  rale  of  the  text 
in  which*  the  moon’s  hour-angle  is  involved,  as  pointed  out  in  the  note 
to  iv.  24-25  (p.  140,  above).  We  noW  proceed 


801. 


iv.]  Calculation  of  a Lunar  Eclipse. 

b.  To  find  tlie  hotir-anglc,  and  the  corrected  hour-angle. 

At  the  moment  of  opposition,  the  moon’s  hour-angle  is  evidently  the 
same  with  that  of  the  sun.  lienee  it  may  be  found  as  follows  f ' • 


Time  of  opposition  reckoned  from  sunrise,  37n  3iv,  or  i3,5o6p 

deduct  the  whole  day,  9,192? 

remains  1 4,3  i4P 

deduct  from  tlie  half-night,  6,a35P  - 

Sun's  distance  in- time  from  inferior  meridian,  1,921? 


Tlie  moon's  distance  eastward  from  the  upper  meridian  is  accordingly 
19^ IP.  This  is  corrected,  or  reduced  to  its  proportional  value  as  a part 
of  the  moon's  urc;  of  revolution  from  the  horizon  to  the  meridian,  by  the 
follow  i ng  proportion : 

G4iGp  : 900  : : 1921?  : aG°  57' 

The  moon’s  ebrrreted  hour-angle,  then,  is  20°  57'  : its  sine  is  1557'. 

(*..  To  determine  the  amount  of  deflection  for  latitude  (valan&ngdsy  or 
dkska  valma — iv.  24 ). 

Tin;  sine  of  the  latitude  of  Washington,  38°  54',  15  2158'.  Hence 
the  proportion 

3438' ; t5>7#  : : aifjS*  : 9“,7/=sin  iG°  3i' 

give*  us  K»°  31'  as  the  value  of  the  quantity  sought.  The  moon  being 
in  the  eastern  hemisphere,  it  is  to  be  reckoned  as  north  in  direction, 
cl.  To  determine  the  amount  of  deflection  for  ccliptfc-dcviation  (dyana 


valuta — iv.  23). 

Moon's  distance  from  vernal  equinox,  4P  1G0  21 f 

add  a quadrant,  3* 

their  sum,  7*  iri°  ai' 

arc  determining  sino,  4(5°  21' 

bine,  2486' 

llenco,  hy  ii.  28,  the  proportion 


3438' : j397'  : : 248G' : 1010' =sin  170  G' 

gives  us  17°  O'  as  the  amount  of  declination  of  the  point  of  the  ecliptic 
which  is  a quadnyit  in  advance  of  the  moon,  and  this  is  the  deflection 
required.  Its  direction  is  south.  We  are  now  ready  for  the  tiual  process, 
c.  To  ascertain  the  net  amount  of  deflection  ( valana ),  in  digits. 


From  the  ecliptic-deflection,  170  6'  S. 

deduct  the  deflection  for  latitude,  iti9  3i'N. 

remains  the  net  deflection,  in  arc,  35'  S. 

divide  t:.v.  2j)  by  70 

Deflection  in  digits,  oJ  5o  9. 


It  thus  appears  that,  at  the  moment  of  opposition,  the  part  of  the 
ecliptic  in  which  the  moon  is  situated  very  nearly  coincides  in  direction 
wiln  an  east  and  west  circle.  The  amount  of  deflection  is  so  small  that 
39 


802  S&ryaSiddhdnta}  tw- 

in our  projection,  given  in  connection  with  the  sixth  chapter,  we  were 
obliged  to  exaggerate  it  some wb at-,  in  order  to  make  it  perceptible. 

2-  For  the  beginning  of  the  eclipse. 

As,  owing  to  the  moon's  motion  in  latitude  and  longitude,  her  decli- 
nation, and  so  also  her  ascensional  difference,  are  not  precisely  the  same 
at  .the  beginning  and  end  of  the  eclipse  as  at  the  moment  of  opposition, 
we  ought  in  strictness  tu  repeat,  the  first  pail  of  the  preceding  calcula- 
tion, determining  anew  the  length  of  the  moon's  half-day,  as*  it  would 
he  if  she  lflade  her  whole  revolution  about  the  earth  with  those  declina- 
tions respectively.  This  we.  take  the  liberty  of  omitting  to  do,  as  the 
modification  thus  introduced  into  the  process  would  be  of  very  small  im- 
portance. 


a.  To  find  the  moon's  corrected  hour-angle. 

And  first,  for  the  sun's  hour-angle  : _ 

Time  of  first  contact,  reckoned  from  sunrise,  3an  5i*  4P,  or  n,83o? 
deduct  the  whole  day,  9,192? 

remain  * 4,638? 

deduct  from  the  half-night,  6,a35p 

Sun's  distance  in  time  from  inferior  meridian,  3,697? 


This,  then,  is  the  hour-angle  of  the  centre  of  the  shadow  at  the  time 
of  contact.  The  distance  of  the  centre  of  the  moon  in  longitude  from 
that  of  the  shadow 'was  found  above  (under  VIII)  to  be  61'  35".  This 
is  reduced  to  its  vglue  in  right  ascension  by  the.  proportion 

1800' : 1796^ : : 61' 35" : 61  P.4  * 

Now,  then, 

from  the  hour-angle  of  the  shadow,  3,597? 

deduct  the  difference  of  the  moon's  right  ascension,  61 P 

- Moon's  hour-angle  at  beginning  of  eclipse,  3,536p 

This  is  virtually  an  application  of  the  process  taught  in  iii.  50. 

Thp  moon’s  hour-angle  is  now  corrected,  as  before,  by  the  proportion 

64i6p  : 90°  : : 3536i>  : <19°  36' 

The  sine  of'  49°  30'  is  20 1 7'. 
b.  To  find  the  deflection  for  latitude. 

The  proportion  • 

3438' : ai58' : : 2617' : i643'=  sin  28°  34' 
gives  us  the  deflection  for  latitude  as  28°  34#,  which  is  north,  as  before. 


c.  To  find  .the  ecliptic-deflection. 

Moon's  distance  from  vernal  equinox  At  opposition,  4a  160  21' 

deduct  motion  during  4n  39*  2P,  z°  6' 

do.  at  time  of  contact,  41  i5°  i5' 

add  a quadrant,  3a 

sum,  7*  i5°  i5' 

■ arc  determining  sine,  45°  i5# 

sine,  2441' 


>▼•]  ' Calculation  of  a Lunar  Eclipse.  $63 

Next,  the  proportion 

3438' : 1397' : : a44i' : 99a'  = sin  160  47' 

■hows  us  that  the  ecliptic-deflection  is  16°  47' ; it  is,  as  in  the  former, 
case,  south. 

d.  Tq  find  the  deflection,  in  digits. 


From  the  deflection  for  latitude, 

aB°  34'  nr. 

deduct  the  ecliptic-deflcclion, 

160  47'  S. 

remains  the  uct  deflection,  in  arc, 

• 

ii°  47' If- 

its  sine  is 

70a' 

divide  by 

70 

Deflection,  in  digits, 

ioJ.o3  N. 

3.  For  the  end  of  the  eclipse. 

Of  this  process,  which  is  throughout  closely  analogous  to  the  last,  wo 
shall  present  only  a brief  statement  of  the  results. 


IIour*ngle  of  the  centre,  of  the  shadow,  3-i?P  E. 

Distance  of  the  centre  of  the  moon  in  right  ascension,  -S9P  E. 

Moons  hour  angle,  1 38ipE.  * 

do.  corrected,  5°  20' 

Sine,  3ao' 

Deflection  for  latitude,  3°  21  ’ N. 

Moon's  distance  from  vernal  equinox  + 3*.  7*  170  24' 

Arc  determining  sine,  " 47°  *4' 

Sine,  253o' 

Jh’liptic- deflect  inn,  170  ?4'  S. 

Nut  deflection,  in  arc,  * i4°  3'S. 

do.  in  digits,  11  <>.93  S. 


The  inode  of  application  of  these  quantities  in  making  a projection 
of  an  eclipse  is  sufficiently  explained  in  the  notes  to  the  sixth  chapter, 
and  illustrated  by  the  figure  there  given,  which  is  adapted  to  the  condi- 
tions" of  the  eclipse  here  calculated.  All  the  quantities  entering  into  tho 
projection,  however,  of  which  the  value  has  been  stated  in  minutes,  re- 
quire also  to  be  reduced  to  digits,  according  to  a scale  determined  by  the 
following  process. 

X.  To  determine  the  scale  of  projection  of  the  disks  and  latitudes 
(iv.  20).  ■ 

This  process  we  will  perform  only  for  the  moment  of  opposition,  or 
for  the  middle  of  the  eclipse.  At  this  time,  as  has  been  seen  above,  w# 
have 


Moon's  hnlf-duy, 

64iGp 

do.  liour-anglc  (uafa), 

1931? 

do.  altitude  iu  time  (vnnota). 

4495P 

add  64iGp  X 3 * 

19,548? 

the  sum  is 

*3,?43P 

divide  by 

6.4'6p 

the  quotient  is 

3-7 

809  S&rya-Siddhanta , 


[* 


same  with  those  illustrated  by  us  inrtho  notes  to  i.  21-23, 24, 48, 48-51v 
above.  It  will  be  noticed  that  the  Hindu  astronomer,  at  least  when’ 
working  out  au  illustrative  process,  like  the  one  in  hand,  scorns  to  make 
use  of  any  of  the  means  for  reducing  the  labor  of  computation  which 
.the  text  directly  or  impliedly  permits,  and  of  which,  in  our  own  calcu- 
lations, we  have  been  glarl  to  avail  ourselves. 

II.  To  ascertain  the  mean  longitudes  of  the  snn,  the  moon,  the  sun’s 
apsis,  the  moon’s  apsis,  and  the  moon’s  node,  for  mean  midnight  on  the 
Hindu  meridian,  at  the  given  interval  from  the  creation. 

The  amount  of  motion,  since  the  creation,  of  the  bodies  named,  in- 
their  order,  is  found  by  the  following  series  of  proportions : 

1,577,917,828  : 714,404,106,527  ::  4,320,000 : i ,955,884,955™  j«  120  i4'  *4" 
i.577.9'7, 8a8  : 714^04,106,527  ::  57,753,336  : 26,147,889,118™  n 9°  44'  29" 

*,577k9i  7,828,000  : 714,404,106.527  ::  387  : 175™  2i  170  17'  a3/; 

# 1,577.917,828:714^04,106,527::  488,203  : ' 22,134,467™  2"  210  56'  9" 

*,577,917,828  : 7 1 4,404* 06,527  ::  932,238  : 105,146,020™  io«  170  x i'  5o” 

Rejecting  whole  revolutions,  and,  in  the  case  of  the  moon's  node, 
subtracting  tlic  fraction  from  a whole  revolution,  we  have,  as  the  mean 
longitudes  required  : 


Sun,  !■  120  i4'  i4" 

Moon,  !■  90  44'.  99" 

Sun’s  apogee,  • 2*  170  17'  23" 

Moon's  apogee,  2«  21 0 56'  ■ 9" 

Moon’s  node,  i«  1904H'  10" 

• 

The  Ilindu  calculator  has  taken,  in  the  case  of  the  moon’s  apsis 
and  node,  the  numbers  of  revolutions  given  by  the  text-,  omitting  the 
correction  of  the  bija . We  have  not,  in  order  ta  test  the  accuracy  of 
his  arithmetical  operations,  wprkcd  over  again  tne  proportions,  except' 
ing  in  two  instances,  the  first  and  last:  our  results  differ  but  slightly 
from  those  above  given  (we  find  the  seconds  of  the  sun’s  place  to  be  40#\ 
and  the  minutes  ami  seconds  of  the  node’s  motion  to  be  12'  43"): — not 
enough  to  render  any  modification  necessary. 

IIL  To  ascertain  the  values  of  the  same  quantities  at  mean  sunrise 
on  the  equator,  or  G o'clock. 

In  order  to  this,  we  must  add  to  each  planet's  longitude  one  fourth 
the  amount  of  its  mean  motion  in  a day. . We  require,  then,  the  mean 
daily  motions.  They  are  found  as  follows,  taking  the  sun  as  an  example : 

1,577,91 7, 8 28d  : 4,3 20, ooornv : ; id  ; 59'  8"  itV"  io"".4 

We  omit  the  other  proportions  and  their  results,  as  the  latter  have  been 
fully  stated  in  the  tabie  of  mean  motions  of  the  planets  (note  to  i.  29-34). 
Adding  a quarter  of  the  daily  motion,  we  have  as  follows : 


Sun, 

Moon,  * 
Sun’s  apogee. 
Moon’s  apogee, 
Moon’s  node, 


Long,  at  midnight.  Correction.  Lonff.  at  sunrise. 

i»  120  i4#  i4"  + 1 4'  47"  = 1*  120  29'  1" 

is  90  44'  39"  + 3°  17'  39"  = i*  i3°  a'  8" 

as  17°  17'  23"  + 0 =a*  170  17'  a3" 

a«  ai°  56#  9"  + i#  4o"  = #■  210  57 9 49" 
!■  ia°  48'  10"  C-  48"  = 1*  ia°  47'-aa/< 


v.]  ' Calculation  of  a Solar  Eclipse.  801* 


IV.  To  ascertain  the  values  of  the  same  quantities  at  mean  sunrise 
upon  the  equator,  on  the  meridian  of  the  given  place. 

Adopting  75°  50'  as  the  longitude  of  the  Hindu  meridian  cast  from 
Greenwich,  wc  have,  as . the  interval  in  longitude  of  Williams*  College 
from  it,  140°  2'  30",  which  is  equal  to  24“  50v  2p.  The  latitude  i\ 
42°  42'  51".  \Vc  have,  then,  first,  to  determine  the  distance  of  the 
place  in  question,  upon  its  own  parallel  of  latitude,  from  the  Hindu 
meridian. 

The  equatorial  circumference  of  the  earth  has  been  found  above  (note 
to  i.  50-60)  to  be  5059.64  yojanas.  Its  circumference  upon.the  paral- 
lel of  latitude  of  Williams’  College  is  found  (i.  GO). l>y  the  following 
proportion : 

3438'  (=R):  a5aS'(=cos  4a°  4*2  5i") : : 5o59Y.64  : 37157.97 

Thu  depdntara , or  difference  of  longitude  in  yojanas,  is  then  deter- 
mined thus : 

Cion  : a4°  5ov  ap  : : 37157.97  : i538y.4i 


And  {fre  depdntaraphala , or  correction  for  difference  of  longitude,  ie 
calculated  from  the  daily  motion  of  each  body,  by  such  a proportion  as 
the  011c  subjoined,  which  gives  the  sun’s  correction : 


• 37 1 5y. 97  : 1 5387.4 1 : : 5/  8" : ?4f  2 7 " 

Wc  omit  the  other  proportions,  and  merely  present  their  results  in 
the  following  table : 


Sun, 

Moon, 

Sun's  apogee, 
Moon's  apogee, 
Moon's  ijode, 


Sunrise  at  Luiiksl.  Correction.  Sunrise  on  giv.  mcrid. 
in  ia°  29'  1"  + . 24'  27”  = ig  120  53'  28" 

i*u3°  a'  8"  + 5 27  12  = is  1 8°  29*  20" 

as  1 70  17'  23"  +0  = 2s  170  17'  23" 

2s  210  57'  49"  + a'  45"  = 2s  22%  o'  34" 

*!■  ia°  47' 22"  - i'  19"  = IS  12°  46'  3" 


Wc  have  already  (note  to  i.  63-65)  called  attention  to  the  excessively 
awkward  and  cumbrous  character  of  this  process  for  making  the  correc- 
tion for  difference  of  meridian. 

V.  To  find  the  sun’s  true  longitude. 


From  the  lougitudo  of  the  sun's  apsis, 
deduct  sun's  mean  longitude  (ii.  12*J)f 

Sun's  mean  anomaly, 

Sine, 


2®  17°  17'  53" 
i»  12°  53'  28" 

1*  4°  a3'  55" 
1927' 


The  diminution  of  the  sun’s  epicycle  is  now  found  by  the  following  pro- 
portion (ii.  38) : # 

3438' : 20' : : 1927' : u'  12"^ 


The  dimensions  of  thc.cpicycle  arc,  then  (ii  34),  14°  — 11*  12",  or 
13°  48*  48".  Next,  the  proportion  (ii.  39) 

36o°  : i3°  48'  48" : : 1927' : 74'  1 1"  . 


gives  us  the  sun’s  equation  of  the  centre,  which,  by  ii.  45,  is  additive.. 
Hence  to  the  # • ■ 


Sun's  mean  longitude, 
add  the  equation, 
Sun’s  true  longitude, 


is  ia°  53'  28" 
i°  1 A’  11" 

it  U°  7'  39" 


806 


S&rya-Siddh&nta,  [v. 


Thi*  calculation  exhibits  a rather  serious  error : the  sine  of  34°  24', 
the  anomaly,  is  1942',  not  1927'.  The  final  result,  however,  is  not  per- 
ceptibly mollified  by  it : the  equation  ought  to  be.  1°  14'  30",  and  the 
true  longitude  1*  14°  7'  58". 

, VI.  To  find  the  moon’s  true  longitude. 

From  the  longitude  of  the  month's  npsis,  2»  a a0  o'  34" 

deduct  moon's  mean  longitude,  i»  i8°  29'  20" 


Moon's  mean  anomaly, 
Sine, 

Diminution  of  epicycle, 
Dimensions*  of  epicycle, 
Equation  of  the  centre, 


ib  3°  3i'  i4" 
1898' 
1 1 ' 2" 
3i°  48'  58" 

+ *°  47' 


Hcucc,  to  the 


Moon's  mean  longitude, 
add  the  equation. 

Moon's  true  longitude, 


1 8 1 8°  21/  20" 

Is  21°  iff”  20" 


VIL  To  calculate  the  true  daily  motions  of  the  sun  and  moon. 

The  equations  of  motion  for  the  sun  and  inoori  have  been  found  by 
■ the  calculator  of  the  •eclipse  by  the  following  proportion:  as  ihe  whole 
orbit  of  either  planet  i*  to  its  epicycle,  so  is  its  mean  dftily  motion  to 
the  required  equation.  That  is  to  wiy,  for  the  sun, 

3(5o°  : 1 3°  48'  48"  : : 5c/  8"  : a'  ifi" 

which,  bv  ii-  49,  i*  subtractive.  ITcucc  the  sun's  true  motion  is  59'  8" 
-~2' 16",  or  56' 5i!" 

Againf  for  the  moon, 

36o° : 3i°  48'  58"  : : 790'  35" : 69'  36''  . 

And  the  moon’s  true  motion  is  790'  35"  — 69'  3G",  or  720'  .59", 

These  calculations  are  exceedingly  incomplete  and  erroneous,  as  may 
readily  be  seen  by  referring  to  the  corresponding  process  in  the  other 
eclipse,  or  to  that  given  hs  an  illustration  in  the  note  to  ii.  47-49.  The 
actual  value  of  the  sun’s  equation  of  motion,  as  fully  calculated  l>v  the 
method  of  our  treatise,  is  only  1'  51";  that  of  the  moon  is  only  58'  49" : 
whence  Ihe  true  motions  are  57'  17"  and  731'  40"  respectively.  These 
arc  clcincnls  of  so  much  importance,  and  they  enter  so  variously  into 
the  after  operations,  that  wo  hir  e hesitated  as  to  whether  it  would  not 
be  better  to  .cancel  the  whole  work  of  the  Hindu  calculator  from  tlm 
point  onward,  and  to  perform  it  anew  in  a more  exact  manner ; hui  we 
have  finally  concluded  io  present  the  whole  as  it  is,  as  a specimen  — 
although,  we  hope,  not  a faxorablc  one — of  native  work;  pointing  out, 
at  the  same  time,  its  deficiencies,  and  cautioning  against  its  results  being 
accepted  as  the  bqst  that  the  system  is  capable  of  affording. 

We  have  thus  far  found  the  true  longitudes  of  the  sun  and  moon  for 
the  moinent^f  mean  sunrise  at  the  equator,  upon  the  meridian  of  the 
given  place.  Wc  desire  now  farther  to  find  the  same  data  for  the  mo- 
meutjpf  sunrise  upon  the  same  meridian  in  latitude  42°  42'  51"  X. 

‘ VAT.  To  find  the  longitudes  of  the  sun  and  moon  ut  sunrise  in  long. 
149°  2'  30",  lat.  .42°  42'  51"  N. 


*•] 


Calculation  of  a Solar  Eclipte. 


800 


L To  calculate  the  precession  of  the  equinoxes  (iii.  9-18). 

Tne  proportion 

I»577i9i7i8a8d : 6oo«t  : : 714,404,106,527 : 271,650*®*  8®  70  45'  22" 

gives  us  the  amount  of  the  motion  of  the  equinox  in  its  own  circle  of 
ubratory  revolution,  since  the  beginning  of  things.  Rejecting  complete 
revolutions,  and  deducting  6*  from  the  fraction  of  a revolution,  we  nave 
the  distance  of  the  equinox  from  the  origin  of  the  sidereal  ■ sphere,  in 
terms  of  itsf  own  revolution,  as  67°  45'  22" : three  tenths  of  this,  or 
20°  19#  38",  is  the  amount  of  the  precession. 

2.  To  calculate  the  sun’s  declination.  # 

Sun's  longitude,  u i4°  7#  89" 

Precession,  ao°  19'  36" 


Sun's  distance  from  vernal  equinox,  a®  4°  *lr  i5" 

Sine,  3ioe' 

Then,  by  ii:  28, 

• 3438':  1397'::  3ioi':  1260'=  sin  ai°  3if  3" 

the  sun’s  declination  is  therefore  21*  31#  3#/.. 

3.  To  calculate  the  sun’s  ascensional  difference. 

The  radius  of  the  sun’s  diurnal  circle  (dyujyd — ii.  60)  is  3199f. 

The  equinoctial  shadow  in  the  given  latitude  is  11*07,  being  found 
by  the  proportion  (iii.  17) 

cos  lat. : sin  lat. : : gnom. : eq.  shad, 
or  : 233n' : : 12*1 : iid.07 

Again, ^;o  find  the  earth-sine  (kujyd — ii.  81), 

1 a«l  : 11*1.07  : : 1260' : 1162'  • 

And,  to  find  the  sine  of  ascensional  difference, 

3199'  : 3438'  : : 1162'  : 1249' 

The  corresponding  arc  is  21°  19',  or  1279';  and  since  a minute  of 
arc  is  equivalent  to  a respiration  of  time,  the  sun’s  ascensional  difference 
in  time  is  1279P,  or  213*,  or  3U  J33*  rejecting  the  odd  respiration. 

4.  To  calculate  the  length  of  the  sun’s  day. 

The  sun  being  in  the  third  sign,  T>f  which  the  equivalent  in  right  as- 
cension (iii.  42-45)  is  1935P,  the  excess  of  his  day  over  60 1 Adis  is  found 
by  the  proportion 

1800' : I935P  : : 59'  8" : 63p 

whence  the  length  of  his  day  is  21,G63P.  ‘ 

Iu  this  calculation  of  tlic  length  of  the  sun’s  day,  the  operator  has  to- 
ken the  mean,  instead  of  the  true,  motion  of  the  sun,  which  is  obviously 
less  accurate,  and  which  is  contrary  to  the  11  waning  of  the  jjule  of  the 
text  (ii.  59),  as  explained  by  the  commentator. 

Now,  in  order  to  find  the  difference  between  the  sun’s  longitude  at 
sunrise  on  the  equator  and  sunrise  011  the  given  parallel  of  north  latitude, 
we  make  a proportion,  as  follows : if  in  his  whole  day  the  sun  moves 
an  amount  equal  to  his  daily  motion,  how  much  will  be  move  during  ah 
interval  corresponding  to  his  ascensional  difference  f of  ■ * 

2x,663p:  fy  &,r::  1279P:  3'  29" 

? 40 


810 


['• 


The  sun’s  declination  being  north,  sunrise  on  the  given  parallel  pre- 
cedes sunrise  on  the  equator,  and  hence  this  result — which  is  called  the 
cdrakal&s, 14  minutes  (kald)  of  longitude  coiTesponding  to  tlie  ascensional 
difference  (cara)” — is  to  be  subtracted  from  the  sun’s  longitude  as  for- 
merly found.  That  is  to  say, 


Sun’s  longitude  at  equatorial  sunrise, 
deduct  the  correction  (carakahia),  ‘ 

Sun's  longitude  at  sunrise,  lat  4wj°  4*f  5i"  X., 
long.  i4y°  2r  3o"  W.  from  LankA, 


i®  1 4°  7'  39" 
3'  29" 

JR  |40  4/  jo" 


In  finding  the  corresponding  value  of  the  moon's  longitude  tve  apply 
first  a correction  for  tlic  sun's  equation  of  place  ; it.  is,  in  fact,  the  equa- 
tion of  time,  calculated  sifter  the  entirely  insufficient  method  which  wc 
have  already  fully  exposed,  in  connection  with  part  V of  the  preceding 
process.  The  proportion  is  (ii.  40)  as  follows : 

' 21.600' -.790' 35"::  i°  i4'  11":  2' 43" 

Here,  again,  bad  is.  made  worse  by  taking  as  the  second  tenp  of  the 
proportion  the  moon’s  mean,  instead  of  her  true,  rate  of  motion.  It  is 
to  be  noticed  that  a like  correction  should  have  been  applied  also  to  the 
suii’s  longitude,  but  was  omitted  by  tlic  calculator.  AVo  have,  then, 


Moon’s  longitude,  mean  equatorial  sunrise,  iB  21 0 16'  20" 

add  the  correction  for  the  equation  of  time,  . 2'  43" 

Moon's  longitude,  true  equatorial  sunrise,  i>  ai°  191  3" 

Now  we  apply  farther  the  correction  for  the  sun’s  ascensional  differ- 
ence (1 carasanskdra ) ; it  is  calculated  in  the  same  manner  wffli  that  of 
the  sun,  and  i(s  Amount  is  found- to  be  47'  5111. 


Moon's  longitude,  true  equatorial  sunrise, 
deduct'the  correction  for  the  sun's  asc.  cliff.. 

Moon's  longitude  at  sunrise,  lat.  4a°  4a'  5i"  N., 
long.  149°  a'  3o"  W.  from  Lanka, 


JR  a*  19'  3'' 

47' 

i*  20'  3lf  I2,# 


On  coinparing  the  longitudes  of  the  sun  and  moon,  as* thus  deter- 
mined,  it  is  seen  that  tire  time  of  conjunction  is  already  past.  Ilencc 
the  calculation  is  carried  a day  backward,  by  subtracting  from  tlic  lon- 
gitude of  each  body  its  motion  during  a day.  That  is  to  say, 


1-ongilmlc,  , 1 nfetion  Longitude, 

■utiriBe  following  eclipse.  ua’  “ ™“  on•  sunrise  preceding  cclijis 

Sun,  is  14°  4'  10"  - 56'  5a''  = i«  i3°  1 18" 

Moon,  i»  ao°  3i'  ia"  - ia°  o'  59"  = i«  8°  3c/  i3" 

Moon's  node,  i®ia°46'  3"  + 3'  ii"  = 

Tliis  is  an  entirely  uncallcd-for,  and  a highly  inaccurate  proceeding. 

By  the  ruff  given  in  our  text  (ii.  66),  it  is  just  as  easy  an<l  regular  a 
process  to  find  from  any  given  time  the  interval  to  the  beginning  of  the 
current  lunar  day  by  reckoning  backward,  as'thpt  to  the  end  of  the  day 
by  reckoning  forward.  And  to  assume  that  the  whole  calculation  may 
be  transferred  from  one  sunrise  back  to  the  preceding  by  simply  deduct- 
ing the  amount  of  motion  in  a day  as  determined  for  the  former  time  is 
to  take  a most  unwarrantable  liberty,  and  to  ignore  the  change  during 


811 


v.]  Calculation  of  a Solar  Eclipse . 


the  interval  of  many  of  the  elements  of  the  calculation,  as  the  sun’s  and 
moon’s  rates  of  motion,  the  sun’s  declination  and  ascensional  ^fference, 
etc.  In  making  the  transfer,  moreover,  the  longitude  of  the  moon’s 
node  has  been  taken  as  found  for  mean  equatorial  sunrise,  without  any 
correction  for  the  equation  of  time,  or  for  tnc  sun’s  ascensional  difference. 

IX.  To  find  the  time  of  true  conjunction,  and  the  longitudes  of  the 
sun,  moon,  and  moon’s  node  at  that  time.  By  ii.  66,  from  the*:-  * . 

Moon’s  true  longitude,  i*  8°  30*  t3" 

deduct  the  sunfe  do.,  i®  i3°  i 18" 


remains 

divide  by  the  portion  of  a lunar  day, 
the  quotient  is 

deduct  the  remainder  from  a whole  portion, 


ii*  a5°  aa'  55" 
7ao ' 

29s  and  44 2'  55" 
720' 


remains  277'  5" 

This  process  shows  us  that  the  moon  lias  still  277'  5"  to  gain  upon 
the  sun, sin  ordqr  to  arrive  at  the  end  of  the  thirtieth  or  last  day  of  the 
lunar  month,  or  at  conjunction  with  the  suu. 

Next,  from  the  ; 

Moon’s  true  daily  motion,  720’  59" 

deduct  the  sun’s  do.,  56*  5a" 


Moon’s  daily  gain  in  longitude, 


664’  7" 


Hence  the  proportion 

664'  7"  : 6on  : : 277'  5"  : 2^  av 

gives  us  the  time  of  conjunction,  reckoned  from  sunrise,  as  25“  2V. 

Now,  hv  iv.  8,  we  proceed  to  find  the  longitudes  for  that  time.  The 
amounts  of  motion  during  25n  2V  are  found  by  the  following  proportions : 

/ 56'  5?”  : a3'  43" 

Gon  : a5n  av ::  J 720'  59" : 3oo’  48" 
l 3;u":  1*19" 

Then,  to  the 


Sun’s  longitude  at  sunrise, 
add  the  correction, 

Sun’s  longitude  at  conjunction, 

Moon’s  longitude  at  sunriso, 
add  the  correction, 

Moon's  longitude  at  conjunction, 

Node's  longitude  at  suniise, 
deduct  the  correction, 


i*  i3°  7/  18" 
23'  43" 

4M3°  3i'  iV 

i*  8°  3o'  i3" 
5°  o' 48" 

i*  1 3°  3i'  i" 

i>  1 2®  49'  i4" 
V 19" 


Node’s  longitude  at  conjunction. 


i*  1 a°  47'  55" 


The  mode  of  proceeding  adopted  by  us  above,  in  the  lunar  eclipse, 
for  finding  the  time  of  the  middle  of  the  eclipse,  and  the  longitudes  of 
the  sun  and  moon  at  that  time,  is,  as  will  not  fail  to  be  observed,  quite 
different  from  that  of  the  native  calculator  of  this  eclipse.  That  fol- 
lowed by  Davis,  or  his  native  assistants  (As.  Res.,  ii.,273  etc.),  varies 


812 


[*• 


considerably  from  both.  Our  own  method,  though  varying  in  some 
respects  fora  that  contemplated  by  the  text,  is  a not  less  legitimate  ap- 
plication of  its  general  methods  than  either  of  the  others,  and  it  pos- 
sesses this  important  advantage  over  both,  that  we  were  able  to  verify 
it,  and  to  show,  by  calculating  the  mean  and  true  places  for  the  given 
instant,  that  the  latter  was  actually  the  one  at  which  the  system  made 
the  opposition  of  the  sun  and  moon  to  take  place : while,  on  the  con- 
trary, in  the  process  now  in  hand,  so  many  errors  have  been  involved, 
that,  were  the  same  test  to  be  applied,  we  should  find  the  centres  of  the 
sun  and  moon  many  minutes  apart  at  the  moment  fixed  upon  as  that  of 
conjunction,  and  the  place  of  conjunction  as  far  removed  from  the  point 
of  longitude  above  determined  for  it. 

X.  To  find  the  apparent  diameters  of  the  sun  and  moon. 

These  Quantities  arc  determined  by  means  of  the  following  propor- 
tion : as  tne  mean  daily  motion  in  yojanas  is  to  the  mean  diameter  in 
yojanas,  so  is  the  true  motion  in  minutes  to  the  true  diameter  in  min- 
utes. That  is  to  say,  for  the  sun  and  moon  respectively, 

11,858]?  : 65ooy  : : 56'  5a" : 3i'  10"  • r 

11,858}?  : 48oy : : 720'  59"  : 29'  2" 

This  method  is  in  appearance  quite  different  from  that  which  is  pre- 
scribed by  our  text  (iv.  2-3),  hilt  it  is  in  fact  only  a simplification,  or 
reduction,  of  the  rules  there  given.  Thus,  for  the  moon,  the  text  gives 
m.  mot.  in  minutes : true  mot.  in  min. : : m.  diam.  in  yoj. : true  diam.  in  min.  X 15 

Transposing,  now,  the  middle  terms,  transferring  the  factor  lfr  from  the 
fourtlr  term  to  the  first,  and  noting  that  the  mean  motion  in  minutes, 
when  multiplied  by  15,  gives  the  value  of  the  same  in  yojanas,  we  have 
the  former  proportion,  namely, 

m.  moL  in  yoj. : m.  diam.  in  yoj. : : true  mot.  in  min. : true  diam.  in  min. 


Again,  in  the  case  of  tlic  sun,  the  rules  of  the  text  give 

m.  mot.  in  min. : true  mot.  in  min : : m.  diam.  in  yoj  . true  diam.  in  yoj. 
and  true  diam.  in  yoj.=  true  diam.  in  min. X 1 5 X (sun's  orbit  -r  moon's  orbit) 


Now  transposing  the  second  and  third  terms  of  the  proportion,  sub- 
stituting for  the  fourth  its  equivalent  as  here  stated,  and  transferring  to 
the  first  term  the  last  two  factors  of  that  equivalent,  we  have 


. . ...»  suns  orbit  . . , ....  .. 

m.mot  in  min.X  15X  . r---  : m.  d. m y. : : true  mot.  in  min. : true  diam.  in  inin.  • 

moon  s orbit  J 


But  the  first  term,  as  thus  constructed,  is,  by  the  method  of  determina- 
tion of  the  planetary  orbits  (see  xii.  81-83),  equal  to  the  sun’s  mean 
daily  motion  upon  his  orbit  reckoned  in  yojanas : hence  the  proportion 
becomes  for  the  sun,  as  for  the  moon, 

m.  mot.  in  yoj. : m.  diam.  in  yoj. : : true  mot  in  min.  : true  diam.  in  min. 

XI.  To  calculate  the  parallax  in  longitude  (lambana),  and  the  time 
of  apparent  conjunction  (v.  3-9). 

1,  To  find  the  orient  ccliptic-point  ( lagna ) at  the  moment  of  true 
conjunction  (iii.  46-48). 

In  order  to  this,  we  require  to  have  first  the  equivalents  in  oblique  as- 
cension (uday&savai)  of  the  several  signs  of  the  zodiac  for  the  latitude 


818 


r.]  Calculation  of  a Solar  Eclipse.  * 

«f  William*’  College,  42°  42'  51"  N.  We  present  annexed  their  values 
as  employed  by  the  calculator  of  the  eclipse,  and  also  as  calculated  by 
o™lveB  according  to  the  method  taught  in  our  text  (iii.  42-45).  It 
vill  be  noticed  that  the  differences  are  not  inconsiderable,  and  evince 
much  carelAstiess  on  the  part  of  the  native  astronomer ; who,  moreover, 
employs  vin&dls  only  in  his  processes,  rejecting  the  odd  respirations, 
which  is  an  inaccuracy  not  countenanced  by  the  S dry  a-Siddh&nta. 


Equivalent  In  oblique  ucenaion  : 
occ.  to  calculator.'  arc.  to  us. 

ist  sigh 



ioo8p 

iath  sign 

and  M 

ia38p 

nth  u 

3rd  “ 

a87v  or  172  JP 

1699, 

10th  " 

4th  " 

359V  or  2i54p 

ai7ip 

9th  M 

5th  ■ 

387V  or  a3aap 

a35ap 

8th  “ 

6th  “ 

388*  or  a3a8p 

a33ap 

7th  11 

The  equivalents  assigned  by  the  Hindu  calculator  to  the  3rd  and  4th 
signs  are  moreover,  it  may  be  remarked,  inconsistent  with  one  another, 
since  tlfo  one  ought  to  fall  short  of  1935P  by  as  much  as  the  other  ex- 
ceeds that  quantity. 

Now,  then,  to  the 

Sun's  longitude  at  conjunction,  i*  i3°  3if  3 " 

add  the  precession,  # " ao°  19'  36" 

Sun's  distance  from  the  equinox,  a«  3°  5o;  37" 

It  appears,  accordingly,  that  the  sun  is  in  the  3rd  sign,  and  26°  9'  28" 
from  the  beginning  of  the  fourth.  Hence  the  proportion  (iii.  46) 

• 3o°  : 287V  : : 26°  9'  23"  : a5ov 

give  us  250*  as  the  ascensional  equivalent  of  the  part  of  a sign  to  be 
traversed  ( bhogy&savas ).  The  time  of  the  clay,  or  the  sun’s  distance  in 
time  from  the  eastern  horizon,  is  25°  2V,  or  1502v.  Then,  from  the 


Time  of  conjunction,  i5oav 

deduct  use.  equiv.  of  part  of  3rd  sign,  a5ov 

remains  " 1 a5av 

deduct  asc.  equiv.  of  4th,  5th,  and  6th  signs,  1 i34v 

remains  u 118* 


This  remainder  of  time,  or  of  ascension,  is  reduced  to  its  value  in  arc 
of  the  ecliptic  by  the  proportion  (iii.  49) 

388v : 3o° : : ii8v;9®  7'  *5" 

Add  this  result  to  the  whole  signs  preceding,  and  the  longitude  of  the* 
orient  ccliptic-point  (1 lagna ) is  found  to  he  6 1 9°  V 25":  its  sine  is  544' 
(more  correctly,  645'). 

2.  To  find  the  orient-sine  (udayajyd. — v.  3). 

This  is  found  by  the  proportion 

a5a5';  j397,::544,:3oi/ 

2525/  being  the  cosine  of  the  latitude,  and  1397' the  sine  of  the  inolina- 
■ lion  of  the  ecliptic  (ii.  28). 

3.  To  find  the  meridian  ecliptic-point  (madhyalagm — iii.  49). 


3U 


S&rya-Siddh&nta, 


Iv- 


in order  to  this,  wo.  must  first  know  the  sun’s  hour-angle  (note),  or 
distance  in  time  from  the  meridian  ^ it  is  determined  aB  follows : * 


A quarter  of  the  complete  day,  »5“  or 

add  the  sun’s  ascensional  difference,  . ■ • 3»  33v 

The  sun’s  half-day,  i8n  33* 

deduct  from  time  of  conjunction,  a5n  av 

Sun's  hour-angle,  west,  1 6n  29* 


Tlie  sun's  distance  from  the  beginning  of  the  fourth  sign  was  found 
above  to  be  26°  9'  23".  Its  equivalent  in  right  ascension  ( lankodayd - 
savas ) is  found  by  the  following  proportion  (iii.,49)' : 

3u°  : 3a3v : : a(i°  9'  a3"  : a85* 

Now,  from  the 

Sun's  hour-angle,  6n  ?9t,  or 
deduct  the  result  of  the  last  proportion, 

remains 

and  tliis  remainder,  being  less  than. the  equivalent  of  a sign,  is  reduced 
to  its  value  as  longitude  by  the  proportion  (iii.  48) 

3a3v : 3o°  : : iivfv  : 90  3'  jp" 

Tlie 'longitude  of  the  meridian  ecliptic-point  is  accordingly  3*  9°  3' 57" : 
its  sine  is  3393'.  • 

In  criticism  of  tlic  process  as  thus  conducted,  we  would  only  remark 
that  the  quarter  of  the  sun’s  day  should  have  been  called  15"  2\  4n  (sec 
above,  V1IL  4),  and  that  to  take  323v  as  the  equivalent  in  right  ascen- 
sion of  the  third  and  fourth  signs  is  inaccurate,  the  value  given  it  by 
our  treatise  being  1935P,  or 

4.  To  find  the  meridian-sine  ( madliyojyti — v.  4-5).  * 

First,  the  dccliuation  of  the  meridian  ecliptic-point  is  determined  by 
the  proportion  (ii.  28) 

3438' : 1397' : : 3393' : i078'=  sin  a3°  3y'  37" 

Its  value  being  north,  it  is  deducted  from  the  latitude  of  the  place  for 
which  the  calculation  is  made,  since  this,  though  by  us  reckoned  as 
north,  is  to  the  Hindu  apprehension  (iii.  14)  always  Boutl^  being  meas- 
ured south  from  the  zenith  to  tin;  equator.  That  is  to  say, 

From  the  given  latitude,  4*°  4a'  5 1 " 

deduct  decl.  of  mcrid.  ecliptic-point,  a 3°  39'  37" 

Meridian  zenith-distance  (natdnpda),  I90  3'  i4" 

The  sine  of  this  arc,  which  1117',  is  the  meridian-sine. 

Here  is  another  blunder  of  the  calculator : the  sine  of  19°  3'  14"  is 
actually  1122'. 

5.  To  find  the  sine  of  ecliptic  zenith-distance  ( drickshepa ),  and  the 
sine  of  ecliptic-altitude  (drggati). 

First*  by  v.  5,  • 


389* 

a«5v 

-f  — 

iu4v 


3438' : 3oi' : : 1117' : 97'  48" 


M Qakuhlwn  of  a Solar  Eclipse.  315 

Now,  then,  by  v.  6, 

^Square  of  last  result,  9,564' 

deduct  from  square  of  mcr.-sine,  1,247,689' 

remains  - * 1,238,125' 

Square-root,  m3' 


Tliis,  then,  is  the  sine  of  ecliptic  zenith-distance.  The  sine  of  eclip- 
tic-altitude is  found  by  subtracting  its  square  from  that  of  radius,  and 
taking  the  square-root  of  the  remainder ; it  is  found  to  be  3253'. 

6.  To  find  the  divisor  ( chcda ),  and  tlve  sun’s  parallax  in  longitude 
(1 lambana ). 

The  sine  of  one  sign,  or  30°,  is  1719'. 


■ Square  of  sin  30°, 
divide  by 

Divisor  (cheda\ 


2,954.961 

3.253 

908 


Next,#to  find  the  interval  011  the  ecliptic  between  tlic  sun’s  place  and 
the  meridian : 

• . 

Longitiido  of  meridian  ccliptic-point,  3«  90  V 67" 

do.  of  sun,  a«  3°  5o'  3?" 

Interval  in  longitude,  1"  5°  i3'  20"  • 


■Of  this  the  sine  is  1950',  and,  upon  dividing  it  by  908,  the  divisor 
(chcda)  al5)ve  found,  the  value  of  the  parallax  in  longitude  (lambana)  ia 
ascertained  to  be  ‘i11  2 l\ 

Here  #somc  of  tlic  worst,  blundering  which  we  have  yet  met  with. 
The  sine  of  35°  13'  is  actually  198*2',  not  1950';  and  upon  dividing  it 
by  008,  wc  find  the  quotient  to  be  only  2n  llv.  * 

The  calculator  assumes  the  time  of  apparent  conjunction  to  be  deter- 
mined by  this  single  correction.  As4,hc  text,  however  (v.  9),  directs 
that  the  process  be  repeated,  to  insure  a higher  degree  of  accuracy,  we 
shall  finally  quit  at  this  point  the  guidance  of  liis  computations,  and  go 
on  to  apply  in  full  the  rules  of  the  SGrya-Siddhanta. 

The  sun  being  west  of  the  meridian,  or  his  longitude  being  less  than 
that,  of  tlic  meridian  ccliptie-point  (v.  9),  the  correction  for  parallax  is- 

additive  to  the  time  of  true  conjunction,  lienee,  to  the*  - 

■ 

Time  of  true  conjunction,  a5»  2 v 

add  the  correction, , an  it» 

1 Time  of  conjunction  once  equated,  27"  i3v 

For  tlic  time  thus  found,  we  now  proceed  to  calculate  again  the  value 
of  the  parallax.  The  results  of  the  calculation  are  briefly  presented 


below : • 

Sun's  longitude  at  corrected  time  of  conjunction,  a*  3°  5a'  4i" 

Orient  ecliptic-point  ( lagna ),  6*  180  5o'“ 

Its  sine,  1110' 

*Orient-sino  (udayajyd),  6i4' 

Sun's  hour-angle,  3io3p 


Meridian  ecliptic-point  (madhyalagna)t 
Its  sine, 

Its  declination, 

Its  cenith-diBtancc, 

Me  rid  inn -sine  (madJiyajyd), 

Sine  of  ecliptic  zenith-distance  (drkkthepa), 
Sine  of  ecliptic-altitude  (drggati), 

Divisor  (i ekeda ), 

Sine  of  sun's  (list,  in  long,  from  meridian, 
Parallax  in  longitude  (lambana), 
add  to  time  of  true  conjunction, 

^Time  of  conjunction  twice  equated, 


3a  5/ 

3 1 88'  • 
aa°  9'  N. 
ao°  34'  S. 

iao7# 
1188' 
3aa6' 
916' 
a 558' 

2"  48* 
a5“  av 


37n  5ov 


Once  more,  we  repeat  the  same  calculation ; its  principal  results  are 
as  follows : 


•Orient  ccliptic-point, 

6*  210  4i' 

Orient-sine, 

Meridian  ccliptic-point, 

3»  a5°  26' 

Meridian-sine, 

• 1241' 

Sine  of  ecliptic  zenith-distance, 

12l5' 

Sine  of  ediptic-altitude, 

3a  16' 

Divisor, 

9*9' 

Parallax  in  longitude, 

2n  55» 

add  to  time  of  true  conjunction, 

25ft  2* 

Time  of  apparent  conjunction, 

27“  57r 

A farther  repetition  of  the  process  would  still  yield  an  appreciable 
correction,  but  as  so  many  errors  have  been  involved  in  the  preceding 
parts  of  the  calculation  as  to  render  any  exactness  of  result  unattaina- 
ble, and  as  enough  has  been  done  to  illustrate  the  method  of  correction 
by  successive  approximation  auJtlic  comparative  value  of  the  results  it 
yields,  we  stop  here,  and  rest  content  with  the  last  time  obtained,  as  that 
of  the  apparent  conjunction  of  the  sun  and  moon,  or  of  the  middle  of 
the  eclipse,  at  Williams’  College. 

XII.  To  calculate  the  parallax  in  latitude  (nati)  for  the  middle  of  the 
eclipse. 

This  is  given  11s  by  the  proportion  (v.  10) 

3438' : 73i'  a ■>"-=-  i5  : : iai5' : 17'  14"  S. 

in  which  1215'  is  the  &ine  of  ecliptic  zenith-distance,  as  found  in  the  last 
process.  * 

XIII.  To  calculate  the  moon’s  latitude,  and  her  apparent  latitude, 

for  the  middle  of  the  eclipse.  - * 

We  require  first  to  fiqd  the  longitude  of  the  moon,  and  that,  of  her 
node,  for  the  moment  of  apparent  conjunction,  by  adding  to  their  lon- 

£’tudcsvas  already  found  (above,  IX)  for  the  time  of  true  conjunction, 
eir  motion  during  2n  55v.  The  amount  of  motion  is  found  by  the  pro- 
portions 

eon:3.55v::j7>0'59":35'3" 


V.] 


317 


Calculation  of  a Solar  Eclipse. 


Now,  then,  to  the 


‘Moon's  longitude  at  true  conjunction, 

it  i3°V  i» 

add  the  correction, 

35'  3". 

Moon's  longitude  at  apparent  conjunction , 

i-i4°  6'  4" 

Farther,  from  the 

Node's  longitude  at  true  conjunction,' 

i»  is0  47'  45" 

deduct  the  correction, 

, 9" 

Node's  longitude  at  apparent  conjunction, 

H 12°  47'  46" 

deduct  from  moon's  longitude, 

isi4°*6'  4" 

Moon's  distance  from  node, 

i°  18' 

Sine, 

78' 

■ 

Hence  the  proportion  (ii.  57) 

343S' : 27o' : : 78' : 6'  8" 

gives  us  tho 

Moon's  true  latitude, 

fi1  8"  N. 

dedret  from  parallax  in  latitude  (v.  12), 

17'  id"  S. 

Moon’s  apparent  latitude, 

11'  6"  S. 

XIV.  To  find  the  amount  of  obscuration  (ffrasa)  at  the  moment 

apparent  conjunction. 

By  iv.  10,  we  add  to  the 

Diameter  of  the  eclipsing  body,  the  moon, 

■19-  2" 

Diameter  of  the  eclipsed  body,  the  sun, 

3('  10" 

Sum  of  diameters, 

60'  i 2" 

Half-sum  of  diameters, 

3o'  6" 

deduct  moon’s  apparent  latitude, 

11'  6" 

Amount  of  greatest  obscuration, 

19'  0" 

This  remainder  being  less  than  the  sun's  diameter,  the  eclipse  (iv.  11)  is 
partial  only. 

XV.  * To  determine  the  times  of  the  beginning  and  caul  of  the  eclipse 
respectively. 

As  the  eclipse  is  a partial  one  only,  we  have  not  to  calculate  the  times 
of  the  beginning  and  end  of  total  obscuration  ; and  indeed,  we  may  well 
suppose  that  the  Hindus  would  never  venture  to  calculate  those' times 
in  a solar  eclipse  : it  is  even  questionable  wlu-thef  the  accuracy  of  their, 
methods  would  justify  them  in  ever  predicting  with  confidence  that  an 
eclipse  would  be  total. 

In  the  first  place,  we  assume  that  the  moon's  apparent  latitude,  as  cal- 
culated for  the  moment  of  conjunction,  remains  unchanged  during  the 
whole  duration  of  the  eclipse,  and  calculate,  by  iv.  12-13,  what  would 
be,  upon  that  assumption,  the  interval  between  the  middle  of  the  eclipse 
and  either  contactor  separation  of  the  disks.  That  is  to  say  (iv.  12), 
from  the 


41 


318 


Stlrya-Siddh&nta i, 


l*- 


Square  of  sum  of  Romi -diameters  (30'  6"),  906'  1" 

deduct  square  of  moon's  latitude  (1 V - fi"),  1 a3'  1 3" 

remains  782'  48" 

Square  root  of  remainder,  27'  59" 


This  result  represents  the  distance,  ns  rudely  determined,  of  the  fwo 
centres  nt  the  moments  of  contact  and  separation.  To  ascertain  the 
corresponding  interval  of  time,  wc  say  (iv.  13) 

GG4'  7" : '■ : 27'  .r>9"  : an  3a* 


Now,  then,  from  and  to  the 

Time  of  apparent  conjunction,*"  2711  57* 

% subtract  and  add  the  half  duration,  an  -3^ 

Beginning  of  ccjipsu,  2r>n  2:> 

End  of  eclipse,  3c>n  79V 


This  is  as  far  as  the  operation  was  carried  hy  the  native  calculator, 
and  with  data  and  results  somewhat  different  from  those  here  given, 
owing  to  his  neglect,  to  repeat  the  process  of  determination  of  the  par- 
allax in  longitude  in  finding  the  time  of  apparent  conjunction.  Un- 
fortunately, however,  tfie.  te\t  (iv.  14-15;  v.  13-17)  proscribes  a long 
and  tedious  scries  of  modifications  and  corrections  of  the  results  so  far 
obtained,  of  whieh  wc  shall  proceed  to  perform  .at.  least  enough  to  illus- 
trate the  method  of  the  process,  and  the  comparative  importance  of  the 
corrections  which  it  furnishes. 

We  have  first  to  find  the  longitude  of  the  sun,  moon,  and  node,  at 
the  moments  thus  determined  as  those  of  contact  and  separation;  they 
arc  as  follows: 


1®  i3°  3i'  1" 
aa" 


Sun's  long,  at  true  conj.  (25»  2v), 
add  for  his  motion 

Sun's  long,  at  beg.  and  end  of  eclipse, 
add  the  precession, 

Sun’s  distance  from  the  vernal  equinox,  2®  3°  5o;  59" 

Moon's  long,  at  app.  con j.  ia  z4°  0'  4" 

subtract  and  mid  motion  in  2»  32vf  3o'  26" 


1®  i3°  3r'  *3" 
3«°  19'  3G" 


1*  i3°  3i'  1" 
5'  10" 

1®  1 3°  36'  11" 
20°  19'  30" 

2®  3 3 55'  47" 
i®  i4°  O'  4" 
3o'  26" 


Moon's  long,  at  beg.  and  end  of  eclipse,  1®  i3°  35'  38" 


Node's  long,  at  app.  conj., 
add  and  subtract 


is  120  47'  4G" 
8" 


is  140  30'  3o" 

is  120  47'  40" 
8" 


Node's  long,  at  beg.  and  end  of  eclipse,  i®  120  47'  54't  i«  120  47'  38” 

• • 

To  find,  then,  the  moon’s  true  latitude  at  contact  and  separation,  we 
have 


Mooe'b  distance  from  node, 
Sine, 

Moon’s  latitude, 


47'  44"  i°  48'  52" 
48'  109' 

3'40"N.  8'  34"  N. 


Next  are  calculated  the  moon’s  parallax  in  latitude,  and  her  apparent 
latitude,  at  the  beginning  and  end  of  the  eclipse,  by  a process  of  which 
the  main  results  are  the  following  : 


Calculation  of  a 

Solar  Eclipse . 

819 

Orient  ecliptic* point, 

6«  io°  28' 

7-3°  59' 

Sine, 

6a5' 

1921' 

Orient-pine, 

345' 

io63' 

Sun's  hour-angle, 

a455p 

4279P 

Meridian  ecliptic-point, 

3«  i i°  54' 

4>  ii°  7' 

Sine  or  do., 

3363' 

2590' 

Zenith-distance  of  do., 

19°  16' 

a4°  53' 

Meridian-sine, ' 

11 34' 

i445' 

Sine  of  ecliptic  zenith-distance, 

iiafi' 

i374' 

Parallax  in  latitude, 

16'  o"S. 

19'  29,f  S. 

deduct  true  latitude, 

3'  46"  3T. 

8'  34"  N. 

Moon's  apparent  lat.  at  beg.  and  end  of  rolipse,  i a'  i4"  S. 

lo'gjl"  S. 

'inally,  from  the 

Square  of  sum  of  numi-diamctcra. 

906'  1" 

906'  1" 

deduct  squares  of  app.  latitude, 

1O0'  39" 

119'  11"  * 

' rdtnain 

755'  22" 

786'  5o" 

Distance  of  centres  in  longitude, 

27 7 29" 

28'  3" 

Corresponding  interval, 

an  39* 

2"  3av 

Corrected  times  of  beginning  and  end  of  eclipse,  a5n  afiv 

3on  39V 

It  is  evidently  unnecessary  to  carry  any  farther  this  part  of  the  pro- 
cess ; at  the  time  of  the  eclipse,  the  increase  of  the  moon’s  latitude  north- 
ward, and  the  increase  of  her  parallax  southward,  so  nearly  balance  one 
another,  that  the  additional  correct  ion  yielded  liy  a new  computation 
would  be  quite  inappreciable — as  indeed,  has  been,  in  ouc  of  the  two 
eases  that  already  obtained.  In  malting  this  corrective  calculation  we 
have  not  followed  with  exactness  the  directions  given  in  the  commentary 
under  v.  14-17.  It*  is  there  taught  that,  after  making  the  first  rough 
determination  of  the  half-duration,  based  upon  the  moon’s  apparent  lati- 
tude at.  apparent  conjunction,  we  must  turn  back  to  the  true  conjunction, 
find  the  posilious  of  the  planets  and  node  at  intervals  of  the  liailf-dura- 
tioii  from  that  point,  and  make  these  positions  the  data  of  our  farther 
approximative  processes.  The  text  itself,  as  already  remarked  by  ns 
in  the  notes,  shows  an  utler  and  provoking  want  of  explicitness  with 
regard  to  the  whole  matter,  and  may  bo  regarded  as  fawning  equally 
tlie  method  of  the  commentary,  our  own,  or  any  other  that  might  be 
devised.  We  have  taken  our  own  course,  then,  because  we  were 
unable  to  see  any  sutlicicut  reason  for  reverting  from  apparent  to  true 
conjunction,  as  directed  by  the  commentator. 

With  regard  to  the  next  stops,  the  language  of  the  text  is  less  ambigu- 
ous: it  distinctly  orders  us  to  deduct  from  am  add  to  tlic  time  of  true 
conjunction  ( tiihyanta ) the  intervals  found  as  the  former  and  latter  half- 
duration,  and  from  the  moments  thus  determined  to  compute  anew,  by 
a repeated  process,  the.  parallax  in  longitude.  This  is  a very  laborious 
operation,  and  not  altogether  accurate,  although  perhaps  as  much  so 
as  any  which  the  Hindu  methods  admit.  As  we  are  supposed  to  have 
already  ascertained  how  far  apart  tlic  two  centres  must  l>c  at  the  mo- 
ments of  contact  and  separation,  the  problem  is,  evidently,  to  determine 


320  SGtrya-Siddh&nia, 

■ 

at  what  moment  of  time  they  will,  allowing  for  tlie  parallax  in  longi- 
tude, he  at  that  distance  from  one.  another.  Now  as  formerly,  to  find  the 
time  of  apparent,  conjunction,  we  started  from  that  of  true  conjunction, 
and 'arrived  at  the  desired  result,  by  a series  of  approximative  calcula- 
tions of  the  parallax  in  longitude,  so  now,  starting  from  points  removed 
from  true  conjunction  by  the  given  intervals,  wo  shall  ascertain,  by  a 
similar  series  of  approximations,  the  limes  when  the?  distances  repre- 
sented bv  those  intervals  will  be  apparent,  or  the  moments  to  wbicli 
contact  and  separation  0MI10  disks  will  be.  deferred  by  parallax  in  lon- 
gitude. The  results  of  the  calculations,  as  made  by  us,  arc  as  follows : 


Time  of  true  con  junction,  £ 

a5»  av 

a5n  ajf' ' 

Subtract  and  add, 

an  vqv 

a»  3av 

Times  of  true  contact  and  Reparation, 

a an  33  v 

2711  34v 

bun's  longitude,  with  precession, 

2s3°48'iG"  2.  3°  53'  i" 

‘Orient  eel  ip  tic-point, 

5*  270  9' 

G * ao°  27' 

Orient-sine, 

95' 

6fi4' 

Meridian  ecliptic-point, 

as  a5°  fia' 

3*  56' 

Meridian-sine, 

1107' 

1 226' 

bine  of  ecliptic  zcnilh-di.staiicc. 

11  ofi' 

1 21*3' 

bine  of  ccliptic-altiLudi-, 

3a55' 

3a  11/ 

Divisor, 

1/.8 

918 

Moon’s  longitude, 

a«  3^  ui ' 

as  4®  21/ 

Distance  from  meridian  ccliptic-puint. 

aa°  3j' 

Is  iy°  3r»' 

Sine, 

l3i(i' 

2617' 

Parallax  in  longitude, 

1 « ‘JnV 

an  5iv 

Again,  we  go  on  to  correct  these  results  bv  repealed 

calculations  oi 

the  parallax,  in  the -inode  which  lias  already  been  sulliciently  illustrated, 
Annexed  arc  the  results  only  : 

Times  of  contact  and  separation, 

22ii“33v 

27«  34v 

ad£  correction  for  parallax, 

1 n 3-7V 

a«  5iv 

Times  of  contact  and  separation,  once 

equated,  a4,».  a a 

3on  2f)V 

Correspond! ng  parallax, 

I a 54v 

3«  aov 

add  to  times  first  obtained, 

aa»  33 v 

2711  34  v 

Times  of  contact  and  separation,  twice  equated,  a.pi  37V 

3o"  r)4v 

Corresponding  parallax, 

an  av 

3»  a4v 

Without  taking  the  trouble  to  carry  the  calculations  any  farther,  we 
may  accept  Ihoc  as  the  finally  determined  values  of  the  parallax  in 
lungiludc  at  the  times  of  apparent  contact  and  separation.  Tm-n, 
by  v.  10, 


Parallax  in  longitude  at  contact  and  separation, 

an 

2V 

3» 

24v 

do.  at  apparent  conjunction, 

211 

55v  ■ 

an 

55v 

Difference  of  parallaxes, 

53  v 

29V 

add  to  former  and  latter  mean  half-duration, 

an 

29V 

2n 

32V 

True  former  and  latter  half-duration, 

3n 

22V 

IV 

subtract  and  odd  from  and  to  time  ofyipp.  conj., 

27n 

5?v 

27n 

5?v 

Times  of  apparent  contact  and  separation, 

»4n 

35v 

3on 

58v 

321 


v-1 


Calculation  of  a Solar  Eclipse . 


The  calculation  of  the  elements  of  the  eclipse  is  thus  completed. 
For  the  purpose,  however,  of  illustrating  the  rules  of  the  tc^  (iv.  18-21) 
for  determining,  in  the  case  of  a solar  eclipse,  the  amount  of  obscura- 
tion at  any  given  moment  during  the  continuance  of  the  eclipse,  we  add 
also  the  following  process : 

XVI.  To  find  the  amount  of  obscuration  of  the  sun,  2n  38T  after 
first  contact. 

We  make  choice,  of  this  time,  which  is  equivalent  to  27“  13v  after  sun- 
rise, because  the  data  for  finding  the  parallax  in  latitude  at  the  zAoment 
have  already  been  calculated  (see  above,  XI).  By  iv.  18,  from  the 

True  former  half-duration  {sphuta  tpa&atthityardha ),  3n  aav 

deduct  the  given  interval*  Sfr  38v 


Interval  to  apparent  conjunction  (i madhyagrahana ),  44r  ' 

To  reduce  this  interval  in  time  to  distance  in  longitude  of  the  centres* 
we  say  (iv.  18) 

Gun  : 064'  7 " : : 44* : 8'  7" 

ThiS,  then,  would  be  the  interval  in  longitude  between  the  two  centres 
at  the  given  moment,  if  there  were  no  change  of  the  moon’s  parallax 
in  longitude  during  the  eclipse,  or  if  the  moon  actually  gained  in 
2n  29v,  instead  of  in  3n  22v,  the  distance  intervening  between  her  centre 
and  the  sun’s  at  the  moment  of  first  contact.  That,  however,  being 
not  the  case,  wc  must  reduce  the  result  thus  found  in  the  ratio  of 
3n  22v  to  2n  2DV,  or  of  the  true  to  the  mean  half-duration.  That  is  to 
say  (iv.  19), 

311  aav ; an  39V  ; : 8'  7"  : 5'  69" 

aiul  this  result,  5*  59",  is  the  true  distance  of  the  two  centres  in  longi- 
tude, 27n  13v  after  sunrise. 

A briefer  and  more  obvious  method  of  obtaining  the  quantity  in 
question  would  have  been  to  make  a proportion  as  follows : if,  at  the 
time  of  the  eclipse,  the  moon  gains  upon  the  sun  *27'  29"  in  311  2‘2V, 
what  will  she  gain  during  44v  I or 

3n  aav  ; :,7'  39"  ::44v  : 5'  59" 

Upon  computation,  we  find  the 


Hoon’a  parallax  in  latitude,  27  n 13v  after  sunrise, 

16' 

5i"  S. 

Moon’s  true  latitude, 

5' 

25"  N. 

Mooii’b  apparent  latitude, 

77'" 

26" 

Its  square, 

i3o' 

43" 

Square  of  distance  in  longitude  (5'  59"), 

35' 

59" 

Their  sum  (iv.  20), 

166' 

14" 

Actual  distance  of  centres, 

12' 

54" 

deduct  from  sum  of  semi-diameters, 

3o' 

6" 

Amount  of  obscuration  at  given  time, 

• *7' 

12" 

If  it  were  desired  to  project  the  eclipse,  we  should  now  liavc  to  cal- 
culate (by  iv.  24-25)  the  deflection  ( yalana ) for  the  moments  of  contact, 
.conjunction,  and  separation,  and  likewise  (by  iv.  20)  the  scale  of  projec- 
tion. As  wc  do  not,  however,  intend  to  present  here  a projection,  and  as 


322 


[v- 


Surya-SidJlt&nla , 

the  subject  of  the  deflection  has  been  sufficiently  illustrated  already,  in 
the  notes  unoii  tlie  text  and  in  the  calculation  of  the  lunar  eclipse,  we  re- 
gard it  as  unnecessary  to  go  through  with  the  labor  required  for  making 
the  computations  in  question.  Finally,  we  annex,  as  in  the  ease  of  tho 
lunar  eclipse  formerly  calculated,  a summary  comparison  of  the  princi- 
pal results  of  the  Hindu  processes  with  the  elements  of  the  eclipse  in 
question  as  determined  by  Prut  Coffin,  in  his  work  referred  to  above, 
it  must  be.  borne  in  uiiud,  however,  that,  owing  to  the  faulty  manner  in 
which  -many  of  the  computations  of  the  native  astronomer  have  been 
made,  the  comparison  is  not  entirely  trustworthy ; a more  careful  adhe- 
rence to  the  methods  of.  the  ttiddh&utu  would  have  given  somewhat 
different  results:  in  the  ease  of  the  daily  nations  of  the  sun  and  moon, 
the  trilb  calculations,  as  performed  by  us  (see  p.  308),  give  more  correct 
values;  in  other  instances,  the  contrary  might  perhaps  have  been  tlie 
1 ease. 


* Surva-SidrihAiita. 

Frof.  Coffin. 

Hindu  error. 

Time  of  true  conjunction  in  longitude, 

ah  3o»» 

3h  56m 

— 

i h 26m 

Sun’s  and  moon's  longitude, 

G3°  5o'  37" 

65°  12'  37" 

- 

1°  ,12' 

Moon's  distance  from  node, 

43'  6" 

4°  1 a'  22" 

— 

3°  29'  ifi" 

Sun’s  daily  motion  in  longitude, 

55'  5a" 

57'  45" 

- 

51" 

Moon’s  do.  do. 

i a°  o'  59" 

ia°  7'  12" 

— 

(V  1 J" 

Sim's  apparent  diameter, 

3i'  10" 

3i'  37" 

- 

27" 

Moon’s  do.  do. 

29'  2" 

29'  45" 

— 

43" 

Time  of  apparent  conjunction, 

3h  4um 

5h  3am 

— 

lh  f»2m 

Parallax  in  longitude,  in  time, 

ill  ium 

ill  3(>m 

— 

a 6 m 

Amount  of  greatest  obscuration, 

19' 

.30*  59" 

— 

1 1'  59" 

Time  of  first  contact. 

aum 

4h  1 5m 

— 

ill  55>n 

Time  of  separation, 

4h  5o»n 

6h  38m 

— 

lb  4H111 

Duration  of  eclipse, 

all  3oni 

ah  a3i» 

+ 

7m 

SIC.  pp.  183-200.  Prof.  Weber,  of  licrlin,  has  favored  us  in  a pri- 
vate communication  with  a number  of  additional  synonyms  of  the  names 
of  the  asterisins,  derived  from  ihe  literature  of  the-  Bralmisma  period. 

Mrga^iras,  the  fifth  of  the  series,  is  also  styl'd  andhukd , “tlie  blind,” 
apparently  from  its  dimness ; uryika,  “honorable,  worthy;”  ijmiXw,  of 
doubtful  meaning:  this  latter  epithet  is  aiso  found  in  some  manuscripts 
of  tho  Amarakoca,  as  various  rending  for  Uvula,  which  Is  there  ex- 
pressly declared  (T.  i.  2. 25)  to  designate  the  stars  in  the  head  of  the 
antelope. 

Ardra,  the  sixth  asterism,  is  called  b&hu , “aim.”  Taking  this  nanu' 
in  connection  with  that  of  the  preceding  group,  it  seems  probable  that 
the  Hindus  ligured  to  themselves  the  conspicuous  constellation  Orion 
as  a running  antelope,  of  which  »,  y,  (t,  and  x mark  the  feet:  «,  then,  is 
the  left  ford- foot,  or  arm.  Perhaps  the  name  AlrgavyiVlha,  “antelope- 
hunter,”  given  to  the  neighboring  Sirius  (viii.  10),  is  connected  with  the 
same  fancy.  * 

The  Magluis  arc  called  in  a hymn  of  tho  last  book  of  the  Rig-Veda 
(x."85. 13 j atfh&s : the  word  means  literally  “evil,  base,  siufiil”  and  its 
application  to  one  of  the  asterisins  is"  so  strange  that,  if  not  found  clsc-# 
where,  we  should  be  inclined  to  conjecture  a corrupted  reading. 


v“i-  9-]  Additional  Notes,  etc.  823 

Phalgunl,  ojthc  IMialgunls,  forming  the  eleventh  and  twelfth  groups, 
sire  styled  also  i trjuni,  “bright,  shining.”  , 

Qravana,  the  twenty-third  astcrism,  receives  the  name  apvnttha , which 
is  properly  that  of  a tree,  tip  Ficus  religiusa ; the  reason  of  the  appella- 
tion is  altogether  obscure. 

Hhfidrapad&,  the  hist  double  astcrisrn,  is  called  pratUhthAna , “stand, 
support,”  in  evident  allusion  to  the  disposition  of  the  four  bright  stare 
which  compose  it,  like  the  four  feet  of  a stand,  table,  bedstead,  or  the  like. 

27.  p.  200.  Wc  offer  herewith  the  stellar  chart  to  which  reference 
was  made  in  the  note  on  p.  205,  and  which  is  intended  to  illustrate  the 
positions  and  mutual  religions  of  the  Hindu  nakshatras , the  Arab 
manuzil  ul-kamar , and  the  Chinese  sicu.  We  add  a brief  explanation 
of  the  manner  in  which  it  has  been  constructed,  and  the  form  in  which 
it  is  presented. 

The  form  of  the  map  is  that  of  a plane  projection,  having  the  ecliptic- 
as  its  central  line.  It  would  have  better  illustrated  the  Hindu  method 
of  defining  the  positions  of  the  junction-stars,  and  the  errors  of  the  po- 
sitioners defined  bv  them,  if  the  cqnator  of  A.  I).  500,  instead  of  the 
ecliptic,  had  been  made  the  central  line  of  the  projection.  This,  how- 
ever,-would  have  involved  the  necessity  of  calculating  the  right  ascen- 
sion and  declination  of  every  star  laid  down,  a labor  which  wru  were  not 
willing  to  undertake.  Moreover,  the  ecliptic  is,  in  fact,  the  proper  cen- 
tral line  along  which  the  groups  of  the  Hindu  and  Arab  systems,  at 
least,  are  arranged,  and  the  form  given  to  the  chart  also  facilitates  the 
laying  down  of  the  equator  of  H.  0.  2«‘150,  which  we  desired  fo  add,  for 
the.  purpose  of  enabling  our  readers  to  judsro  in  a more  enlightened 
manner  of  the  plausibility  of  M.  Iliol’s  views  respecting  the  origin  of 
the  rhinesc  system  : it  is  drawn  tfitli  a broken  line,  while  the  equator 
of  A.  1).  500  is  also  represented,  by  an  entire,  line.  As  the  zone  of  the 
heavens  represented  is,  in  the  main,  that  bordering  the  ecliptic,  the  dis- 
tances and  the  configuration  of  the  stars  arc  altered  and  distorted  by 
the  plane  projection  to  only  a very  slight  degree,  not  enough  to  l>e  of  any 
account  in  a merely  illustrative  chart,  £iir,h  as  this  is.  As  a general  rule, 
we  have  laid  down  all  the  stars  of  the  first  four  magnitudes  which  are 
situated  near  the  ecliptic,  or  in  that  part  .of  the  heavens  through  which 
the.  line  of  the  astcrisms  passes;  stars  of  the  fourth  to  fifth  magnitude 
are  also  in  many  cases- added;  smaller  ones  are  npted  only  when  they 
enter  into  the  groups  of  the  several  systems,  or  when  there  .were  other 
special  reasons  for  introducing  them.  The  positions  are  in  all  cases 
taken  from  Flamsteed's  Catalogue,  and  the  magnitudes  arc  also  for  the 
most,  part  from  the  same  authority : in  many  individual  cases,  however, 
we  have  followed  other  authorities.  \Ve  have  endeavored  so  to  mark 
the  members  of  the  three  different  scries  tl  it  these  may  readily  be 
traced  across  the  map;  but,  to  assure  and  facilitate  the  comparison,  we 
also  place  upon  the  page  opposite  it  a conspectus  of  the  nomenclature, 
constitution,  and  correspondence  of  the  three  systems,  referring  to 
pages  18H-200  for  a fuller  discussion  of  these  matters,  and  an  exposition 
of  what  is  certain,  and  what  more  or  less  hypothetical,  or  exposed  to 
doubt,  with  regard  to  them. 


m 


S&ryaSi<M.Mnta, 


[vi'ri.  9. 


Hindu  uttrinu. 

I.  Agvirii. 

P and  7 Arietta. 

а.  BharanL 

35,  MR,  and  41  Ariciia. 

3.  KrttikA. 

n Tauri,  etc.  (Pleiades). 

4-  RohinL 

u,  3,  7. 0,  e TaurL 

5.  Mrga^ir.iH. 

A,  (pi,  (pa  Orionis. 

б.  Ardr.l 

a Orionta. 

7.  Punarvasu. 

р,  a Guininoriim. 

.8.  Pushy  a. 

3,  5,  7 Cancri. 

9.  Agnail  A.  - 

с.  0,  c1,  n,  g nydrre. 

10.  MagbA 

S *1  7*  Ji  U,  « 1-couis. 

11.  Ptirva-Phalguni. 

O,  3 Lconta. 

1 a.  llttam-Phalguni. 

P,  03  Lconta. 

1 3.  Haata. 

0,  7,  e,  o,  p Coni. 

1 4-  CitrA. 

a Virginta. 

1 5.  Sv&ti. 

a BooLis. 

16.  Viy/ikhA. 

ii  v,  p,  a Libra?. 

17.  AnurftclhA. 

0,  p,  v Scorpionta. 

r 8.  JyeshtM. 

ax  crj  t Scorplunta. 

19.  Mula. 

A,  11,  w,  3,  n,  {,  a,  £ Scorp. 
.20.  Pflrva-AtMdhA. 

0,  c Sngili-'irii. 
ar.  TJttarn-AsluidhA. 

cr,  J Siigtilnrii. 

22.  Ahhijit.  ■ 

a,  £,  i Lyra*. 
a3.  (Jravana. 

a,  p,  7 A([u11.t. 

24-  (j-ravtalitlifi. 

p,  a,  7,  0 Delphi  11  i. 

25.  rtatabhishAj. 

&Aqiiairii  etc. 

26.  FOryu-BliAilrapadA. 

a,  p Pcgas'i. 

27.  Uttara-Bliftdrapadd. 

7 Pcgiisi,  a Andromcdre. 

28.  Bevaii. 

i Finciuin,  eic. 


Arab  mauzc'/. 
x.  ash-Sharat&n. 

P iuiil  7 Arletis. 

2.  al-Butaiu. 

35,  30  and  41  Arietta. 

3.  ath-ThuraiyA 

n Tauri  etc.  (Pleiades). 
4-  ad-Dnbardn. 

a,  m 7,  0,  e Tauri. 

5.  al-Hak'ali. 

A,  <pi,  (pa  Orionis. 

6.  uUInn’ah. 

n,  u,  v,  7,  $ Gcminorum. 

7.  odh-Dliirfi'.  * 

P,  a Ge  minor  um. 

8.  an-Nnthraii. 

7, 0 Ciuu-ri,  awl  Prwscpe. 

9.  al-Tarf. 

*5  Cancri,  a.  Lconta. 

10.  aj-Jabhnh. 

a,  Ti,  7,  J Lconta. 


Chineie  atau. 
27«*Leu. 

p Arietta. 

28.  Oei. 

35  Arictis. 

1.  Mao. 

n TaurL 

2.  Pi. 

e Tniiri. 

3.  Tsc. 

K Orionis. 

4-  Tann. 

0 Orionis. 

5.  Tsing. 

# h Gcinmonun. 

6.  Kuci. 

3 Cancri. 

7.  Lieu. 

0 Hydra1. 

8.  Sing. 

a Hydra:. 


xx.  az-Zubrah. 

0|  3 Lconta. 

12.  aH-Snrfnh. 

P Lconta. 

1 3.  al-Auw;V. 

P,  n,  7,  0,  t Virginta. 
1 4-  as-SiniAk. 

a Virginta. 

1 5.  &1-G1infr. 

i,  *,  K Virgiifls. 

16.  az-Zubftnun. 

a,  p Libra*. 

17.  nl-Tklil. 

p,  5,  ir  Scnrpionis. 


9.  Chang. 

Ui  Hydra1. 

10.  Y. 

a Crnfcrta. 

11.  Cliin. 

7 Cor\  i. 

12.  Kio. 

a Virginia. 

1 3.  Kang. 

n Virginia. 
i4-  Ti. 

«a  Libra*. 

1 5.  Fang. 

v Scorpion  in. 


18.  al-Kalh. 

a Scorpion!*. 

19.  ash-Sliniilnh. 

A,  u Scorpion  ta. 

20.  an-^N  a aim. 

' 7a,  \ 1 1 n,  <T,  0 1 • ■ { Sagittarii. 


>0.  Sin. 

a-  Scorpion  in. 

17.  Uc.i. 

g*  Scorpionin. 

18.  Ki. 

72  Sagittarii. 


21.  nl-Baldab. 

N.  of  ir  Sagittarii. 

22.  SaM  adh-Dhabih. 

a,  p CiijM'icurui. 


19.  Ten. 

<p  Sagittarii. 

20.  Nicu. 

P Capricorn i 


23.  SaM  Biila1. 

i,  a,  v Aquarii. 

24.  SaM  Ajs-Sii’iid. 

p,  % Aquarii. 


21.  Nii. 

e Aquarii. 

22.  Hiii. 

P Aqnarii. 


25.  SaM  al-Akhbiyah. 

a,  7,  f,  ti  Aquarii. 

26.  al-Fargb  al-Mukdim. 

o,  p Pcgasi. 

27.  al-Fargh  al-Mukliir. 

7 Pegani,  a Andromeda;. 

28.  Bate  al-Hut. 

P Andromcdte,  ete. 


23.  Goei. 

a Aquarii. 

24.  Clie. 

a Fcgasi. 

25.  Pi. 

7 Pegasi. 

26.  Koei. 

2 Andromeda.*. 


825 


• viii.  9.]  Additional  Nbtes1  etc . 

28-  p.  20T:  We  have  perhaps  expressed  ourselves  in  a manner  liable 
to  misconstruction  ns4o  the  want  of  reason  or  authority  for  giving  to 
the  asterisms  the  name  of  “ lunar  mansions/’  “ houses  of  the  moon/’  and  4 
the  like.  We  would  by  no  means  be  understood  as  denying  that  in  tlio 
Hindu  science,  especially  its  older  forms,  and  in  the  Hindu  mythology, 
they,  are  brought  into  particular  and  conspicuous  relations  with  the 
.moon.  Indeed,  whether  they  were  originally  selected  and  established  with 
reference  to  the  moon’s  daily  progress  along  the  ecliptic,  as  lias  been, 
until  lately, -the- ■universal  opinion,  or  whether  wc  are  to  believe  with  M. 
Biot  that  they  had  in  the  iirst  instance  nothing  to  do  wiiJi  the  moon, 
aiul  only  came  by  chance  to  coiucide  in  number  with  the  days  of  her 
sidereal  revolution — it  is  at  any  rate  altogether  probable  that  to  the 
Hindu  apprehension  this  coincidence  formed  the  basis  of  the  system. 
We  may  even  conclude,  from  the  fact  that  the  asterisms  are.  so  fre- 
quently spoken  of  in  the  early  literature  of  the.  lhuhinaiia  period* 
while  nevertheless  there  is  no  distinct  mention 'of  the  planets  uiftil  lat»r 
(Weber,  lml.  Lit.,  p.  222),  that  fur  a long  time  the  Hindus  must  have 
confuted  1 heir  attention  :unl  observations  to  the  sun  and  moon,  paying 
no  heed  1o  the  lessor  planets:  and  yet  we  cannot  regard  it  as  in  any 
degree  probable — hardly  as  possible,  even — that  any  nation  or  people 
could  e-lablisli  a system  of  zodiacal  astcr'i'mis  without  discovering  and 
taking  note  of  Jthe.  planets;  or  that  such  a system  could  have  been  cem- 
lnunieated  to,  and  applied  by,  the  Hindus  without  a recognition  eu 
their  part  of  those  ruutpicuous  and  evcr-moiing  stars.  It  may  fairly  1 c 
clyiniejJ.^JuMi,  that  the  a?»t.eri<ms,  as  a Hindu  institution,  arc  an  origin- 
ally mtiar  division  of  tin-  zodiac;  hm  wc  ohicM.  none  the  lc**  to  their 
being  styled  " lunar  mansions,"  or.  culled  by  any  equivalent-  name;  bc- 
cam-e,  in  the  iirst,  place,  the  Hindus  themselves  have,  given  them  no  liamo 
denoting  a special  relation  to  the  moon,  and  no  name  signifying  “house, 
mansion,  station,’  or  anything  of  the  kind;  and  because,  in  the  second 
place,  as  slum  and  as  far  as  the  I limlu- .astronomy  extended  itself  beyond 
its  limitation  to  observations  of  the  moon,  jusi  so  far  and  so  soon  did 
il  employ  the  system  of  asterisms  as  a general  method  of  division  of 
the  ecliptic;  so  that  finally,  as  pointed  out  by  us  above,  the  i&fcritu:* 
have  come,  to  be  divested,  in  the.  properly  astronomical  literature  of 
India,  of  all  special  connection  with  the  moon.  With  almost  the  same 
propriety  might  we  call  the  Hindu  signs  11  limi-solar  mansions" — since 
they  arc,  by  origin,  the  parts  of  the  ecliptic  occupied  by  llie  sun  during 
caoLsuvecssive  synodical  revolution  of  flic  moon— as  denominate  the 
of  the  Siddh&iitas  tm  lunar  mansions.” 

29.  p.  209.  We  should  have  mentioned  farther,  that  an  addition# 
inducement— anfl  one,  probably,  of  no  small  w light — to  the  reduction  of 
Ihc  number  of  asterisms  from  twenty-eight  .o  twenty-seven;  is  to  bo 
i ccognizcd  in  the  fact  that  the  time  of  the  mom’s  sidereal  revolution  in 
days,  though  intermediate  between  the  two  numbers,  is  yet  decidedly 
nearer  to  twenty-s^eu,  exceeding  it  by  less  than  a third.  M.  Biot 
might  even  claim  with  some  reason  that  the  choice  of  the  number 
twenty-eight  tended  to  prove  the  whole  system  not  a lunar  one  by 
origin:  yet  it  might  be  replied  that,  the  time  of  revolution  being  dis- 
tinctly more  than  twenty-seven  days,  the  larger  number  was  fully  adm>- 
43 


326 


Sfirya-Siddh&nta, 

Bible,  and  that  it  was  also  in  some  respects  preferable,  as  being  one  that 
could  be  halved  and  quartered.  # 

30.  p.  273.  In  bringing  this  work  to  a close,  we  deem  it  advisable 
to  present,  in  a summary  manner,  but  more  distinctly  and  connectedly 
than  could  properly  be  done  in  the  notes  upon  the  text,  our  conclusions 
as  to  certain  pointB  in  the  history  of  the  Stirya-Siddlifimta,  and  of  the 
astronomical  science  which  it  represents.  * 

In  the  first  place,  Bentley’s  determination  of  the  age  of  the  treatise 
we  conceive  to  be  altogether  set  aside  by  the  considerations  which  we 
have  adduced  against  it  (note  to  i.  29-34) ; there  is  no  reasonable 
ground  for  questioning  thattho  Sftrya-Siddh&nta  is,  as  the  Hindus  have 
long  believed  it  to  be,  one  of  the  most  ancient  and  original  of  the  woiiks 
which  present  tlicir  modem  astronomical  science.  Ilow  far  the  text  of 
which  the  translation  has  been  given  above  is  identical  in  substance  and 
extent  with  that  of  the  original  Sftrya-Siddh&nta,  is  another  question, 
and  out  not  easy  to  solve.  Tluil  it  is  not  precisely  the  same  is  evident 
enough.  Even  the  modern  manuscripts  differ  from  one  another  in  sin- 
gle readings,*  in  details  of  arrangement,  in  added  or  omitted  verses.  A 
comparison  of  the  texts  adopted  and  established  by  the  different  com- 
mentators would  be  highly  interesting,  as  carrying  the  history  of  the 
trcatiac  a step  farther  back : but  to  us  only  one.  commentary  is  accessi- 
ble, nor  do  we  find  agywlierc  .any  notices  respecting  the  versions  given 
by  the  -others:  in  the  absence  of  such,  wc  may  conclude  that  all  pre- 
sent substantially  the  same  text,  and  so  are  alike  posterior  to  the  model- 
ling of  the  work  into  its  present  form  and  with  its  presem.  ' ontents. 
But  the  indications  of  addition  and  interpolation,  which  wc  have  nad  in 
60  many  cases  to  point  ont  in  our  notes,  are  sometimes  too  telling  to  be 
misinterpreted.  Farther  than  this  we  may  not  at  present  go : any  de- 
tailed discussion  of  the  subject  must  remain  unsatisfactory,  until  a fuller 
acquaintance  with  other  of  the  ancient  treatises,  and  a more  careful 
comparison  of  them  with  ouc  another,  shall  throw  upon  it  new  light. 
A point  of  special  interest  connected  with  it  is,  whether  the  elements  of 
mean  motions  of  the  planets  do  actually  date  from  about  the  time 
pointed  out  by  Bentley’s  calculations.  With  regard  to  this  we  arc  far 
Jroin  being  confident;  but  we  do  not  regard  it  as  impossible,  or  even  as 
very  improbable,  that  those  elements,  as  presented  by  our  text,  have 
been  Che  same  from  the  beginning,  never  having  undergone  correction 
until  the  application  of  the  bija , about  A.  D.  1500  (p.  19  etc.).  And 
the  date  of  that  correction  is  calculated  at  least  to  suggest  the  susp:  ion 
that  Muslim  science  may  have  had  something  to  do  with  That 
observation,  and  the  improvement  of  their  system  by  deductions  from 
* observation,  were  ever  matters  of  such  serious  earnest  with  the  Hindus 
that  they  pliould  have  been  led  to  make  such  amendments  independ- 
ently, is  yet  to  be  proved.  The  most  important  alteration  of  which 
anything  like  direct  proof  is  furnished  is  that  which  concerns  the  pre- 
cession of  the  equinoxes  (note  to  iii.  9-12) ; and  even  here  we  would 
not  undertake  toa  eay  confidently  what  is  the  conclusion  to  be  drawn. 
AH  such  inquiries  must  remain  conjectural,  •mere  gropings  in  the  twi- 
light, until  die  position  of  the  Sftrya-Siddhftnta  in  the  Siddh&nta  litera- 
ture sJiali  be  better  understood.  "What  has"  given  it  so  much  greater 


827 


Additional  Notes , etc. 

prominence  and  popularity  than  are  enjoyed  by  the  other  works  of  its 
class,  or  from  what  period  its  preeminence  dates,  is  Unknown.  There 
arc  treatises,  like  the  £fikalya-Sankit&  (add.  note  1),  which  agree  with 
it  in  all  essential  features;  there  arc  yet  others,-  like  the  Soma  and  Va- 
sishtha  Siddhanlas,  which1  arc  said  (add.  note  6)  to  vary  little  from  it: 
whether  any  one  among  them  all  is  original — and  if  any,  which— 
whe^cr  in  each  case  the  relation  is  one  of  co-ordination  or  of  subordi- 
nation— we  must  be  content  for  the  time  to  be  ignorant. 

One  thing,  however,  is  certain : underneath  whatever  variety  may 
characterize  the  separate  treatises,  there  exists  a fundamental  unity; 
tlieir  differences  arc  of  secondary  importance  as  compared  with  their 
resemblances ; they  all  represent  essentially  a single  system.  . And  this 
by' no  means  in  the  same  sense,  in  which  all  modern  astronomical  works 
may  be  said  to  represent  a single  system.  For  the  Hindu  system  is  not 
one  of  nature ; it  is  not  even  a peculiar  method  of  viewing  and  inter- 
preting nature,  from  which,  afler  it  had  once  been  devised  by  some  con- 
trolling intellect,  others  had  not  the  force  and  originality  to  deviate:  it 
is  a thoroughly  artificial  structure,  full  of  arbitrary  assumptions,  of  ab- 
surdities even,  which  have  no  foundation  in  nature,  and  could  be  in- 
vented by  one  as  well  as  another.  \Vc  need  only  to  refer,  n&  instances, 
to  the  frame-work  of  monstrous  chronological  periods  (i.  14-23) — to 
the  common  epoch  of  the  commencement  of  the  Iron  Age  (note  to  i.  . 
i 29- 3 1),  with  its  exact  or  nearly  exact  (add.  note  G)  conjunction  ot  all 
the  planets— to.  the  form  of  statement  of  the  mean  motions,  yielding 
mMirriijttVoiijmictions,  at  longer  or  shorter  intervals — to  the  assump- 
tion df  a starting-point  for  the.  planets  from  at  or  near  5 Piscium  (note 
to  i.  27) — to  the  revolutions  of  the  apsides  and  nodes  of  the  planets 
(i.  41— 1 4) — to  the.  double  system  of  epicycles  (ii.  34-38) — to  the  deter- 
mination of  the  planetary  orbits  (xii.  80-90),  etc.,  etc.  These  arc  plain 
indications  that  the  Hindu  science  emanated  from  one  centre ; that  it 
was  the  elaboration  of  a period  and  of  a school,  if  not  of  a single  mas- 
ter, who  had  power  enough  to  impose  his  idiosyncracy  upon  the  science 
of  a whole  nation.  The  question,  then,  of  the  comparative  antiquity 
of  single  treatises  is  lost  in  the  higher  interest  of  the  inquiry — when, 
where,  and  under  what  iriUueiice  originated  the  system  which  they  all- 
agree  in  representing? 

W hat  our  opinions  arc  upon  these  points  will  not 'be  a matter  of 
doubt  with  any  one  who  may  have  carefully  looked  through  the  preced- 
ing sdthougli  they  have  nowhere  been  explicitly  stated.  We  re- 

gjiriltlSJlindu  science  as  an  offshoot  from  the  Greek,  planned  not  far 
from  th  ecbin  menccra  ent  of  the  Christian  era,  and  attaining  its  fully  dc-%^ 
v eloped  form  in  the  course  of  the  fifth  and  sixtl  centuries.  The  grounds 
of  this  opinion  we  will  proceed  briefly  to  state. 

In  considering  such  a question,'  it  is  fair  to  take  first  into  account,  the 
general  probabilities  of  the  case.  And  there  can  be  no  question  that, 
from  what  we  know  in  other  respects  of  the  character  and  tendencies 
of  ihe  llimlu  iniud,  wo  should  not  at  all  look  to  find  the  Hindus  in  pos- 
session of  an  astronomical  science  containing  so  much  of  truth.  They 
have  been  from  the  beginning  distinguished  by  a remarkable  Inaptitude 
and  disinclination  to  observe^  to  collect  facts,  to  record,  to  make  indue- 


328  S&rya-Sidtihdnta , 

tire  investigations.  The  old  belief  under  the  influence  of  which  Bailly 
could  form  lii.s  strange  theories— the  belief  in  the  immense  antiquity  of 
the  Indian  people,  and  its  immemorial  possession  of  a highly  developed 
civilization— the  belief  that  India  was  the  cradle  of  language,  myth- 
ology, arts,  sciences,  and  religions— has  long  since  keen  proved  an  error. 
It  is  now  well  known  that  Hindu  culture  cannot  pretend  to  a remoter 
origin  than  2000  B.  C.,  and  that,  though  marked  by  striking  and^mi- 
nent  traits  of  intellect  aucl  character,  the  Hindus  have  ever  been  weak, 
in  positive  science;  metaphysics  and  grammar — with,  perhaps,  algebra 
and  arithmetic,  to  them  the  mechanical  part  of  mathematical  science — 
being  the  only  branches  of  knowledge  in  which  they  have  independently 
won  honorable  distinction.  That  astronomy  would  come  to  constitute 
an  exception  to  the  general  rule  in  this  respect,  there  is  no  antecedent 
ground  for  supposing.  The  infrequency  of  references  to  the  st^rs  in 
the  early  Sanskrit  literature,  the  late  date  of  the  earliest  mention  of  the 

Slanets,  prove  that  there  was  no  special  impulse  leading  the  nation  to 
evote  itself  to  studying  the  movements  of  the  heavenly  bodies.  All 
evidence  goes  to  show  that  the  Hindus,  even  after  they  had  derived 
from  abroad  (p.  204)  a systematic  division  of  the  ecliptic,  limited  their 
attention  to  the  two  chief  luminaries,  the  sun  and  moon,  and  contented 
thcmselves'with'  establishing  a method  of  maintaining  the  concordance 
of  the  solar  year  with  the  order  of  the  lunar  months.  If,  then,  at  a later 
period,  wc  find  them  in  possession  of  a full  astronomy  of  the  solar  sys- 
tem, our  first  impulse  is  to  inquire,  whence  did  the^  obtain  it.  ? A 
closer  inspection  docs  not  tend  to  inspire  ns  with  confidence  ns  of 
Hindu  origin.  We  find  it,  to  be  sure,  thoroughly  Hindu  in  its  external 
form,  wearing  many  strange  and  fantastic  features  which  arc  to  be  at 
once  recognized  as  of  native  Indian  growth ; but  wo  find  it  also  to  con- 
tain much  trne  science,  which  could  only  be  derived  from  a profound 
and  long-continued  study  of  nature.  The  whole  system,  in  short,  may 
be  divided  into  two  portions,  whereof  the  one  contains  truth  so  success- 
fully, deduced  that  only  the  Greeks,  among  all  other  ancient  nations,  can 
show  anything  worthy  to  be  compared  with  it;  the  other,  the  frame- 
work in  which  that  truth  is  set,  composed  of  arbitrary  assumptions  and 
absurd  imaginings,  which  betray  a close  connection  with  the  fictitious, 
cosmogonies  and  geographies  of  the  philosophical  and' I ’uranic,  literature 
of  India.  The  question  presses  itsoif,  then,  strongly  upon  us,  whether 
these  two  portions  can  possibly  have  the  same  origin  : whether  the  sci- 
entific habit  of  mind  which  could  lead  to  the  discovery  of  the  oivi  is* 
compatible  with  those  traits  which'  would  permit  its- ad  mixture  wSJi  the 
other.  Bift  most  especially,  could  a system  founded — as  thif/if  origi- 
nal, mnst  have  been — upon  sagacious,  accurate,  and  protracted  observa- 
tion of  the  heavenly  bodies,  so  entirely  ignore,  the  ground-work  upon 
which  it  rested,  and  refuse  and  deny  all  possibility  of  future  improve- 
ment by  like  means,  as  does  this  llindu  system,  in  whose  text-books 
appears  no  record  of  an  observation,  and  no  confessed  deduction  from 
observations;  in  which  the  astronomer  is  remanded  to  his  text-book  as 
the  sole  and  sufficient  source  of  knowledge,  nor  ever  taught  or  coun- 
selled to  study  the  heavens  except  for  the  purpose  of  determining  his 
longitude,  his  latitude,  and  the  local  time ! Barely,  we  have  a right  to 


829 


Additional  Notes , etc. 

say  that  the  system,  in  its  form  as  laid  before  ns,  must  corne  from  an- 
other people  or  another  generation  than  that  'which  laid  its  scientific 
foundation  ■,  that  it  must  be  the  work  of  a race  which  either  had  never  # 
known,  or  had  had  time  to  forget,  the  observing  habits  and  the  induc- 
tive methods  of  those  who  gave  it  origin.  But  the  hypothesis  that  an 
carlicE*gencration  in  India  itself  performed  the  labors  of  which  the  later 
sys^pm-makers  ’ reaped  theVruit,  is  well-nigh  excluded  by  the  absence, 
already  referred  to,  of  all  evidence  in  the  more  ancient  literature  of 
deep  astronomical  investigation:  the  other  alternative,  of  derivation 
from  a foreign  source,  remains,  if  not  the  only  possible,  at  least,  the  only 
probable  one.  We  come,  then,  next  to  consider  the  direct  evidences  of 
a Greek  origin.  ■ 

First  in  importance  among  these  is  the  system  of  epicycles  for  repre- 
senting the  movement,  and  calculating  the  positions,  of  the  planets. 
This,  the  cardinal  feature  in  both  systems,  is  (ii.  114-43)  essentially  alike  B 
and  the  same  in  both.  Now,  notwithstanding  the  taut  that  such  second- 
ary circles  do  in  fact  represent,  to  a certain  degree,  true  quantities  in 
nature,  there  is  yet  too  much  that  is  strange  and  arbitrary  in  them  to 
leave  any  probability  to  the  supposition  that  two  nations  could  have  de- 
vised them  independently.  I hit  there  arc  sufficient  grounds  for  believ- 
ing the  Greeks  to  have  actually  created  their  own  system,  bringing  it 
bv  successive  steps  of  elaboration  to  the  form  in  which  Ptolemy  finally 
presents  it.  In  the  history  of  the  science  among  the  Greeks,  everything 
is  clear  and  open ; they  tell  us  what  they  owed  to  the  Egyptians,  what 
to  the-  ( JJialdoans : we  trace  the  conceptions  which  were  the  germs  of 
• the i ^scheme  of  epicycles,  the  observations  on  which  it  was  based,  the 
inductive  and  deductive  methods  by  which  it  was  worked  out  and  estab- 
lished. In  the  Hindu  astronomy,  oil  the  other  hand,  all  is  groundless 
assumption  and  absurd  pretense : we  find,  as  basis  lor  the  system,  neither 
the  conceptions — fur  these,  are  directly  or  impliedly  denied  or  ignored 
— nor  the  observations — for  not  a mention  of  an  actual  observation  is 
anywhere  to  be.  discovered — nor  the  methods:  the  whole  is  gra\ely  put 
forth  as  a complete,  and  perfect  fabric,  of  divine  origin  and  immemorial 
antiquity.  On  the  agreement  of  the  two  sciences  in  point  of  numerical 
data  we  will  not  lay  any  stress,  since  it  might  well  enough  he  supposed 
that  two  nations,  if  oneo  set  upon  the  same  track  toward  the  discovery 
of  truth,  would  arrive  independently  at  so  near  an  accordance  with  na- 
ture and  with  one  another.  We  jvill  look  for  other  evidences,  of  a less 
ambiguous  character,  to  sustaiu  our  main  argument.  The  division  of 
theS^cle,  into  signs,  degrees,  minutes,  and  seconds,  is  the  same  in  both 
Bystems^and,  being  the  foundation  on  which  all  numerical  measurements 
and  calculations  are  made,  is  an  essential  and  integral  part  of  botu 
Now  the  names  of  the  first  subdivisions,  th  t signs,  are  the  same  in 
Greece  and  in  India  (see  note  to  i.  58) : but  wi.h  the  Greeks  they  belong 
to  certain  fixed  arcs  of  the  ecliptic,  being  derived  from  the  constellations 
occupying  those  arcs ; with  the  Hindus  they  are  applied  to  successive 
arcs  of  30°,  counted  from  any  point  that  may  be  chosen : this  is  an  un- 
ambiguous indication  that  the  latter  liavo  borrowed  them,  and  forgotten 
or  neglected  their  original  significance.  But  farther,  the  ordinary  Hindu 
name  of  that  division  of  tho  circle  which  is  in  most  frequent  use,  the 


830  Sunja-Siddh&nta ? 

minute,  is  no  Sanskrit  word,  but  taken  directly  from  the  Greek,  being 
liptbi  which  is  Again,  the  planets  arc  ordinarily  named  in ‘the 

Siddhhntas  in  the  order  in  which  they  succeed  one  another  as  regents 
of  the  days  of  the  week;  and  not  only  lias  it  beeu  shown  above  that 
the  week  is  no  original  Hindu  institution,  but  it  has  even  appeared  that, 
on  tracing  it  to  its  very  foundation,  wc  find  ^hcrc  another  Greek  word, 
fyn i represented  by  hortt.  Once  more,  in  the  cardinal  operation  of  find* 
ing  by  means  of  .the  system  of  epicycles  the  true  place  of  a planet,  we 
see  that  one  of  the  most  important  data,  the  mean  anomaly,  is  called 
by  another  name  of  Greek  origin,  namely  kendra , which  is  xivifpv. 
These  three  words,  occurring  where  they  do,  not  upon  the  outskirts  of 
the  Hindu  science,  but  in  its  very  centre  and  citadel,  amount  of  them- 
selves almost  to  full  proof  of  its  Greek  origin : taken  in  connection  with 
the -other  concurrent  evidences,  they  form  an  argument  which  can.  nei- 
ther be  set  aside  nor  refuted.  Of  those  other  evidences,  wc  will  only 
mention  farther  here  that  Hindu  treatises  and  commentaries  of  an  early 
date  often  refer  to  the  yavanas , “ Greeks”  or  “westerners,”  and  to  ?/a- 
van&caryas . “ tlic  Greek  (or  western)  teachers,”  as  authorities  on  astro- 
nomical subjects — that  astronomical  treatises  arc  found  hearing  names 
which  come  more  or  less  distinctly  from  the  West  (note  to  i.  4-G)  —and 
that  floating  traditions  arc  met  with,  to  - the  effect  that  some  of  the 
Siddliantas  were  revealed  to  their  human  promulgators  in  Komnka-city, 
that  is  to  say,  at  Home.  Farther  witness  to  the  same  truth,  deducible 
from  other  coincidences  of  the  two  systems,  we  pass  unnoticed  here, 
since  it  is  not  our  object  to  discuss  the  question  exhaustively,  only 
to  bring  forward  the  main  grounds  uf  our  opinions.  v 

.The  question  next  arises,  when,  and  in  what  maimer  the  knowledge  of 
astronomy  was  communicated  from  Greece  to  India.  - In  reply  to  this, 
only  probabilities  offer  themselves,  yet  in  some  points  the  indications 
are  pretty  distinct.  It  is,  in  our  own  view,  altogether  likely  that,  the 
science  came  in  connection  with  the  lively  commerce  which,  during  the 
first  ccutnries  of  our  era,  was  carried  on  by  sea  between  Alexandria,  as 
the  port  and  mart  of  Home,  and  the  western  coast  of  India.  Two  con- 
siderations especially  favor  this  supposition  : first,  that  the  chief  site  of 
the  Hindu  science  is  found  to  be  the  city  whi^h  lay  nearest  to  the  route 
of  that  commerce  (note  to  i.  62) : secondly,  that  Koine  is  the  only  west- 
ern city  or  country  which  is  distinctly  mentioned  in  the  astronomical 
geography  (xii.  69),  and  the  one  with  which,  as  above  noticed,  the  astro- 
nomical traditions  connect  themselves.  Had  the  Hindus  derived  tho.'r 
knowledge  overland,  through  the  Syrian,  Persian,  and.  Bactriiu^jntig- 
doms  which  stood  under  Greek  government,  or  in  which  Greek  influence 
was  predominant,  and  Greek  culture  known  and  prized,  the  name  of 
Koine  would  have  been  vastly  less  likely  to  stand  forth  with  such  promi- 
nence, and  the  capitals  of  Hindustan  proper  would  more  probably  have 
been  tlic  cradles  of  the  new  science*  The  absenco  from  the  Hindu 
system  of  any  of  the  improvements  introduced  by  Ptolemy  into  that  of 
the  Greeks  (note  to  ii.  43-45)  tends  strongly  to  prove  that  the  transmis- 
sion of  the  principal  groundwork  of  the  former  took  place  before  his 
time : nor  can  we  think  it  likely  that  the  numerical  elements  adopted 
by  the  Hindus  would  vary  so  much  as  in  many  cases  they  are  found  to 


S81 


Additional  Notes , etc. 

do  from  those  of  the  Syntaxes,  if  the  latter  had  been  already  in  existence, 
and  acknowledged  as  the  principal  and  roost  authoritative  exponent  of 
Greek  astronomy.  Whether  the  information  was  transmitted  through  • 
the  medium  of  Hindus  who  visited  the  Mediterranean,  or  of  learned 
Greeks  who  made  the  voyage  to  India,  or  by  the  translation  of  Greek 
treatises,  or  by  what  other  rocthpds,  wc  would  not  at  present  even  offer 
a conjecture ; and  the  point  is  one  of  only  subordinate  consequence. 

Whatever  may  have  been  the  date  of  the  first  communication  of  the 
elements  out  of  which  the  Hindu  system  was  elaborated,  there  is  good 
reason  to  suppose  that  its  final  reduction  to  its  present  form  did  pot 
take  place  until  some  time  dfiring  the  filth  and  sixth  centuries.  That 
period  is  distinctly  pointed  out  by  the  choice  of  the  equinox  of  A.  D. 
570  as  the  initial  and  principal  point  of  the  fixed  sphere  (uote  to  i.  271, 
by  the  definition  of  position  of  the  junction-stars  of  the  astcrisins  (p.  211), 
and  by  the  Hindu  traditions  which  refer  to  that  time  the  names  of 
greatest  prominence  and  authority  in  the  early  history  of  the  science, 
it  is  evident  that  the  elaboration  of  the  s\stcm  must  have  been  a work 
of  time,  probably  of  many  generations:  what-  were  the  forms  which  it 
wore  in  tho  interval  wc  do  not  know ; here,  as  in  many  other  depart- 
ments of  the  Hindu  literature,  all  record  of  the  steps  of  development 
appears  to  he  lost,  onlj  the  final  and  fully  formed  product  being  pre- 
served and  transmitted-  to  us : yet  more  light  upon  this  point  may  still 
he  hoped  for,  from  the  careful  examination  of  all  documents  now  ac- 
cessible, or  of  sucli  as  may  hereafter  be  discovered.  The  process  of 
a^siniilv^on  and  adaptation  to  Hindu  conceptions  and  Hindu  methods 
was^thoroughly  and  completely  performed.  Among  the  changes  of 
method  introduced,  the  most  useful  and  important  was  the  substitution 
of  sines  for  chords  (p.  Gil) ; the  general  substitution  of  an  arithmetical 
for  a geometrical  form  also  deserves  particular  notice.  That  no  great 
amount  of  geometrical  science  is  implied  in  any  part  of  the  system,  is 
\ cry  evident : it  is  distinguished  by  the  constant  and  dexterous  applica- 
tion of  a few  simple  principles : the  equality  of  the  square  of  the  hy- 
po! hcuuse  to  the  sum  of  the  squares  of  the  base  and  perpendicular — tho 
comparison  of  similar  right-angled  triangles — the  formation  and  com- 
bination of  proportions,  the  rule  ot  three — are  the  characteristic  features 
•of  the  early  Hindu  mathematical  knowledge,  as  displayed  in  the  S&rya- 
Sidilhanta.  Of.  other  treatises,  of  an  earlier  or  later  period,  as  those  of 
Brahmagupta  and  Bliftskara,  which  (see  Colebrooke’s  Hindu  Algebra) 
gi^c  evidence  of  knowledge  more  profound  in  arithmetic  and  algebra, 
we  c’Jtvjiot  at  present  speak ; hut  we  hope  at  some  future  time  to  be  able 
to  rnveit  to  the  subject  of  the  Hindu  astronomy,  in  connection  with 
these  or  other  of  the  text-books  by  which  it  is  repress  ulcd. 

Bov.  Mr.  Burgess,  having  placed  his  translation  and  notes  in  the 
hands  of  the  Committee  of  Publication  for  farther  elaboration,  has  very 
liberally  allowed  them  entire  freedom  in  their  work,  even  where  their 
deductions,  and  the  views  they  expressed,  did  not  accord  with  his  own 
opinions.  The  most  important  point  at  issue  between  us  is  that  dis- 
cussed in  ilie  next  preceding  pages,  or  the  originality  of  the  Hindu 
astronomy ; upon  tfris,  then,  he  is  desirous  of  expressing  independently 
his  dissenting  views,  as  in  the  following  note. 


382 


S&rya-Siddh&nta 


Concluding  Note  by  tiie  Translator. 

It  may  not  be  improper  tor  me  to  state,  in  a closing  note,  that  I bad 
prepared  a somewhat  extended  and  elaborate  essay  on  the  history  of 
astronomy  among  the  Hindu*,  to  be  published  in  connection  with  the 
preceding  translation.  Hut  the  length' of  this  essay  is  such — the  subject 
matter  oV  it  not  being  material  to  the  illustration  of  the  Siddh&nta,  and 
the  translation  and  notes  having  already  occupied  so  much  space — that 
it  was  not  thought  advisable  to  insert  it  here. 

Yet  as  my  investigations  have  led  m<?  to  adopt  opinions  on  some 
points  differing  from  those  advanced  by  Prof.  Whitney  in  liis  very  valu- 
able additions  to  the  notes  upon  the  translation,  truth  and  consistency 
secin  to  require  me  to  present  at  least  a brief  summary  of  the  results  at 
which  I arrived  in  that  essay  in  reference  to  the  points  in  question.  "By 
so  doing,  I free  myself  from  any  embarrassment  under  which  1 should 
labor,  if  hereafter — as  1 now  intend — I shall  wish  to  express  the 
grounds  for  my  opinions  on  these  points,  in  this  Journal  or  elsewhere. 

The  points  to  which  I allude  bear  upon  the  claims  of  the  Hindus  to 
the  honor  of  original  invention  and  discovery  in  astronomical  science — 
especially,  their  claims  to  such  an  honor  in  comparison  with  the  Greeks. 

Prof.  Whitney  seems  to  hold  the  opinion,  tlfht  the  Hindus  derived 
their  astronomy  and  astrology  almost  bodily  from  the  Creeks — and 
that  what  they  did  not  borrow  from  the  Greeks,  thevMcrived  from  other 
people,  as  the  Arabians,  Chaldeans  and  Chinese  (see  pp.  34,  £01,  206, 
et  al.).  I think  he- does  not  give  the  Hindus  the  credit  due  fSsJiem, 
and  awards  to  the  Greeks  more  credit  than  they  are  justly  entitled  to. 
In  advancing  this  opinion,  however,  I admit  that  the  Greeks,  at  a later 
period,  were  the  more  successful  cultivators  of  astronomical  science. 
There  is  nothing  among  the  Hindu  treatises  that,  can  compare  with  the 
great  SVutaxis  of  Ptolemy.  And  yet,  from  the  light  1 now  have,  1 
must  think  the  Hindus  original  in  regard  to  most  of  the  elementary 
facts  and  principles  of  astronomy  as  found  in  their  systems,  and  for  the 
moat  part  also  in  their  cultivation  of  this  science  ; and  that  the  Greeks 
borrowed  from  them,  or  from  an  intermediate  secondary  source,  to 
which  these  facts  and  principles  had  come  from  India.  I might  perhaps, 
so  far  modify  this  statement  as  lo  admit  the  supposition  that  neither 
Greeks  nor  Hindus  borrowed  the  one  from  the  other,  but  both  from  a 
common  source.  Hut  with  my  present  knowledge,  I cannot  concur , in 
the  opinion  that  the  Hindus  are,  to  any  great  extent,  indebted!^!,  o 
Greeks  for  their  astronomy,  or  that  the  latter  have  any  wrcll  grounded 
•claims  to  the  honor  of  originality  in  regard  to  those  elementary  facts 
and  principles  of  astronomical  science  which  arc  common  to  their  own 
and  other  ancient  systems,  and  which  arc  of  such  a nature  as  indicates 
for  them  a single  origin,  and  a transmission  from  one  system  to  another. 
For  the  sake  of  clearness,  it  is  well  that  L should  state  more  specifically 
a few  of  the  more  important  facts  and  principles  that  come  under  the 
class  above  referred  to.  They  are  as  follows : 

-1.  The  lunar  division  of  the  zodiac  into  twenty-seven  or  twenty-eight 
asterisms  (sec  transl.,  cli.  viii).  This  division  is  common,  with  slight 
modifications,  to  the  Hindu,  Arabian,  and  Chinese  systems. 


sss 


Concluding  Note . 

2.  The  solar  division  of  Ihc  zodiac  into  twelve  signs,  with  the  names 
of  the  latter.  ' These  names  are,  in  their  import,  precisely  the  same  in 
the  Hindu  and  Greek  systems.  The  coincidence  is  sncli  that  the  theory  * 
ot  the.  division  and  the  names  of  the  parts  having  proceeded  from  one 
original  source  is  unquestionably  the  correct  one. 

3.  The  theory  of  epicycles  in  accounting  for  the  motions  of  the  plan- 

ets, and  in  calculating  their  true  places.  This  is  common  to  the  Ilindn 
and  Greek  astronomies.  At  least,  there  is  such  a coincidence  in  the  two 
systems  in  reference  to  the  epicycles  as  almost  to  preclude  the  idea  of 
independent  origin  or  invention.  * * 

4.  Coincidences,  and  even  a sameness  in  some  parts,  between  the 
systems  of  astrology  received  among  the  Hindus,  Greeks,  and  Arabians, 
strongly  indicate  for  those  systems,  in  their  primitive  and  essential  ele- 
ments, a common  origin. 

fi.  The  names  of  the  live  planets  known  to  the  ancients,  and  tile  ap- 
plication of  these  names  to  the  days  of  the  Week  (s»-o  notes,  i.  52). 

In  regard  to  these  specifications  L remark  in  general : 

Fir>t,  in  reference  to  no  one  of  them  do  the  ‘-laiins  of  any  people  to 
the  honor  of  having  been  the  original  inventors  or  discoverers  appear  to 
be  better  founded  than  tliose.of  the  Hindus. 

Secondly,  in  reference  to  most  of  them1  the  evidence  of  originality  I 
regard  as  clearly  in  favor  oi  the  Hindus;  and  in  regard  to  some,  and 
those  the  more  important,  this  evidence  appears  to  me  nearly  or  quite, 
conclusive. 

1 lia)**flot  space  for  detail,  nor  is  it  the  design  of  this  note  to  enter 
into  tno  details  of  argument  on  any  point  whatever.  A brief  remark, 
however,  for  the  sake  of  clearness,  seems  calk'd  for  in  reference  to  each 
of  the  above  live  specifications  of  facts  and  principles  common  to  sonic 
or  all  of  the  ancient  systems  of  astronomy  and  astrology. 

1.  As  to  the  lunar  division  of  the  zodiac  into  twenty -seven  or  twenty- 
eight  asterisms.  The  undoubted  antiquity  of  this  division,  even  in  its 
elaborated  form,  among  the  Hindus,  in  connection  with  the  absence  or 
paucity  of  such  evidence  among  any  other  people,  incline  me  decidedly 
to  the  opinion  that  the  division  is  of  a purely- Hindu  origin.  This  is 
still  my  opinion,  notwithstanding  the  views  advanced  by  M.  Biot  and 
others  in  l’avor  of  another  origin. 

L\  As  lu  the  solar  ^division  of  the  zodiac  into  twelve  parts,  and  the 
names  of  those  parts.  The  use  of  this  mvision,  and  the  present  names 
of  tlkiysigns,  can  be  proved  to  have  existed  iu  India  at  as  early  a period 
as  in  aifyhqthcr  country : and  there  is  cvylcuce  less  clear  and  satisfac- 
tory, it  is  true,  yet.  of  such  a character  as  Lo  create  a high  degree 
probability,  that  this  division  was  known  to  tin  Hindus  centuries  before 
any  traces  cun  be  found  in  existence  among  an)  other  people. 

As  corroborative  of  this  position  in  part,  or  at  least  as  strongly  favor- 
ing the  idea  of  .an  oastern  origin  of  the  division  of  the  ecliptic  in  question, 

I nun  be  allowed  to  adduce  the  opinions  of  ldeler  and  Lcpsius,  as  quoted 
by  iiunibuldt  (Cosmos,  Harper’s  ed.,  iii.  120,  note): . “ldeler  is  inclined 
to  believe  that  the  Orientals  had  names,  but  not  constellations,  for  the 
Dodccatomeria,  and  Lcpsius  regards  it  as  a natural  assumption  ‘that 
the  Greeks,  at  the  period  when  their  sphere  was  for  the  most  part 
43 


334 


S&rya-Siddhdnta, 

unfilled,  should  have  added  to  their  own  the  Chaldean  constellations 
from  which  tlic  twelve  divisions  were  named.’  ” Whether  Ideler  meant 
by  “ Orientals”  tlic  Chaldcaps,  or  some  other  eastern  people,  the  appli- 
cation of  the  term  in  this  connection  to  the  Hindus  exactly  suits  the 
supposition  of  the' Indian  origin  of  the  division  in  question,  since  in 
Indian  astronomy  the  ntanes  of  tlic  signs  arc  merely  namcB  of  the 
twelfth  parts  of  the  ecliptic,  and  are  never  applied  to  constellations. 
Humboldt’s  opinion  is,  that  the  solar  divisions  of  the  ecliptic,  with  the 
names  of  the  signs,  came  to  the  Greeks  from  Chaldea.  1 think  the  evi- 
dence preponderates  in  favor  of  a more  eastern,  if  not  a Hindu,  origin* 

:i.  The  theory  of  epicycles.  The  difference  in  the  development  of 
this  theory  in  the  Greek  and  Hindu  systems  of  astronomy  precludes 
the  idea  that  one  of  these  people  derived  more  than  a hint  respecting  it 
from  the  other.  And  so  far  ns  this  point  alone  is  concerned,  we  have  ns 
much  reason  to  suppose  the  Greeks  to  have  been  the  borrowers  as  the 
contrary ; but  other  considerations  seem  to  favor  the  supposition  that 
the  Hindus  were  the  original  inventors  of  this  theory. 

4.  As  regards  astrology,  there  is  not  much  honor,  in  any  cstiuyition^ 
connected  with  its  invention  ami  culture.  The  coincidences  that* exist 
between  the  Hindu  and  Greek  systems  arc  too  remarkable  to  admit  of 
the  supposition  of  an  independent  origin  for  them.  Hut  the  honor  of 
original  invention,  such  as  it  is,  lies,  1 think,  between  the  Hindus  and  the 
Chaldeans.  The  evidence  of  priority  of  invention  ami  culture  seems,  on 
the  whole,  to  be  in  favor  of  the  former;  the  existence  of  three  or  four 
Arabic  and  Greek  terms  in  the  Hindu  system  being  accounted  for  on 
the  supposition  that  they  were  introduced  at  a coinparativolyrecent 
period.  In  reference,  however,  to  the  word  hora , Greek  figa  (see  notes 
to  i.  52 ; xii.  78-79),  it  may  not  be  inappropriate  to  introduce  tlife  tes- 
timony of  Herodotus  (IJ.  II,  ch.  109):  “Tlic  sun-dial  and  the  gnomon, 
with  the  division  of  the  day  into  twelve  parts,  were  received  by  the 
Greeks  from  the  Babylonians.”  There  is  abundant  testimony  to  the 
tact  that  the  division  of  the  day  into  twenty-four  hours  existed  in  the 
East,  if  not  actually  in  India,  before  it  did  in  Greece.  In  reference, 
farther,  to  the  so-called  (freak  words  found  in  Hindu  astronomical  treat- 
ises, I would  remark  that  wc  may  with  entire  propriety  refer  them  to 
that  numerous  -class  of  words  common  to  tlic  Greek  and  Sanskrit  lan- 
guages, which  either  came  to  both  from  a common  source,  or  passed 
from  the  Sanskrit  to  the  GrcSk  at  a period  of  high  antiquity ; for  no 
one  maintains,  so  far  as  1 am  aware,  that  the  Greek  is  the  parent  ofi.  the 
Sanskrit,  to  the  extent  indicated  by  this  numerous  class  of  wg^ds,  and 
by  the  similarity  of  grammatical  inflections  in  the  two  languages. 

5.  As  to  the  names  of  the  planets,  T remark  that  the  identity  of  all 
of  them  in  the  Hindu  and  Greek  systems  is  not  to  iny  mind  clearly 
made  out.  However  this  may  bo,  I think  the  present  names  of  the 
planets  in  Greek  astronomy  originated  at  least  as  far  cast  os  Chaldea. 
Herodotus  says  (B.  II,  eh.  52) . . . “ tlic  names  of  the  gods  came  into 
Greece  from  Egypt”  The  names  of  the  planets  arc  names  of  gods. 
Herodotus’s  opinion  indicates  tlic  belief  of  tlic  Greeks  in  reference  to 
the  origin  of  these  names.  Other  considerations  show  for  them,  almost 
beyond  a question,  an  origin  as  far  east,  to  say  the  least,  as  Chaldea. 


SS5 


Concluding  Note . 

As  tq  the  application  of  the  names  of  the  planets  to  the  days  of  tlio  ' 
week,  it  is  impossible  to  determine  definitely  where  it  originated.  Re- 
specting this  matter,  Prof.  H.  II.  Wilson  expresses  his  opinion — in  which  • 
I concur — in  the  following  language : “ The  origin  of  this  arrangement 
is  not  very  precisely  ascertained,  as  it  was  unknown  to  the  Greeks,  and 
not.  adopted  by  the  Romans  until  a late  period.  It  is  commonly 
ascribed  to  the  Egyptians  and  Babylonians,  but  upon  no  very  sufficient 
authority,  and  the  Hindus  appear  to  have  at  least  as  good  a title  to  the 
invention  as  any  other  people”  (Jour.  Roy.  As.  Soe.,  ix.  84). 

One  word  on  the  claims  of  the  Arabians  to  the  honor  of  originakin- 
veution  in  astronomical  science.  And  first,  they  themselves  claim  no 
such  honor.  They  confess  to  having  received  tlicir  astronomy  from 
Tndia  and  Greece.  They  had  at  an  early  period  some  two  err  three  of 
the  first  Hindu  treatises  of  astronomy,  “iutlic  reign  of  the  second 
Abbassidc  Khalif  Almaiisiir  ...  (A.  D.,7'i*rl),  as  is  related  in  the  preface 
to  the  astronomical  tables  of  licn-Al-Adami,  published  ...  A.  D.  920, 
au  Indian  astronomer,  well  versed  in  the  science  which  he  professed, 
visit/d  the  court  of  the  Lvlmlif,  bringing  with  him  tables  of  the  equa- 
tions of  planets  according  to  the  mean  motions,  with  observations  rela- 
tive to  both  solar  and  lunar  eclipses,  and  the  ascension  of  the  signs; 
taken,  as  he  affirmed,  from  tables  computed  by  an  Indian  prince,  whose 
name,  as  the  Arabian  juitlior  writes  it,  Piiihijah”  (Colcbrookc’s 
Hindu  Algebra,  p.  lxiv).  That  the  Arabians  wore  thoroughly  imbued 
with  a knowledge  of  the  Hindu  astronomy  before  they  became  ac- 
qn'tmtyri'with  that  of  the  Greeks,  is  evident  from  their  translation  of 
Ptolfmy’s  Syntaxis.  Jt  is  known  that  this  great  work  of  the  Greek 
astronomer  first  became  known  in  Europe  through  the  Arabic  version. 
Tn  the  Latin  translation  of  this  version,  the  ascending  node  (Greek  <ha- 
auvSeuuo^)  is  called  nqflus  capitis , “node  of  the  head,”  and  the 
descending  node  (Greek  xttTafhfi&^oiv  ov>d&(Tuog\  nodus  caudoe , “node  of 
the  tail” — which  are  pure  Hindu  appellations  (sec  Latin  Translation  of 
Almagest,  11.  iv,  cli.  4 ; B.  vi,  cli.  7,  et  id.).  This  fact,  with  other  e\  idcnce, 
clearly  shows  the  influence  of  Hindu  astronomy  on  that  of  the  Arabians. 
In  fact,  this  latter  people  seem  to  have  done  little  more  in  this  science 
than  work  over  the  materials  derived  from  their  eastern  and  western 
neighbors. 

Another  fact  showing  the  belief  of  tlio  Arabians  themselves  respect- 
ing their  indebtedness,  in  matters  aof  science,  to  the  Hindus,  should  be 
m&itjoiicd  here.  They  ascribe  the  invention  of  the  numerals,  the  nine 
digits^he  credit  of  whose  invention  is  quite  generally  awarded  to  the 
Arabians),  to  the  Hindus.  “All  the  Arabic  and  Persian  books  of  aritB- 
nictic  ascribe  the  invention  to  the  Indians”  (Stracncy,  on  the  Early 
History  of  Algebra,  As.  lies.,  xii.  184  sec  likewise  ( Jolcbrookc’s  Hindu 
Algebra,  pp.  lii-liii,  where  the  same  is  shown  from  a different  authority. 
Strachcy’s  article  was  published  subsequently  to  the  w ork  of  Colcbrooke). 

The  above  facts  and  considerations,  showing  the  indebtedness  of  the 
Arabians  to  the  Hindus  iu  regard  to  mathematical  and  astronomical 
science,  clearly  have  an  important  bearing  on  tlio  question  of  priority 
of  invention  in  regard  to  the  lunar  division  of  the  zodiac  into  twentv- 
oight  asterisms,  at  least  so  far  as  the  Arabians  are  concerned.  Taking 


all  Ihe  facts  into  account,  the  supposition  that  this  people  •were  tho 
inventors  is  altogcth  cr  untenable. 

1 close  this  note — already  longer  than  I intended — with  a quotation 
from  that  distinguished  orientalist,  II.  T.  Colcbrooke.  In  a very  valu- 
able essay  entitled  “ On  the  Notions  of  the  Hindu  Astronomers  concern- 
ing the  I Accession  of  the  Equinoxes  and  Motions  of  the  Planets,”  having 
stated  with  some  detail  some  of  the  more  striking  peculiarities  of  the 
Hindu  systems,  and  likewise  coincidences  existing  between  them  and  that 
of  the  Greeks,  with  the  evidence  of  communication  from  one  people  to 
th$  other,  he  says : “ If  these  circumstances,  joined  to  a resemblance 
hardly  to  be  supposed  casual,  which  the  Hindu  astronomy,  with  its  ap- 
paratus of  ecccutrics  and  epicycles,  bears  in  many  respects  to  that  of 
the  Greeks,  be  thought  to  authorize  a belief,  that  the  Hindus  received 
from  the  Greeks  that  knowledge  which  enabled  them  to  correct  and  im- 
prove their  own  imperfect  astronomy,  I shall  not  be  inclined  to  dissent 
from  the  opinion”  (As.  Res.,  xii.  245-6;  Essays,  ii.  411). 

This  is  all  that  so  learned  and  cautious  a writer  could  say  in  favor  of 
the  opinion  that  the  Hindus  derived  astronomical  knowledge  from  the 
Greeks.  Store  than  this  I certainly  could  not  say.  After  the  solar 
division  of  the  zodiac,  with  the  names  of  its  parts,  it  is  evident,  1 think, 
that  only  hints  could  have  passed  from  one  people  to  the  other,  and  that 
at  an  early  period ; for  on  the  supposition  that  the  Hindus  borrowed 
from  the  Greeks  at  a later  period,  we  find  it  difficult  to  sec  precisely 
what.it  was  that  they  borrowed ; since  in  no  case  do  numerical  data  anil 
results  in  the  systems  of  the  two  peoples  exactly  correspond.  d in 
regard  to  the  more  important  of  such  data  and  results — as  for  instance, 
the  amount  of  the  annual  precession  of  tlie  equinoxes,  the  relative  size 
of  the  sun  and  moon  as  compared  with  the  earth,  the  greatest,  equation 
of  the  centre  for  the  sun — the  Hindus  are  more  nearly  correct- than  the 
Greeks,  and  in  regard  to  the  times  of*tlie  revolutions  of  the  planets 
they  arc  very  nearly  as  correct:  it  appearing  from  a comparative  view 
of  the  sidereal  revolutions  of  the  planets  (p.  24).  that  the  Hindus  are 
most  nearly  correct  in  four  items,  and  Ptolemy  in  six.  There  has  evi- 
dently been  very  little  astronomical  borrowing  between  the  Hindus  and 
the  Greeks.  And  in  relation  to  points  that  prove  a communication  from 
one  people  to  the  other,  with  my  present  knowledge  on  the  subject^  I 
am  inclined  to  think  that  the  course  of  derivation  was  the  opposite  to 
that  supposed  by  Colcbrooke — from  east  to  west  rather  than  from  west 
to  east;  and  1 would  express  my  opinion  in  relation  to  astronomy^ in 
tlic  language  which  this  eminent  scholar  uses  in  relation  to  som^eoinci- 
dfcnccs  in  speculative  philosophy  and  religious  dogmas,  especially  the 
doctrine  of  metempsychosis,  found  in  the  Greek  .and  Hindu  systems, 
which-  indicate  a communication  from  one  people  to  the  other : “ I 
should  be  disposed  to  conclude  that  the  Indians  were  in  this  instance 
teachers  rather  than  learners”  (Transactions  of  the  Roy.  As.  Soc.,.i.  570); 

* This  opinion  is  expressed  in  the  last  essay  on  oriental  philosophy  that 
came  from  the  pen  of  Colcbrooke.  E.  II. 

< Boston,  May,  1800. 


SANSKRIT  INDEX 


This  following  Index  contain*  all  the  Sanskrit  words,  excepting  proper  names* 
which  have  been  cited  in  the  text,  and  notes,  in  connection  with  tlieir  translation  or 
more  detailed  explanation.  It  includes  many  terms  of  trivial  importance,  hut  we 
prefer  to  err  upon  the  side  of  fullness,  if  upon  either.  All  the  cases#  of  occurrence 
of  each  word  arc  not  given,  hut  it  is  referred  to  a characteristic  passage,  or  to  the 
note  tflicre  it  is  explained.  The  re  fere  u cos  by  Roman  and  Amine,  figures  are  to 
chapter  and  verse,  and  an  added  a denote*  the  note,  next  following  the  verse  given : 
Arabic  figures  when  u>ed  alone  refer  to  page*. 


anrat  i.  28  n. 
anrvvimardat  vii.  19. 
ak&p cr,  i 60  n. 

ah i tadrkkartnan , vii.  12  n,  ix.  6 n. 

ak:  hhhhd,  iii.  1.1  u. 

akxhoimati , i.  60  n. 

agvajtfd,  iii.  7 n. 

agramdnrvikd f iii.  27. 

agrd,  iii.  7 u. 

ay  hot.  add.  11.  26. 

angdvakt,  add.  n.  3. 

flJir^'V'iii.  5 n,  x.  9. 

aja,  i.  58  n. 

aja  vkapod.  199. 

ann , vii.  1 9. 

rtfintgita.  ii.  1 1 n. 

atifiykra,  ii.  13. 

adili.  xii.  28  u. 

adhihira,  i.  70  ri,  xi.  23  n. 

adhinidm , adh hmhaka,  i.  10  n. 

mUnjnlmo,  xii.  11. 

adhydyo,  xi.  23  n,  xii.  10. 

anurdd/ui.  192. 

twnvakra,  ii.  12. 

annnhaayn,  add.  n.  3. 

an  far  a , xi.  18  n. 

antaralag)nlxav<i8f  iii.  50  n. 

qjtlr/ti , iii.  7 n. 

an  (Via hi , add.  n.  26.  , 

apakramn , i.  70  u. 
apakrnmamandala , xiii.  18  n. 
apabharani,  164. 
aptmiawlafa , xiii.  13  n. 
upanavya , vii.  19. 
apasgvyam , xii.  7‘i  n. 
avmnvatsa , viii.  21  n. 
ahhijit,  195. 
amarcjya , add.  e.  3. 
amdvdsyd,  ii.  66  a,  iv.  7. 
amurta,  i.  10.  ^ 
amrlasrdva , xiii.  19  n. 

ayana,  iii.  10,  249,  xii.  72  n. 

■ 


ayauakahU,  vii.  1 2 ti. 

! uyanngrahtt.  vii.  12  n. 

(t  t/mifulrkkanann*  vii.  12  n. 
ot/anrinfa,  105.  ■ 

; oynndnta,  xii.  72  n. 

c it'ka,  ndil.  n.  3. 
i ttrkaja.  add.  n.  8. 
arkdgrd.  iii.  23. 
arjidii,  nild.  ii.  26. 
idttka.  xiii.  1 6 n. 

, auamt(i%  v.  1 n. 
m vtitlha,  add.  n.  26. 

1S3. 

i trrini,  «» rini,  afvindu,  183 
fi.sh'iilliti,  194, 
awi-a*,  iii.  -io  n. 
j asita,  x.  13  n. 

,j  ana , i.  12  n : and  see  asavas. 
• usnrn,  i.  2,  xii§  53. 
j oata,  ix.  1 n. 

, ax/AW7f/i7«((»/(  xiii.  13. 

|!  a#t  tun  ana,  astamaya,  ix.  1 n. 

wifaltfffiHr,  xiii.  1 5 n. 
j ti.t/tf nrr-th,  ix.  5 n. 

, iisp/i  nta,  v.  7. 

(l  ahankttra,  xii.  20. 
j ahnrynmt , i.'  51  n. 

| a hi  Ludhnya,  199,  ix.  18. 

| afiortitro,  iii.  01  n. 

! lihtrn.  xii.  90  n. 

tlkxhu  drkkanna"  vii.  12  n. 
i d kith  a v /ana.  iv.  25 ii. 

dgwya,  .'iii,  18. 
d di,  xii.  ’ 5. 

aditya , viii.  19,  xii.  28  n. 
•ipa,  dpas,  194,  viii.  21  n. 
i ipya,  viii.  4. 
dyana  graha,  vii.  1 2 n. 
dyana  arkkartnan,  vii.  12  n. 
dyana  valana,  iv.  25  n. 

• drki,  add.  n.  3. 


Surya-Siddhdnta , 


388 

drdrd,  18ft. 

Aryikd,  odd.  IL  26. 
dZi,  i.  6S  n. 
dnftya,  iii.' 1 2d. 
dprcxhd,  188. 
df/cdiz,  188. 
dsannhtd,  Xii.  72  u. 

indit.  add.  n.  3. 
iqvakd,  add.  n.  26. 
ilvald,  add.  n.  26. 

Mu,  add.  n."  16. 
ishta , i.  68  n. 

i erea,  i.  33,  34  n,  ii.  6 D. 
t itkramajyd,  ii.  27  n. 
utkramajydrdhapindaka,  it  22. 
uttara,  vi.  12  n,  189. 
uttara  k hand  a,  xi.  23  □. 

uttardyana . iii-  12  n. 

udaya,  v.  3 n,  ix.  1 n. 
ii dayajyd.  ▼.  3 n.  # 

nduyaprdndt,  ii.  69  n. 
udaydsauat,  iL  59  n,  iii.  43  n. 
udaydtt ddhi kdra,  ix.  I n. 
nnnata,  iii.  39  n,  iv.  26. 
unmandala,  iii.  6n. 
unmandalaranku,  iii.  34  n. 
vnmUana,  iv.  17  n. 
ullekha , vii.  1 8. 

nrdhpam,  xiii.  10  n. 

urdhva  ydrnyoUaravrtta , xiii.  1 6 ii. 

rcat , xii.  17. 

rju , ii.  13. 

rn  , ii.  5 n. 

rtn,  xiv.  10  n. 

rthi,  viii.  21  n,  xiv.  26. 

ckadepa,  xi.  18  n. 
ekayanagata,  xi.  6 nt  18  n. 

dindra , xi.  21. 

oja,  ii.  35. 

kakthd , iv.  3 n;  xii.  65  n,  xiii.  4. 
kadamba,  v.  In. 
kkanydt  i.  58  n. 
kapdfa , y.  17  d,  xiiL  22  n. 
kupila,  vi.  23. 
karaqa,  iL  G7y  69  n. 
karani,  iii.  30.  34 1). 
karka , kurkata,  i.  53  n. 
karna . ii.  41,  iii.  23  n,  iv.  21  n. 
kannan,  ii.  42,  viL  12  n. 
kalana , i.  1 0 n. 

*kaldt  i.  12  11,28.- 
kali,  i.  1 7 n. 
kali  yuga,  i.  17  n. 
kalpa , i.  19.  * 


II  kdpdlika , viii.  18  n. . 
j kdmiuka.  add.  n.  16. 

krila,  L 10  n,  ii.  69  n. 

I kdlagati , ix.  11  n. 
j kdlabhdgdt,  ix.  5 n. 
i!  kdlatddlana , iii.  60. 

Ij  kitldnfdt , ix.  5n. 
i|  kdshthd,  i.  12n. 

!|  kuja,  add.  n.  3. 

| kujyd,  ii.  63  n. 

| k util  a , ii.  12. 

| knmbha,  L 58  n. 

I kula,  vii.  22. 

! krta , i.  17  n. 
j krta  ynga , i.  17  n. 

! krttikd,  184. 

' krshna,  xiv.  17. 
krsh  natdmra,  vi.  28. 
krshna  paksha , i.  51  n. 
kendra , ii.  30  n,  45  n. 

A-ori,  ii.  30  n.  x.  15n,  add.  n.  16. 
! kotijyd , ii.  30  n.  add.  n.  16. 

| kotijydphala,  ii.  39  n. 

kotiphnta , ii.  39  n. 

, A’O/irt,  Iii.  34  n. 

konttrauku,  iii.  34  n. 
krdnti,  i.  70  n. 

;J  A-rifAtf/.vri,  ii.  28  n. 

!.  kninti  pitta,  86. 

knintiptitayati,  iii.  12  n. 
kr tint imantj ala , xiii.  13  n. 

|j  kninthirtia , xiii.  13  u. 

:■  kmm,  i.  60  IL 
kshatja , i.  12n. 

| kthaya , i.  40  n,  xii.  72  n 
kshiti,  ii.  63  n. 
j kshiti ja , iii.  49  n,  v.  1 n. 

I kshitijuti,  ii.  63  n. 

! A'f/ltp,  l.  TO  t;. 

kshetra , ix.  16n,  xiii.  11. 
i kshetrdnrat , ix.  16n. 

A-sA^riyrt.  193. 
j kshepa,  iv.  21  n,  v.  6n. 

| A/mrarn,  add.  n.  22. 
khaedrin,  add.  n.  22. 
khamadhya,  v.  1 n,  xiii.  14. 

</ana,  i.  28  n. 
ganda , xi.  22  n. 
ganddnta , xi.  21,  22. 
flfaii,  v.  6 n. 
garbha , v.  1 n. 
guru,  xiii.  2,  add.  n.  S. 
gurvakthara , i.  12  n. 
guhyakn,  xiii.  3 n. 
poZa,  v.  1 d. 
gduna,  i.  1 3 n. 
gratia,  vi.  1 3,  ix.  9. 
graha , iv.  6 n.  add.  n.*22. 

* grahana , iv.  6 n, , vi.  4. 

grahayutyadhikdra , vii.  1 n. 


Sanskrit  Index. 


839 


grdta,  iy.  11  n,  15  n,  20. 
grdhaka , iy.  9 n. 
grdhya,  iy.  9 n. 

■ 

ghati , xiii.  23  n. 
ghatikd , i.  12  n,  xiii.  23  n. 

cakra,  iii.  121),  xiii.  2l  d. 
caturaxra,  iii.  5 n. 
catnryvga , i.  15,  17  n. 
catushpada , ii.  69  n. 
candra,  add.  n.  3. 
candragrahanddhikdra,  iy.  26-n. 
candradifas,  x.  15  n. 
earn,  ii.  03  n,  08,  xiv.  6n. 
carakald *,  310. 
carakhanda , iii.  44  n. 
carajyd , iii.  36  n. 
car  a dal  a , ii.  63  n. 
ca/tf.  ii.  40.  • 

I karnti , ii.  42  n. 

cdV'i,  add.  n.  16. 
rife  190. 

chandtiR , xii.  15. 
chiulttka . iv.  9 n. 
chud; /a,  iv.  9 n. 
chiti/ti , iii.  Oil. 
chrda,  iii.  35,  v.  7. 
chedyaka , vi.  1 n. 

jamlnidripa,  xii.  44  n. 
jay  hi,  vii.  21. 
vii.  20. 

jfii'a,  add.  n.  3. 

ii.  27  n. 
jiia,  add.  n.  3. 

ii.  27  n,  add.  n.  16. 
jytipini/a,  ii.  27  n. 
jyupindaka , ii.  31. 
jydrdha.  ii.  27  n. 
jydrdhapinda , ii.  16. 
jyttshthd,  192.  ^ 

jyolixhopanishadadhydy* , xiii.  3 n. 
jyotis,  i.  3 n. 

%if,  xii.  12. 
tatpara , i.  lin. 
taw  a*,  vl5  11. 
tallagnd*avant  ix.  11. 
tdjika,  vii.  23. 

JrintJhd,  tdrd,  vii.  In,  viii.  16, 19,  xii. 43?l 
t^dymAa,  vii.  1 n. 
ligmdnfu,  add.  n.  3.  . 

i.  13.  ii.  66  n. 
tilhikxhaya , i.  40  n. 
lithyanta,  v.  13n. 
tout,  iii.  5 n. 
ttryaknUra^  x.  1 5 n. 

< iryaaiyd,  xiii.  13  n. 
trihya,  187. 
tikihndnpi  add,  n.  8. 


fu/d,  i.  68  n. 
torana , 191. 

I trinrathrlyas,  iii.  12 1). 
trhu'tUkrlvax,  iii.  12  D, 
trikmta , iii.  34  n. 
trimiuhkarna , vii.  14  n. 
tr/jivci,  ii.  60  n. 
trijyd,  ii.  60  n. 
triprafntidJrikiira , ii.  69  n. 
tribhajivd,  -jyd,  -m&urvikd,  ii.  60  n. 
tribhonalagua,  v.  In. 

, fn/fi.  i.  1 2 n. 

| iwfd  i.  17  n. 

! dal'dhnru  vi.  12n.j 
I dnk-hhjdyana,  iii.  12  n. 

! duijdn.  i.  l 2 n,  60  n. 
dasru , viii.  9. 
dimJcara,  add.  n.  3.  * 
divard'L  i.  28 n,  51  n. 

; dhianydsadula , ii.  60  n. 
tUodkara,  add.  n.  3. 

■ did  ii.  69  ii,  V.  2. 
drkharman,  vii.  12  n.' 

■ drkkdirpa,  y.  6n. 

, drkhdyntd , vii.  18n. 

drkfutya  elf..  xii8n. 
i dryputi,  v.  6 n. 
j drat fatij it'd,  v.  7. 

■ d raj  yd . v.  0 n. 

j dry  fa  whan ",  V.  1 n: 
ita,  v.  1 n. 

j dff,  ii-  14,  iii.  34  n,  v.  6n. 
drryditrd* . ix.  5n. 
df'#/.  ii.  09  n,  v.  2. 

i.  01  n. 

drdmtaraphala,  ii.  39  n,  290. 

ddirata , ii.  10. 

doijyd , ii.  4S. 

dirwi,  ii  30  n,  add.  n.  16. 

' dyrtgana,  i.  51  u. 
dgitjyd,  ii.  60  n. 
dedpura  yaga,  i.  17  n. 
doixeablldva , xiv.  4. 

■ dtnpa,  xii.  14  n. 

dhana , ii.  5 n. 
dhania,  196. 

dhanixhthd,  196.  t 

dltann  i.  58  n,  60  n,  xiii.  21  n,  add.n.  IB, 
dhishnyi , viii.  1 ii,  xi.  21. 
d/trura,  i.  67,  viii.  ] n.  * 

dhruvaka.  viii.  In.  • 

d/truvalard , xii.  43. 

flff&ft/mftvt,  207.  . . 

* fil-xlmlraffrahayutyadhikdrO)  viiL  Id. 
unfa,  iii.  16,  17  u. 

it  at  aj  yd,  iv.  25  n.  1 

natabhdyns,  iii.  17. 
natdnfds,  iii.  21. 

|]  nati,  v.  1 n.  fl 


Sdrya-Siddh&nla, 


840 

nara,  xiii.  22  n. 
narayantra,  xiii.  24. 
ndkHhr.tr a , X.  5 n. 

ii»  01,  00  n,  xii.  S3. 
ndtfi,  i.  1 2 n.  xiii.  23  n. 
naif  ik rt,  i.  12  n,  xiii.  23  o. 
9»?i»f  £/#t »cj>,  iv.  17n. 
nimruha,  i.  12  ii. 
iiiraksha , xii.  44  n. 
fiirr/r,  103. 
nifdkara,  add.  n.  3. 
fiifri/Mi/i,  ndd.  n.  3. 
nixhtyd,  191. 

pakttha,  ii.  00  n.  - 
pada,  ii.  20,  viii.  5,  197. 
para , i.  21  n. 
paranta,  i.  70  n. 
paramakrduli , -ji/rf,  ii.  28  n. 
parmti'inn . i.  1 2 n. 
paramo  pa  kraut  a . ii.  28  n. 
jmraui  d i/n n,  i.  2 1 n. 
parardha , i.  2 1 n. 
paridhi.  ii.  3Sn. 
paritekha . vi.  1 n. 
par ilckh'hlhik- tint f vi.  1 n. 
paryanka.  180. 
parvau,  iv.  fi  n,  xiv.  16  n. 
parvar.-ttfihin,  iv.  8 n. 
parvorhuidi/ns , v.  3.  . 
pari- do ta,  xiv.  1 6 n. 
pal  a.  i.  12  ii,  xiii.  23  n. 
palabhii . iii.  1 3 n. 
pacc&l.  vi.  1 2 n. 

/>d/a,  i.  33,  xi.  5 n. 
pdtddhikira , xi.  5 n. 
pulfila . xii.  33. 
pudtna,  i.  23  D. 
pfh'ad  rru,  xiiirjfti  D. 
pint! a , ii.  27-4£; 
pitaraH , 188. 
pitrya , viii.  T8. 
punaruasn , 180. 
pnrnxha,  xii.  12. 
paxhya,  187. 

purnamu,  purnimri , ii.  GO  n. 
pnrnimdnta,  xiv.  16  n. 
pur  tut,  189. 

join: a khan  da,  xi.  23  n. 
pushnn,  199. 
pr*htha,  v.  1 n. 
jiufirjMjfircAi,  ii  00  n. 
pdnshnya,  xi.  21. 
prnkrli.  xii.  13. 
prayraha, , iv.  1 5 n. 
pray rub  ana;  v.  1 0. 
prat itthfhf tna,  add.  u.  26. 
prabhri, , iii.  5 n. 
pramuaa , v.  13. 
pravahd,  ii.  3. 
pra$na,  275. 
jprdci,  iv.  2tt  a,  add.  n.  23. 


jirdiic,  vi.  12  n. 

;jr«wi,  i.  12n. 
pra*htha,  197. 
proshthnpadd , 197. 

phoht,  iii.  3-1  n. 
phalyuvi,  189.  , 

yi/irr/V/aai,  189. 

6a/fi,  vii.  20. 

/#«/;.  102. 
bal in.  vii.  21. 
h:hmhti*patyat  viii.  18. 

/m/V/rf  jrjP<rf//a  mritta,  i.  65  n. 

Ar//*//(  ii.  Hun,  add.  n.  16,  ‘28. 
bdhnjifd,  ii.  :;u. 
kuhnphtda,  ii.  39  n. 

I 0*/*it  i.  0 n.  :M  n. 

; hitdhu , arid.  n.  3. 

1 br/tospart.  add.  n.  3. 

|'  bmhnutn.  xii.  12. 

! kwh  nut  firdnya,  vtii.  12  n. 

| 7//m.  i.  27  n,  iii.  12  n. 

■ bhnytnti,  i.  27  n,  ii.  1,  xii.  6. 
i bkurukm,  ii.  40. 

| bhmlro.  1 '.'7. 

1-  bhndnfpnd  • 107. 

181. 

■ • Umsitudhi.  >:i.  21  n. 

hfr\  in.  .*i  n. 

Ith  ■ •tfti , i 2S  n. 

| bh.idropad.i.  107. 

A//  //#m,  arid.  ii.  3. 

Lit t* ran i’t1,  add.  n.  3. 

■’  bluish  tra,  a Id.  n.  3. 

; /*/< if .Wifjfif i'if  i,  iii.  40  u. 

bfmkti.  i.  27  n. 
i.  27  ii. 

hknpt,  ii.  3>)ii,  iii.  5 n,  add.  n.  16. 
j #/i .■//.#/!/.;  ii.  30  ii,  add.  n.  1G. 

r (•/•••j>[}mnrphilfnt  li.  !,9  vi. 

. b/injnjdut /<£,  ii.  39  n. 

j f-'ti/jttx  I.iVif,  iii.  f». 

!i  hUinpdo.  _:ii.  32. 
i bhuynlddhynya.  xi.  23  n. 

Ih/ftpofro.  mill.  ii.  3. 
bh'tbhaydtr.  xiii.  3 n. 
bhdtniyoln , xiii.  3 n. 
kbit  mi  point,  add  n.  3. 

A//ic.w<^/t  add.  n.  3. 
hhryu,  add.  n.  3. 

Ibhrifnja , add.  n.  3. 

AMa.  vii.  18. 
bhnya,  ii.  64.  . 
bhoyyd&avas,  iii.  49  n. 
bhuuma,  add.  n.  3. 
khramana , xii.  76. 

ma£rzra,  i.  68  D. 
taayhd , 188. 
manca,  189. 


Sanskrit  Index. 


341 


piaiylala,  x.  15n,  zL  18  n,  xii.  16. 
matxya,  %ii.  5 n. 
madkya,  i.  70  n,  xiii.  15  n. 
madhyakarna,  ill.  23  n. a 
madhyagrahana,  v.  13  n.  ■ 
madhyajyd,  ▼.  5 n. 
madhynpdta , xi.  5 n. 
madhyabha,  v.  1. 
madhyama,  xiii.  14. 
m adhyamddhikdra,  i.  70  n. 
ma/ihyarekhd , i.  62  n.  . 

madhyalagna . iii.  49  nt  xiiL  1 5 n. 
madhyaxth  ityardha,  t.  18  b. 
madhydhna , x.  8 n. 
madhye,  xiv.  14  n. 
m/inu,  i.  19  n. 

mandf r,  ii.  5 n,  12,  add.  n.  8. 
mandakarman,  vii.  15  n. 
tnandakendra , ii.  30  n. 
mavdatara,  ii.  12. 
mandnparidhi,  ii.  34. 
mandnphala , ii.  44.  f 
mjfvdocca,  i.  34  n. 
tmnvanlara,  i.  19  n. 
nuibarxhu  i.  8.  xli.  35.  • 
mahdbhuta , xii.  23. 
mahdyuga , i.  17  n. 
mahdfankn,  add.  n.  21. 
mdna,  iv.  3 n.  xiv.  9 n. 
mnnddhydya , xiv.  2 n. 
man ibt  knnnan,  ii.  48. 
trifmda  phala , ii.  39. 
mdxhn,  xiii.  23  n. 
mi  Ira,  192. 
mit/nnia,  i.  58  n. 
vKiita,  i.  5S  n.  . 

mnkha . xiv.  6 n. 
mnkhya , i.  13  n. 
muhurta,  \.  12  □. 
mur/a,  i.  1 0 d. 
mu/a,  193. 
mrga,  i.  58  n. 
tnrgavyddha , viii.  12  a, 
inrgafirax,  18b. 
mrgafirxha , 185. 
melaka , vii.  1 n. 

^mexAa,  i.  58  n. 
mdifra,  viii.  1 81 
mokxha,  iv.  1 5 n. 
mdurvikd,  ii.  27  n. 

yajunnhi,  xii.  17. 
gantra , xiii.  19. 
ya*hti,  xiii.  21  n. 

ydinyottarai  ftta,  iv.  25  nt  xiii.  15  p. 

yaga,  i.  ] 7 n,  58  d. 

yugma , ii.  30. 

ySl , vii.  1 n. 

yuddha,\\\.  1 n. 

yogra,  ii.  05  n,  vii.  1 d,  add.  n.  19. 
yagatdrd,  179. 
yogatdrakd . viii.  19. 
yojana , i.  60  D. 


ranhat,  ii.  8 n. 
ran,  add.  n.  8. 
rdkxhaxa,  i.  62. 
rdfi,  L 28  n. 
rdhu,  ii.  8 n. 
rekhd , i.  61  n. 
renugarbha , xiii.  22  n. 
renati,  199. 
rob  ini.  185. 
rdudrarkhka,  ix.  14. 

lagan,  iii.. 48,  49  n. 
lagndntaraprdndM,  ix.  5. 
lagndntardsava* . X.  2. 
lagndxarax,  iii.  47. 
lankodoydx,  xiii.  14. 
lankodaydxavaat,  iii.  49  n. 
lamb,  i.  27  n,  iii.  12  n. ' 
lamba,  i.  60  n. 
lautbajya , i.  HO. 
lambana,  v.  1 n. 
lipid,  i.  28  n. 
liptikd,  i.  28  n. 
hibdhaka , viii.  12  n. 
luka,  xiiL  16  n. 

vakra,  ii.  12. 
vakragati , viii.  16. 
vakrin,  ii.  54. 
varxh’n , xii.  44  n. 
vnlana,  iv.  25  n. 
valandnrds,  iv.  25  n. 
vali,  192.  ' 
vaxn,  186. 
vaxtra,  xiii.  10. 
vdyana,  viii.  19  n. 
i'#ira.  i.  52  n. 
vdraha,  i.  23  n. 
vdxava,  ix.  1 S. 
vikala,  i.  28,  vii.  iO. 
vikxhip,  i.  70  is,  viii.  12. 
rikxbrpa,  i.  70  n. 
vigraha , vii.  22. 
vicrrdu,  193. 
vijita,  vii.  21. 
vitaftti.  iii.  5 n. 
vidic,  iii.  32. 
vidyddbara,  xii.  31  n. 
vidh'i . add.  n.  8. 
vid/n  ta.  vidhrti,  xi.  5 Q. 
viiUtvaxtfL,  vii.  21. 
vinddi,  i.  1 2 n. 
viparitf , xi.  6 n,  xii.  72  n. 
vintarifa,  iv.  15  n. 
vivaxvant,  add.  n.  3. 
vifiikhd,  191.  194. 
vip;e  devax . 1 94. 
vixhama,  ii.  30.  • 

vishnva,  vixhunat,  iii.  0 n. 
vixkuratprabhd,  iii.  13. 
vixhwiadbbd , iii.  7. 
vixhuvaditrtia , iii.  6 n. 
viuhuvanmandala,  iii.  6 n. 


44 


342 


Sdrya:Siddhdnta , 


tfijii,  i.  34  n. 
vrtla,  ii.  33  n. 
vrddhi,  xii.  12  n. 

VTfctka,  i.  58  n. 
vrahan,  i.  68  D. 
vega,  ii.  1 1 n. 
veils i,  xii.  2.7. 
veddnga,  i.  8 n. 
vdidhrta,  vdidhrti,  xi.  5 n. 
vdifva , Tiii.  4. 
vdiahmati,  xiii.  9. 
vdiahnava,  ix.  18. 
vyaksha,  xii.  44  n. 
vyatipdta , xi.  5 n. 

*y mucin,  xii.  30. 

fakq,  add.  n.  12. 
fakuni,  ii.  69  n. 
paiihu,  iii.  5 n,  34  n. 
fanhtjivd,  iii.  22. 
falabhixhaj,  -aha,  197. 
favti,  add.  n.  3.. 
r anairrqra,  add.  n.  3. 
f ayyd,  189. 
fara,  add.  n.  16. 
fapinka,  add.  n.  3. 
f«f v'fl.  Add.  ii.  3. 

add.  n.  3. 
fdka,  add.  n.  ] 2. 
fikhin , 216  ni»rc\ 
f iff  bra,  i.  34  n,  ii.  12. 
fiyhrnktmnan , ii.  37. 

9 fighrakcndrn,  ii.  30  n. 
rifjhratara , ii.  12. 
fighraparidhi , ii.  55. 
righraphala , ii.  44. 
fighrocca , ii.  5 n. 

fitagu , fitadMiti , pifdnfti,  add.  n.  3. 

fiikra,  add.  n.  3. 

puA/a,  x.  4.  9. 

puA/a  pdk*ha , i.  51  a.  s 

pu/6a.  xiii.  22. 

frnga,  x.  1 n. 

{rngata,  195. 

frngonnatyadhikdra,  1. 1 n.  _ 
ft  ah  a,  iii.  5 1 n. 
fdighrya,  ii.  42,  43. 
prawi.  iii.  26,  iv.  21  n. 
fravdna,  iv.  21  D,  196. 

I pravishthd,  196. 
frond,  i9G. 

shadaritimukha,  xiv.  6 n. 

aamyoga,  vii.  1 n. 

famvaf,  tamvaliara,  add.  n.  12. 

MiuAdra,  310. 


I!  aauhitd,  vii.  23  n,  add.  n:  1. 
sail  hr  am  ana , xiv.  10  n. 
arrnA’rcivdi,  xiv.  3 n. 
aadhmnra,  vi.  23. 

Jii.  22  n. 

muni  hit  am  aaraa,  i.  62  n. 
taptarxhayas , xiii.  9. 
fama,  ii.  12,  iv.  26  n. 
aamamandafa , iii.  6 n. 
aamamnndatufavku,  iii  34  n. 
aamaauira,  xiv.  7 n. 
aamdgama,  vii.  1 n,  20,  22. 
aamdsa,  vi.  3. 
anras.  i.  62  n. 
aarpiis , 188. 
aavanti,  xiv.  19  n. 
aavitar , xii.  28  n,  add.  n.  3. 
aavyam,  xii.  12  n. 
atimdui,  xii.  17. 
annipntddyika , vii.  14  n. 
adyiuu r,  295. 

; arirpa,  viii.  19.  • 

, aii v/nta,  i.  12,  xiv.  19  n. 

aiuha,  i.  5H  n. 
j aiddha,  xii.  28. 

| aiddhiinta,  add.  n.  1. 

, aidhyti . 187. 
iKra,  xii.  4 1. 
add,  iv.  5 n. 
adtru,  xiii.  22  n.  , 
auryn , add.  n.  3. 
ad rynt/rah n n tidhikd ra,  iv.  26  n. 
i xdryutnnfiya , add.  n.  3. 

| adryaiirna.  x.  1 5 n. 

\ soma . add.  n.  3. 

■ xdmnya,  viii.  ] 6,  add.  n.  3. 
adurn,  i.  13,  xiv.  3 o. 
athiti,  iv.  15  n. 

at  him,  xiv.  6 n. 
af/tti/u.  viii  19. 
apnrfti,  iv.  1 5 n. 
spnahta,  ii.  58. 
apwht/ulhiknra,  l.  70  n. 

■ jtphtUa,  i.  60. 

! aphntnathilyardha , v.  17  n. 
j aphut  Hear  ana,  ii.  14. 

srotaa,  xii.  26. 

! avuti,  aviiti , 191.  * 

harija , v.  fti. 
hast  a,  i.  60  n,  190. 

| hdni,  xii.  72  n. 

* himadidhiti , himarapni,  himdiigu , add. 
n.  3. 

hirnnyagarhha,  xii.  15. 

IhiUabhuj,  viii.  12  D. 
hard , xii.  79  n. 


GENERAL  INDEX 


The  references  arc  as  in  the  preceding  Index'. 


Abhijit,  22nd  astcrisra — identification  etc.  Jl  Anur&dhfi,  17th  asterism — identification 
105;  omission  from  the  series,  208-1 0.j;  etc.,  102. 

Abu-r- Radian,  see  al-lliruni.*  j Anuvutsara,  4th  year  of  lustrum,  xiv.  17  n. 

Agkisha,  0th  asterism — identification  etc.,  A|Ktniyalsn,  name  of  star  (3-  Virginia),  viii. 

188;  its  last  quarter  unlucky,  xi'.  21.'  |.  A 21. 

Alvina,  6lli  or  7th  month— J i.  51  u,  xiv.  3 n,:  A pas,  name  of  star  (8  Virginia),  viii.  21. 

. 18  n.  | Aphelion,  p.  15 — see  Apsis. 

Ayvini,  1st  asterism — identification  etc.,1-  Apogee,  p.  15 — see  Apsis.. 

183.  , Apparent  longitude,  vii.  12  n;  termhow 

Ay viua,  divinities  of  1st  asterism,  183.  ! u-cd  hy  Uolchrooke,  viii.  J n.  f 

Aditi,  divinity  of  7th  nstcrisui,  187.  j Apsis — term  how  employed  in  this  work, 

AdiWa,  187  etc.,  xii.  28  n.  |.  p.  15:  upsides  of  the  "plane Is,  mode  of 

AOiiJT,  i.  19;  day  of  Brulmia,  i.  20;  names! j action, ii.  1-5  .revolutions, i.  l 1-42; how 

of  past  and  current,  i.  23  n.  V devised,  i.  44  ii;  positions,  acc.  to  dif- 

Agnstyii,  name  of  sLar  (C/nopus),  viii.  10.',  ferent  authorities,  i.  44  n;  compared 
Age — Great  Age,  or  Qiiiulri^  1(%  Age,  how  i with  Ptolemy's,  add.  n.  11. 
composed,  i.  15-17 ; Golden,  bdver,  Bra-];  For  nu ion's  apsis  see  Moon, 
xe.n.aiid  Iron  Ages,j.  17  n ; quarter- Age,1' Arab  astrology,  connection  with  Hindu, 
proper  period  of  this  treatise,  p.  16.  S',  vii.  23  n. 

Agni — divinity  of  3d  asterism,  1H4  ; with  Arab  use  of  sines,  later  than  Hindu,  p.56. 
iiAlra,  divinity  of  16th  asterism,  191  ; Arab  lunar  maiisions,  180;  identified  and 
name  of  star  (J  Tauri),  viii.  1 1.  compared  with  Hindu  and  Chinese,  183- 

Albategnius,  Arab  inventor  of  sines,  p.56.-  200;  character  and  origin  of  system, 

ul-Binlui — visit  to  India,  and  notices  of  203  etc. ; stellar  chart  illustrating,  add. 

liiudu  astronomy,  i.  3 n,  (in;  ideutitica-  ' n.  27. 

tiou  and  description  of  the  asterisms,  Arc — nafies  of,  and  of  its  functions,  add. 
181  etc.,  2U8.  n.  16:  part  of  arc.  determining  sine,  ii. 

['For  other  Arabic  mimes  commencing!  30 ; to  find  arc  of  a given  sine,  ii.  33. 

with  the  article,  sue  the  initial  letter  of,  Ardni,  6th  asterism — identification  etc., 
the  word  following  the  article.]  j.'  18.6,  add.  n.  26. 

Altitude,  sine  of— name,  111,  add.  n.  21 ;:  Arm  diary  splu-re  — construction,  cqtiip- 
how  calculated,  iii.  28-34, 34-36, 37-38 : 1 incut,  and  revolution  of,  xiii.  1-20;  its 
instrument  for  taking  altitude,  xiii.  21  u.  j use,  and  comparison  with  those  of  other 
Altitude  in  time,  iii.  39,  iv.  26.  !'  nations,  xiii.  3n;  its  adaptation  to  ob- 

Amplitude,  sun's  ut  horizon— sine  of,  iii.)1  serving  polar  luugitude  uiul  latitude, 
27:  measure  of,  on  the  dial,  iii.  7;  its>!  viii.  12  n. 

Voustant  ratio  Vj  hypoth.  of  slindow,  iii.  Aryubhatta — his  period  and  writings,  add. 

7 n ; how  calculated,  iii.  22-23,  27-28.  j n.  I ; references  to  his  doctrines,  i.  27  n, 
Amrta,  name  of  a yoga,  iuft.  n.  19.  I i.  60  n,  add.  n.  18 — see  Arya-Siildlid^ta, 
Anala,  24th  year  of  .1  ii|)iler’s  cycle,  i.  55  n. !'  Lagliu-  Arya-Su1  Mi  inta,  AryiUhtayata, 
Anainia — 22ud  year  of  JupiLer's  cycle,  i.  j Dnyagi  iku. 

55  n;  name  of  a yoga,  add.  n.  19.  Aryiibhatu-i,  commentator  on  the  Sfirya- 
Angirus,  40th  year  of  .Jupiter's  cycle,  i.  55  ii.  ! ttiddhai  m,  add.  u.  2. 

Angle,  a quantity  not  employed  in  llindu  jAryainan,  divinity  of  lltli  or  12th  aster- 
astronomy,  115.  i isin,  1 90. 

Anomalistic  revolutions  of  planets,  p.  63  Aryftshtayata,  treatise  by  Ary abhatta,  add. 
Anomaly,  mean — name,  ii.  29;  how  reck-  in.  1. 

oiied,  ii?  29  it.  : Arya-Siddh&ntn,  add.  n.  1 : citations  of  its 

Anqiietil  du  Perron,  notice  of  the  PArsi  | teachings,  p.  24,  i.  44  n,  add.  n.  6. 

asterisms  etc.,  ISO.  |Ascensip»~-see  Right  ascension  and  Ob- 

Antipodes,  Hindu  view  of,  xii.  51-53.  “ lique  ascension. 


344  S&rya-Siddhdnta, 

• 

Ascensional  difference,  how  calculated,  ii.  Atign^da,  6th  yoga,  ii.  65  n. 

61-62.  ul-Auwa’,  ltttli  mmiii,  190. 

Ascensional  equivalents — see  Right  ascen-  Avanti,  name  of  Ujjaytni,  i.  62. 

won  nnd  Oblique  ascension.  Ay  in-  A kbnri— orbits  of  the  planets,  as 

Ashadha,  20th and 21  si asterisms— identi-  given  by,  255  note;  description  of  in- 

fication  etc.,  194.  Blrument  for  measuring  time,  xiii.  28  n. 

Ash&dlia,  3rd  or  4th  month,  L 51  n,  xiv.  Ayushmant,  8rd  yoga,  ii.  65  n. 

3 ii,  16  n. 

Aspects,  unfavorable,  of  sun  and  moon,  nahudhanya,  46th  year  of  Jupiter's 'cycle, 
when  of  like  declination,  xi.  i.  55  n. 

Asterisma— Hindu  name  for,  207 ; how  to  Dnilly— his  views  of  Hindu  astronomy, 
be ’translated,  207,  add.  n.28:  their  por-  iutrod.  n.,  328;  mean  positions  of  the 
tions,  or  divisions  of  the  ecliptic  belong-  planets  at  Beg.  of  Iron  Age,  p.  18 : other 
- ing  to  them,  ii.  64, 179,  207 : their  junc-  references  to  his  works,  p.  74,  289. 
lion-stars,  179;  time  and  motive  of  su-  BAluva,  3rd  etc.  knmna,  ii.  69  n. 
lection,  207;  names,  arid.  n.  19:situa-  al-Bahlah,  21st  manzit,  195. 
tion  in  each  group,  viii.  16-19 ; mode  of  jlkmij,  7th  etc.  karana,  ii  69  n.  « 

definition  of  position,  viii.  In;  defined  Base  of  a right-angled  triangle,  ii.  80  b, 
positions,  viii.  2-9;  illustrative  figure,  | add.  n.  16. 

178;  discordance  of  authorities,  182;  Rose-sine  ss  sine,  ii.  30  n,  add.  n.  16. 
errors  of  position  examined,  and  time  of  jRase  of  the  gnomon-shadow,  iii.  5 n,  23- 
definition  deduced,  211;  mode  of  nb- 1 25'.  t 

serration  of  positions, viii.  1 2 n ; detailed  Ratn  al-FIAt,  28th  vnanz if,  109.  \ 

identification,  of  the  groups  nnd  thcirj;Ruvi&,  2nd  etc.  knnina.  ii.  69  n. 
junction-stars,  with  statement  of  name*.  |j  Bentley,  inlrori.  note ; his  views  or  Hindu 
symbols,  divinities,  defined  positions,;!  astronomical  literature,  i.  8 ii,  p.  24 ; 
etc.,  comparison  with  Arab  innnnzUv  method  of  determining  the  ngu  ftf  a Sid- 
al  kamar  and  Chinese  mVii,  1 83-200 ;!  dhfintft,  p.  20 ; allied  toSOryn-Siildhdn- 
additionnl  synonyms  of  names,  add,  n.i  ta,  and  conclusion  drawn,  p.  21 ; criti- 
26;  iimhility  of  Inter  Hindu  s to  point  cism  of  his  method  and  results,  p.  22  etc. ; 
them  out,  181;  iil-RirQni’a  inlb  mint  ion  general  estimate  of  his  labors,  p.  2-f,  add. 
respecting,  tile m,  181  etc.,  208,  209;  n.  8 \ his  view  of  Hindu  precession.  1 (m  ; 
conspectus  of  correspondences  of  the  of  asterisms,  194 ; other  citut ions  from 
throe'  syftems,  200  ; stellar  map  illus-  and  references  to  his  works,  p.  18, 19, 28, 
tnitif^  their  relations,  ndd.  n.  27;  Bi-  74,  108,  add.  n.  1,  4,  6,8,  326. 
ot’s  views  of  their  origin  and  connec-  Bhi&flrftgvn,  name  of  a clime,  xii.  36. 
tion,  201  etc. ; age  of  the  syBtem  in  in-  BliAdrapuri.'i,  26th  nnd  27th  asterisms — 
dia,  203;  discussion  of  its  character,  identification  etc.,  197,  add.  n.  26. 
connections,  and  origin,  203  etc. ; trans-  Dhfidnipadn,  6th  or  6th  month,  i.61  u,xiv. 
fer  of  first  rank  from  Krttikfi  to  A9vini,  3 n,  16  n. 

206;  relation  to  the  moon,  208,  add.  n Bhngn,  divinity  of  11th  or  12th  osterism, 
28 ; variation  in  number,  uud  omission  190. 

of  Abhijit,  203.  Bliarani,  2nd  osterism — identification  etc., 

conjunction  of  planets  with  asterisms.  184.’ 

vin.  14,  15;  systems  of  yogas  founded  Blulruta,  name  of  a clime,  containing  In- 
upon,  212,  add.  n.  19;  heliacal  setting,  dia,  xii.  89. 

ix.  12-15,  17-18;  orbit  and  revolution,  Bhuskaro,  add.  n.  1 — see  SiddhAnto-Ciro- 
xii.  73,  80,90  n.  mnpi. 

At-rology— generally  treated  in  distinct  Blifiva,  42nd  fear  of  Jupiter’s  cycle,  i.  56  a 
works,  vii.  23  o;  titles  of  astrological  Bhoju-Siddliiintn,  add.  n.  1. 
works,  vii.  23  n;  connection  of  Hindu  Ulirgyn  (1  Vrshyal)  49th  year  of  Jupi- 
wiili  Greek  and  Arab,  vii.  23  n:  astro  tor's  cycle,  i.  55 n. 
logical  import  of  conjunctions  of  plan-  BhQrilinni,  commentator  on  SArya-Sid- 
ets,  vii.  18-23;  of  splitting  of  lloliinfV  dhAnta,  add.  n.  2. 
wain,  viii.  13  n;  of  equality  of  declina-  Bija,  correction  of  mean  motions  of  plan- 
tion  of  sun  and  moon,  xi ; of  Bun's  en-  its,  p.  19  etc.,  i.  9n ; table  of  mean  mo- 
trance  into  a sign,  xiv.  1 1.  tions  as  so  corrected,  p.  20,  add.  ii.  7. 

Astronomy— see  Greek  astronomy,  Hindu  Blot — Ilia  views  of  origin  and  history  of 
astronomy.  Chinese  lira,  181, 201  etc.;  of  Hindu  bs- 

Aationomical  literature  of  Hindis,  sum-  terisms,  206  etc. ; of  omission  of  Abhijit, 
maiy  view  of,  add.  n.  1.  208 ; of  Hindu  Bines,  odd.  n.  16 ; other 


General  Index. 


545 


references  to  and  citations  from  his 
works,  i.  44  ft,  i 87  n,  115,  odd.  n.  10, 
17. 18, 21, 28, 29. 

Brahma— day  of,  i.  20;  length'  of  hw  life, 

&.  21 a,  time  of,  xiv.  21 : divinity  of  22nd 
astor'ism,  105 : name  of  star  (5  Auriga), 
viii.  21  li : 25tli  yoga,  ii.  66  n. 
Brahmagupta,  i.  3 n,  add.  n.  1— see  Brahma- 
•phuta-SiddhAnta  and  Khatydu  Kntaka. 
Brahmahrdaya,  name  of  star  (CapelU), 
viiL  11-12. 

Brahina-SiddhAnta,  add.  n.  1,  G. 
Bnihmn-spliuta-SiddhAnla,  add.  n,  1 ; its 
system,  hoar  different  from  Sdrya-Sid- 
dhAntu,  add.  n.  6 : references  to  its  doc- 
trines, i.  3 n,  40  ii,  60  n,  102,  182  etc., 
viii.  12  n,  add.  n.  18. 

Brlinapati,  divinity  of  8th  nsterism,  187. 
Brliaspati-SiddhiUiia,  add.  n.  1. 

BudhavAra,  Wednesday,  i.  52  n. 
al-hula’,  23rd  mauzil,  106. 
al-Butain,  2nd  mmusit,  184. 

Cabnakalpadruma— its  list  of  SiddhAutas, 
add.  ii.  l.  * 

Cuitra,  12th  or  1st  month,  i.  51  d,  xiv.  3 n, 
16u. 

(Vikalya-SanhitA,  add.  n.  1 : references  to. 
181,  182  etc.,  213,  217,  218,  add.  n.  6, 
etc. 

(,'akuJii,  58th  knrnna,  i.  69  n. 

Calendar,  .sketch  of  a Hindu,  for  the  year 
1850-60,  i.  51  n. 

^Alivuhnea,  ora.  of,  add.  n.  12. 

(j'anivura,  Saturday,  i.  52  n. 

Cara,  name  of  a yoga,  add.  n.  10. 
yarad,  autumn,  xiv.  10n,  16  n. 

Cardinal  directions,  names  of,  vi.  12  n. 
^iirviiri,  8th  year  of  Jupiter’s  cycle,  i.  55  n. 
^.itahlusliaj,  25th  asterisin — identification 
etc.,  107. 

Gatiislmada,  60th  karana,  ii.  60  n. 

Central  ecliplic-point,  v.  In;  sines  of  its 
altitude  and  zenith-distance,  v.  5-6. 
Chang,  0th  mcii.  190. 

Cltattra,  name  of  a yoga,  add.  d.  10. 

Clre,  24  th  «iA,  109. 

Chin/llth  *ieu,  100. 

Chinese  astronomy  and  division  of  the 
heavens— see  Sieu. 

Chord  of  an  arc,  p.  67,  xiii.  13  n,  add.  n.  16. 
Chronological  cycles,  i.  15-21 ; eras,  add. 
n.  12. 

ifira,  cool  season,. xiv.  10  n,  1 6 n. 
ircle— name,  ii.  33  n ; divisions  of,  i.  23 ; 
ratio  of  diam.  to  circumf.,  i.  60  n,  p.57. 
CitrA,  14th  asterisin— identification  eta, 
190. 

CitnibhAnu,  50tli  year  of  Jupiter  s cycle, 
i.  55  n. 

Qiva,  20th  yoga,  ii.  65  n. 

Civil  time,  day— see  Time,  Bay. 


<?loka,  common  Hindo  verse,  introd.  n. 
(jobhnna— 1 1 th  year  of  Jupiter's  cycle,  i. 

55  n;  5th  yoga,  ii.  65  n. 

Co-latitude,  terrust  rial— name,  i.  60  n;how  1 
found,  iii.  13-14, 14-17. 

||Colebrooke,  introd.  n.:  his  atatevnent  of 
the  systems  of  yogas,  ii.  66,  add.  n.  19; 
identification  etc.  of  the  asterisma,  180 
eta ; information  as  to  astronomical  lit- 
erature, add.  n.  1 : other  rcfcrenres’to 
and  citations  from  his  works,  i.  27  n, 
p.  23, 3V,  101  etc.,  viii.  1 n,  10-12  n,  12ny 
19  n,  21  n,  xiii.  3 n,  5 n,  xiv.  16  n,  add. 
n.  2,6,  10,18. 

Color  of  moon  when  eclipsed,  vi.  23. 
Commutation,  mean— name,  ii.  20  n;  how 
reckoned,  ii.  20  n. 

Conjunction  of  a planet— term  how  em- 
ployed in  this  work,  p.  24 ; mode  of  ac- 
tion on  the  planet,  ii.  1-5 ; revolutions, 
i.  20-32  ; orbits,  xii.  85-86. 

Conjunction  aud  opposition  of  sun  and 
moon,  common  name  of,  iv.8  n : true  and 
apparent  conjunction,  nnmes  of,  v.  13  n.  • 
Conjunction  of  planets 'with  one  another, 
vii;  with  listeria  mu,  viii.  14-15;  nunfe, 
general,  vii.  1 n;  particular,  astrological, 
vii.  18-20,  22:  conjunction  viewed  as 
1 taking  place  on  •secondary  to  prime 
vertical,  vii.  6n:  time  and  place  how 
calculated,  vii.  2-11;  illustrative  ob- 
servations of  conjunctions,  vii.  15-18. 
Contact  of  disks,  or  disk  and  shadow,  in 
eclipses,  iv.  15  n;  time  of  first  and  last 
contact  how  determined,  iv.  16. 

Cosine — not  distinctly  recognized,  p.  66,  ii. 
30  ii ; term  corresponding  to,  ii.  30n, 
add.  n.  1 6 ; part  of  arc  determining  co- 
*inc,  ii.  30. 

Cosmogony,  development  of  creation,  xii. 
10-28. 

^ruvniui,  23rd  osterism— identification  etc., 
196,  odd.  n.  26. 

CrAvniui,  4th  or  5th  month,  i.  61  n,  juv. 

3 ii,16  n.  * 

£nivi$hlli.aL,  24th  asterism— identification 
etc.,  106. 

Creation,  time  spent  by  the  Deity  in,  i. 
24 ; us  given  by  other  treatises,  i.  44t> ; 
reason  of  this  allowance,  p.  18. 

^rfdhara,  ratio  of  diam.  to  circumf.  accord- 
ing to,  i 60  n. 

^-rimukha,  list  year  of  Jupiter’s  cycle,  i. 
55  n. 

^risheiia,  author  of  Romaka-SiddhAota, 
gdd.  n.  1. 

rfvatsa,  name  of  a yoga,  add.  n.  19. 
ubha— 23rd  yoga,  ii.  66  n ; name  of  a 
[I  yoga,  add.  n.  19. 

(^ubhakrt,  10th  year  of  Jdpiter's  cycle,  i. 
55  n. 

IlCubit,  i.  60  n,  iii.  5 n. 


U6 


Sttrya-SidtUtdnla, 


t'ukla— 37  th  year  of  Jupiter’s  cycle,  LIIDegree  of  a circle,  i.  28. 

65  n;  24  tli  yoga.  ii.  05  n.  iDelambre,  references  to  and  citations  from 

(JukravfLra,  Friday,  i.  62  a.  his  works,  introd.  n.v  p.  66, 66, 106,  vii. 

* Cikla/tith  yoga,  ii.  65  n.  n 14  n,  add.  n.  16, 17, 18. 

Cusps  of  the  moon— name,  x.  1 n,  16  n . 'Dhfttar,  44th  year  of  Jupiter's  cycle,  i, 

0-8;  de- 


their  elevation  calculated, 
lineated,  x.  10-15. 

Cycle — of  A vc  years,  i.  58  n ; names  of  its| 
years,  xiv.  17  n : of-  sixty  years  of upi- 
ter,  i.  65:  of  twelve  years  of  JupiLer, 
xiv.  17 : their  relation,  xiv.  17  u : vaster j 
chronological  cycles,  i.  15-21 


66  n. 

te-D]li^■Vl  7 tli  manzil , 187. 

;ti,  8th  yoga,  ii.  66  n. 
jDhruva,  12th  yoga,  ii.  66  n. 
jDhdmra,  name  of  u yoga,  add.  n.  10. 
Dhvaja,  name  of  a yoga,  add.  n.  19. 
Dliviinkslia,  name  of  ji  yoga,  add.  n.  10. 
Dial,  construction  of,  iii.  1-7. 

arT-Dabar&n,  4th  manzil,  185.  * jj  Diameter,  relation  of  to  circumference,  i. 

DagagitikA,  treatise  by  Aryabh.it  la,  ndd.:|  COn,  p.  57. 

U.  1.  ” | Digit,  iii.  6 n ; measure  of  the  gnomon  fr, 

DiulA  Illiai.  commentator  on  Silryn-Sid-jj  iii.  5n;  equivalent  in  minutes,  in  pro- 
dli.inta,  add.  n.  2.  j jetting  an  eclipse,  iv.  26 ; measure  of 

Daily  motions  of  planets  etc.,  i.  25-27  ; of  j the  moon's  disk  in,  iv.  1 1 n,  x.  9 n. 

equal  absolute  amount  on  each  orbit /.Directions  on  the  sphere,  how  reckoned,  " 
xii.  90  n:  tables  of  mean  daily  motions1!  187,  vii.  6n:  cardinal  directions,  vi. 
p.  17,  20,  add.  n.  5,  7 ; mean  motions  in!!  12  n. 

Bidefeal  day,  291  : true  duily  motions,  Diurnal  circle,  radius  of,  how  calcuVitcd, 

. how  calculated,  ii.  47-51 ; comparative:!  ii.  60.  * 

table  of.  for  Jan.  1.  I860,  p.  87.  jjDundiihlii,  30tli  yAir  of  Jupiter's  cycle, 

Davis,  references  to  and  citations  from  liis ! i.  55  n. 

essays  in  A>iatic  Itesearclie*,  introd.  n.JjDurutinn  of  an  eclipse,  name  of,  iv.  15  n; 
p.  19,  i.  55  n,  p.  51,74,  xiv.  16  n,  17  n,  ■ how  determined,  iv.  12-15,  v.  13-17. 
add.  n.  17.  289,  29(^  311.  ; Durmati,  29th  year  of  Jupiter's  cycle,  i. 

Day— civil  d.iy,  how  reckoned,  i.  36,  xiv.  | 55  n. 

18;  number  of  in  an  Age,  i.  37  ; varying  Durniukha,  4tb  year  of  Jupiter's  cy.lc,  i. 
length  in  different  seasons,  xii.  45-71:  05  n. 

lunar  day,  i.  13 ; number  of  in  un  Age, 

i.  37 ; its  portion,  ii.  6-1 : curi  e nt  i.ne  how  Earth — form,  position,  and  support,  xii. 
determined,  ii.  66:  oinillcd  lunar  days,  j 32;  apparent  form,  xii.  54;  it*  revolu- 
i.  36 ; number  of  in  an  Age,  i.  38 ; liowj 
•calculated  fur  a given  period,  i.  50:  sid-  ; 

(•real  day,  xiv.  15;  its  divisions,  i.  11- 1 
12;  number  of  in  an  Age,  i.  31 : solar- 
day,  xiv.  3 n : day  of  the  gods,  i.  13-14,  [ 
xii.  45,  47-51,71,  xiv.  20;  day  of  the. 

Fathers,  xii.  77  n,  xiv.  14  ; day  of  lJrn- ! 
jApati,  xiv.  21;  day  of  llrahma,  i.  20,  'Earth's  shadow,  diameter  how  calculated, 
xiv.  21.  iv.  4-  5. 

Dayiofa  planet,  i.  81,  ii.  59 ; its  divisions.  Earth -sin.*1,  ii.  01. 

ii.  62-65.  East  and  west  direction  on  the  sphere,  137. 

Day-measure,  iii.  55  n.  ; East  and  west  hour-circle,  iitti,  xiii.  nfn. 

Day-radius  ii.  60.  ( East-|Kiint,  138,  add.  n.  23. 

D|y  sine,  ii.  GO  ii.  ! Eccentric  circle,  equivalent  to  Hindu  epi- 

Declination — name,  p.  46 ; reckoned  as  in  1 cycle  of  np>ia,  p,  64. 
the  ecliptic,  p.  40,  viii.  1 n;  bow  caIcu-  'Eccentricities  of  planetary  orbits,  compnr- 
l.ited,  ii.  28  ; how  combined  with  Juti-  j alive  table  of,  p.  76. 
tude,  ii.  58;  com  para  live  table  of,  fur  Eclipses — name,  iv.  6n;  rules,  applying 
Jan..  1 I860,  p.  87  : how  found  by  oh- 1 to  sola r aiifJ  lunar,  iv;  rules  for  jinml- 
servatiou,  iii.  1 7- IS.  a jl  lux.  applying  to  solar,  v ; projections  of 

Declination.  equal,  of  the  sun  and  moon—  j ic  I ipnun,  vi : primi'ivc  theory  of  cause 
tiin&  how  calculated,  aud  a^trfjJoglcuJi  of  uclipse,  iv.  tin,  lln:  true  theory,  iv. 
influence,  xi.  •;  9 ■.  occurrence  gf  annular  eclipse  nut 

nl  erVpfa  twin  an  n*\.  wV  x.  Yta\  cjAcuWvvmv  nt  t 

in- projection  1 4 i- i:\ipitt,  iv.  21-25:  Iriw  «-.4q»l-.  *4-1  nfiijciliuli  of  6 *6 

# projected,  vi.  2-9.  mu  ulq**,  157. 


tion  taught  by  Arynhhutta.  i.  27  n;  di- 
mensions, i.  59;  centre  and  surface, 
terms  for,  142;  poles,  xii.  3 1-35;  geo- 
graphical divisions,  xii.  36-40;  zones, 
xii.  59-C9 ; cavities  within  it.  xii.  83; 
measurement  by  urclus  and  arcs  not  ap- 
plied to,  i.  65  n. 


General  Index. 


fEdiptic-nwne.  xjii.  18d;  polo,  143;  di-ljGeopuph/,  xii.  84-48;  of  Puriw,  m. 

l\icir  equatorial  uquiva->]  44  n.  ■ “ni¥w,» 

lwta,  fit.  42-45 : inclination,  ii.  28 ; ori-  nl-GImfr,  15th  manril,  191. 

ent  nncl  meridian  points,  iii.  46-49 ; cen-  \Gnonnni,  in.  1 , 5 n.  • 

tral  point,  y. 1 n:  deflection  from  east  jGoei,  23rd  aicu,  197.  • ' 

and  Treat  direction  at  a given  point,  iv.  Graha-LAghava,  add.  n.  1 ; its  definition  of 
24-25.  position  of  the  astcrisms,  182-198;  of 

Elements,  five.  xii.  28.  fixed  stars,  xiii.  12  n,  21  n. 

Entrance  of  the  Bun  into  a sign,  astrolog-  Greek  astronomy,  relation  of,  to  Hindu, 
ical  character,  xiv.  3, 1 1.  _ 327  etc.— see  Ptolemy. 

Epicycle— name,  ii.  88  n:  dimensions*  for  Greek  words  in  Hindu  tcchnicallanguoge, 
all  {lie  planets,  ii.  34-3^1  change  of  di-  i.  28  n,  52  n,  ii.  80  n,  iii  84  n(  830. 
mentions,  ii.  38  n,  p^lfi,  add.  n.  18;  cpi-  Grfrhma,  summer,  xiv.  10  n,  16  n. 
cycle  of  apsis  equivalent  to  eccentric  Qddlulrtlinprakfl^aka,  nqjne  of  llangan'ft- 
orbit,  p.  Gi : relative  dimensions  of  orbitH  tiin’s  commentary  on  the  Sflrya-Sid- 

deduced  from  epicycles  of  conjunction,  dliunta,  in  trod.  n. 
p.  76 ; comparison  of  Greek  and  Hindu  OuruvAra,  Thursday,  i.  52  n. 
system^  p.  74 ; Greek  origin  of  the 

method,  329.  al-Hak'ah.  5th  manzil,  180. 

hquntiou  of  the  centre— how  calculated,;  Hall,  F.  K. — liin  edition  of  SArraSiddMn- 
11.  89  ; Ploh'iivy’a  mclliod,  for  nun  mid,  ta,  introd.  n,  add.  n 1. 
moon,  p.  67 ; for  other  planet*,  p,  78  :'.B|.Han’ab,  6th  manzil,  186. 
ho*  applied,  with  hiiiiiuiI  equation,  m 'Harshnqn.  14th  yoga,  ii.  G5n. 
filling  true  plneca  of  lower  planets,  ii.|  Hastn,  isth  nstcrism — identificatiBn  etc., 
43-  i 5 ; compurutivc  table  of  value  whenM  j Qq 

greatest,  p.  76.  ijlfonMlnmba,  5tli  year  of  ’Jupiter's  eyefe. 

Equation  of  the  orb,  or  annual  equation — j j_  55  n- 
liow  found,  ii.  40-42  : Ptolemy’s  metli-  lncmants'i,  winter,  xiv.  10  n,  16  n. 

0(1,  p.  73:  how  applied,  with  equation  I Hemisphere — name,  v.  17  n;  eastern  and 
of  centre,  ii.  43-45.  1 western,  of  heavens,  v.  17  11;  northern 

Equation  of  time,  correction  fur,  11.  46;  and  southern,  of  earth,  xii.  45,46. 

■ 1 _ . n2 ■ ■:  ...  _ non  1 __  .....  ...  _ • 


its  insufficiency,  ii.  46  11.  293. 


1, Heliacal  settings  and  risings — of  planets. 
Equation  of  motion  of  a planet,  ii.  47-51.1  \Xm  i-n  ; distance  from  sun  of  omir- 
Equator,  celestial,  iii.  6.  ;!  reiicc.  i*.  6-9;  calculation  of  time,  ix. 

Equator,  terrestrial,  21S.  '!  10-U,  16:  of  uterimw,  ix.  12-17;  ns- 

Equinoctial  sliadow,  iii.  7,  12-13  ; bow  j terisms  which  neVcr  set  lieliacally,  ix. 

found  from  latitude,  iii.  17.  jj  in:  of  moon,  x.  1. 

Equinox,  iii.  6 11:  precession  of — see  Prc‘ji Hindu  astronomy,  discussion  of  its  origin, 
cession.  ij  ago,  and  relation  to  the  Greek,  add. 

Eras  in  practical  use  among  Hindus,  add.j  n 30 

n.  12-  „ JiHiii,  22nd  tint,  197. 

Ether,  fifth  element,  xii. 23  ; orbit  of,  xii.,;U0h<iiigtonl  H.  R. — his  Oriental  Astrono- 
30.  81,  90.  | mer  cited,  introd.  n.,  ii.  13  n,  p.  74. 

EvecLion,  nut  noticed  by  Hindus,  p.  07.  ; Horizon,  iii.  49 11. 

if  lour— name,  Lfitin;  succession  of  regents 
Twig,  1 5th  si>vr.  1 92.  ! of,  xii.  79. 

al-Tiirgli  al-Mukdiin,  2fith  manzil , 199.  jHour-nngle,  distance  in  time  from  meridi- 
al-Fargh  al-Mukhir,  27th  manzil,  190.  an,  iii.  34-36;  corrected  hour-angle,  140 ; 


30.  81,  90. 

EvecLion,  nut  noticed  by  Hindus,  p.  C7. 

Fang,  15th  192.  ! 

nl-T’nrgli  al-Mukdim,  26th  manzil , 199.  j 

al-Pargh  al-Mukhir,  27th  manzil , 190. 
Fathers,  or  Manes — divinities  of  10th  ns- 
terisin,  188;  their  station  and  day,  xii. 
74,  xiv.  14.  | 

Fixed  stars — names  and  defined  positions.! 
of  certain,  viii.  10-12,20-21 ; their  idea®; 
tifieation,  viii.  12  n.  21  n.  jj 

Full  moon,  day  of,  ii.  06  11.  • //' 


Kim's  hour  angle  how  determined  frAn 
observation,  iii. -37-39. 
ypothenuse — name,  iv.  21  n : hypoth.  of 
sliadow  'if  gnomon,  iii.  8;  constant  re- 
lation to  n ensure  <u  amplitude,  iii,  7 a 


Full  moon , day  or,  ii.  66 11.  • jil^vam,  45th  rear  of  Jupiter's  cycle,  i. 

jj  56  n. 

Gadn,  name  of  a yoga,  add  n.  IP.  (JdAvntsara,  3rd  year  of  lustrum,  xiv.  Ifn. 
Honda  lnth  yoga,  ii.  68  n.  ldelcr— identifications  of  Arab  manSzil, 

.1  -j,**  4li  „ jm  0[  u*™, 

2— at .. ..  VSi’A  — • 


Gam,  6th  etc.  knra^ia,  n.  69  n. 
Gwgn,  Garga  Siddhunta,  odd.  n. 


318 


S&rya-Siddh&nla , 


Inclination — of  planetary  orbits  to  ecliptic, 
i 68-70 ; comparative  tabic  of,  i.  70  n : 
of  ecliptic  to  equator,  ii.  28. 

Indm — 26 tli  yoga,  ii.  65  n : divinity  of 
18  th  asterism,  193;  of  others,  lb7  ; with 
Agni.  of  16th,  101. 

Inequalities  of  planetary  motions— how 
produced,  ii.  1-8;  why  of  different  de- 
grees, ii.  9-11. 

Instruments — arm  ill  Ary  sphere,  xiii.  1-20, 
viii.  12  n;  other  instruments  for  meas- 
uring time,  xiii.  20-24 ; for  taking  alti- 
tude, xiii.  21  n ; for  taking  xeni ill-dis- 
tance at  median  transit,  viii.  12  n. 

Iron  Age.  i.  17  n ; its  commencement,  p.  17 ; 
how  determine^  p.  18. 

aj-Jabliah,  10th  manzit , 189. 

JambQdvipa,  cent  ml  continent  in  Puranic 
geography,  xii.  44  n.  ■ 

Jaya^  2nd  year  of  Jupiter’s  cycle,  i.  55  n. 

Jenna,  his  Weights,  Measures,  and  Coins 
of  India,  introd.  n. 

Jn:\na4lhft*kara,  reference  to,  i.  6 n. 

Jflrinn-rAja,  author  of  Siddhanta-SuilUara, 
add.  n.  1.  j 

Jones,  Sir  W.,  references  to  and  citations^ 
from  his  works,  180, 181,  xiv.  16  n,  add. 
n.  1.  | 

Jupi  ter— name*,  revolutions,  «»tc.p  etc.,  sec 
Planets— Jupiter's  cycle  of  sixty  years,| 
i.  55;  of  twelve  years,  xiv..  17;  their' 
relation,  xiv.  17  n. 

Jyfohtha,  2nd  or  3rd  month,  i.  51  n,  xiv. 
8 n,  16  ii. 

JyeshthA,  1 8th  asterism— identification  etc., 
192 ; its  last  quarter  unlucky,  xi.  21. 

Jyotisha,  astronomical  treatise,  i.  3 n. 

Kftladnnda,  name  of  a yoga,  add.  n.  19. 

KAlayukta,  26th  year  of  Jupiter's  cycle, i. 
55  n. 

nl- Kalb,  18th  man  it  l,  193. 

Kamaldknra,  author  of  Tattva-Viveka, 
add.  n.  1. 

Kan  a,  name  of  a yoga,  add.  n.  1 9. 

Kang,  13th  nien,  191. 

Karatya,  half  a lunar  day,  ii.  67-69. 

fcarttika.  7th  or  8th  month,  i.  51  n,  xiv. 
3n,  16  n. 

. Kiulara,  4th  etc.  karana,  ii.  69  n. 

Kctu,  moon's  descending  node,  ii.  8 n. 

Ketumlln,  a clime,  xii.  89. 

Klia^fla-Kataka,  treatise,  or  chapter  of  one, 
by  Brahmagupta— cited  by  al-BirOni  re- 
specting osterisms,  181  etc.,  208,  209. 

Khom,  59th  year  of  Jupiter's  cycle,  L 55  n. 

Kt,  18th  s ieu,  19ft. 

Kilaka,  1 6th  year  of  Jupiter's  cycle,  L ft  5 n. 

Kifistuglina,  1st  karaya,  ii.  69  n. 

Kio,  12  th  lieu,  191. 

Koei,  26th  lira,  199. 


Krodhana,  83rd  year  of  Jupiter's  cycle,  ira 
6ft  n. 

Krodhin,  12th  year  of  Jupiter's  cycle,  i. 
65  n. 

Krttikii,  3rd  asterism — identification  etc., 
184 ; formerly  first  of  the  series,  i.  27  n, 
206. 

Kslmya,  34  th  year  of  Jupiter’s  cycle,  i. 
55  n. 

Kuci,  6 th  wcu,  1S7. 

Kigu,  a clime,  xii.  40. 

Kurukshctra,  jpgioii  in  India,  i.  62  y. 

LA  (Ilia,  astronomical  authority,  i.  3 n. 

Lngadha  or  Lugatn,  author  of  Jyotisha,  i. 

8 n. 

Lnghu-Aryn-SiddhAnta,  odd.  n.  1;  cita- 
tions and  references,  p.  24,  add.  n.  6. 

Lambnkn,  name  of  a yoga,  add.  n.  19. 

LankA,  i.  62  n,  xii.  39. 

LAtn,  culled  by  itl-BirQni  author  of  Surya- 
SiddhAnta,  i.  3 n. 

Latitude,  celestial — name,  i.  70  n,  id  21  n ; 
how  measured,  i.  70  n,  viii.  1 n;  .nean 
greatest  latitude  of  planets,  i.  68-70 : 
latitude  of  planets  how  calculated,  ii. 
50-57  ; bow  combined  with  declination, 

ii.  58. 

Latitude,  terrestrial — name,  i.  60  n;  how 
ascertained  by  observation  of  shadow, 

iii.  13-14,  14-16 : qrcumf.  of  earth  on  a 
parallel  of  latitude,  how  found,  i.  50. 

Leu,  27tli  aiew,  184. 

Li,  Chinese  measure  of  distance,  i.  60  n, 
add.  n.  13. 

Lieu,  7lli  ziev,  1 88. 

Lokriloku,  boundary  of  the  earth,  xii.  44  n, 
xiii.  16n.  * 

Longitude,  apparent— term  how  employed, 

[ vii.  12  n ; how  found,  vii.  7-11. 

Longitude,  celestial,  of  a planet — no  name 
for,  i.  53  n ; mean  longitude  how  found, 
".  53,  54,  60-61,  67;  true  longitude 
how  foiind,  ii.  39-45 : sun's  true  and 
mean  longitude  how  determined  from 
observation,  iii.  17-20,  40-41. 

Longitude,  polar— term  how  employed  in 
this  work,  viii.  1 n ; polar  longitudes  of 
aaterisma,  viii.  2-6 ; of  certain  fixed 
iters,  viii.  10-11,  20-21. 

Longitude,  terrestrial  — name,  i.  61  n ; 
whence  measured,  i.  62;  how  deter- 

< mined,  i.  63-65 ; measured  in  yojanas, 
i.  65  n. 

Lunar  time,  day,  month— see  Time,  Djy, 
Month. 

Lustrum,  cycle  of  five  rain,  i.  68  n ; 
names  of  its  years,  xiv.  17  n. 

Mackenzie  collection — see  Wilson. 

Maghft,  10th  asterism— identification  etc., 
188,  add.  n.  26. 


General  Index. 


849 


M&gha,  10th  or  11th  month,  i.  51  n,  zir. 
3 n,  16  n. 

Maitraf  name  of  a yoga,  add.  n.  19. 
Mallik&rjuna,  commentator  on  SQrya-Sid- 
dhftnta,  add.  n.  2. 

Mammabhatta,  commentator  on  Sfltrya- 
Siddhftnta,  add.  n.  2. 

Mdnasa,  name  of  a yoga,  add.  n.  19. 
Manazil  al-kainar— see  Arab  lunar  man- 
sions. 


Mangalavftra,  Tuesday,  i.  52  n. 

Mamnatba,  3rd  year  of  Jupiter’s  cycle,  i. 

Manu,  citations  and  references,  i.  12  n, 
17  n,  19  n,  23" n,  xii.  28  n,  xiv.  14  n. 

Mao,  1st- sick,  185. 

Miirga^irshsi,  8th  or  9tli  month,  i.  51  n. 
xiv.  3 n,  16  n. 

Mars,  names,  revolutions,  etc.,  etc. — see 
Planets. 

Mntanga,  name  of  ayogn,  add.  n.  19. 

Maya,  recipient  of  revelation  of  Siirya- 
Siddhiiiita,  i.  2,  4,  G n,  7,  xii.  1,  10,  xiv. 

1 24  #7  ; conjectured  identity  of  his  name 
wim  that  of  Ptolemy,  i.  6 n. 

Mean  motions  of  planets — sec  Daily  mo- 
tions etc. 

Mean  places  of  planets — see  Longitude. 

Measure  of  amplitude,  iii.  7. 

Mercury,  names,  revolutions,  etc.,  etc. — 
see  Planets. 

Meridian— nu  distinct  name  for  in  text,  xiii. 
15  n ; name  in  commentary,  139,  xiii. 
15  n. 

Meridian  ecliptic  point,  iii.  49,  v.  4-5,  9 n. 

Meridian,  prime — situation  of,  i.  62 ; why 
chosen,  i.  62  ii. 

Meridian-sine,  v.  5. 

Mem — poles  of  the  earth,  xii.  34-35 ; ill 
Puranic  geography,  xii.  44  n. 

Minute  of  arc,  i.  28. 

Mitra,  divinity  of  17th  aster  ism,  192, 

Month — civil,  i.  12:  lunar,  i.  13;  number 
in  an  Age,  i.  35;  names  of  those  corn- 


month,  i.  51  n:  intercalary  months,  i. 
So  ; number  in  a given  period  how  cal- 
culated, i.  49 : lunar  month  a day  of  the 
Fathers,  xii.  74,  xiv.  14 : sidereal  month, 
i.  12 : solar  month,  i.  13 ; number  in  an 
Ag<J,  i.  39 ; names,  i.  61  n,  xiv.  16  n ; pre-  j 
cise  length  of  the  several  *Bolar  months, 
xiv.  3 n ; division  into  seasons,  xiv.  1 6 n. 

Moon — names,  revolutions,  etc.,  etc.,  see 
Planets— Moon's  apsides  and  nodes,  revo- 
lutions in  an  Age,  i.  33 ; mean  daily  mo- 
tions of,  p.  17,  20,  add.  n.  6,  7 ; in  side- 
real day,  291 ; positions  at  beginning  of 
Iron  Age,  p.  18,  add.  ti.  6 ; orbits,  xii.  87- 
88 : moon’s  dimensions,  iv.  1 ; mean  ap- 
parent diameter,  distance,  and  horizon- 
tal parallax,  iv.  1 n ; orbit,  iv.  1 n,  xii. 


45 


85  ; apparent  diameter  how  calculated, 
iv.  2-.T;  conciser  method,  312 : moon'd 
heliacal  setting  and  rising,  x.4 ; tjmeof 
rising  and  setting,  how  calculated,  X.-.2- 
5 ; elevation  of  cusps,  x.  6-8 ; to  deter- 
mine illuminated  part  of  disk,  x.  9 ; to 
delineate  illuminated  part, and  elevation 
of  cusps,  10-1 5 : moon  the  divinity  of 
5th  nsterism,  1 85 ; relation  to  system 
of  astcrisins,  207,  add.  n.  28 ; equality  of 
declination  with  sun  nnpropitious,  xi.  1 
etc. ; station  of  tlic  Fathers,  xii.  74. 

Motions  of  plauctB — sec  Daily  motions, 
Inequalities. 

MrgayirshsL,  5tli  astcrismr—  identification 
etc.,  185,  add.  n.  26. 

MrgavyAdha,  mime?  of  star  (Sirius),  viii. 

10  -11,  add.  n.26. 

Mrtyu,  name  of  a yoga,  add.  n.  19. 

Mudgara,  name  of  a yoga,  odd.  n.  19. 

Muliurta-Cinlumani,  cited  respecting  &*- 
terisms,  181  etc. 

MuTiQrtorMuld,  cited  respecting  Ahhijit, 
210. 

Milla,  1 9 th  QBtcrism— identification  etc.,1 83. 

Muni^vara,  author  of  SiddbAnla-SArva- 
bhiiuma,  add.  n.  1,  2. 

Musala,  name  of  a yoga,  add.  n.  19. 

nn-Na'Aini,  20lli  mans'll,  195. 

NAdi,  sixtieth  pnrt  of  sidereal  day,  i.  11. 

NViga,  59tli  knrinia,  ii.  67,  69  n. 

mi- Nil jm,  3rii  warn'd , 185. 

Nandana,  GlHli  year  of  Jupiter's  c yde,  i. 
55  n. 

Nnradn,  NArnila-SiddhAnta,  add.  n.  I. 

Nfiradi-Sanliita,  add.  n.  1.  * 

iin-Nathrah,  8th  wanzil,  187. 

New  moon,  day  of,  ii.  66  n. 

Nicu,  20th  i lieu,  196. 

mi-lfiyAt,  stars  in  Scorpio,  193. 

Node  of  a planetary  orbit — name,  i.  34  n, 
xi.  5 n ; only  ascending  node  spoken  of, 
i.  34  ii ; names  of  ascending  and  de- 
scending nodes,  ii.  8 n,  216;  mode  of 
action  on  the  planet,  ii.  6-8 ; revolu- 
tions, i.  42-44 ; how  devised,  i.  44  n ; po- 
sitions, ncc.  to  different  authorities,  i. 
44  u ; compared  with  Ptolemy's,  add.  n. 

11  ; corrections  upplied  to  places  of,  ift 
calculating  latitude,  ii.  56. 

For  moon's  node,  sc  Moon. 

Nrsinlm,  cor.  meutator  on  SArya-$iddhAo- 
ta,  add.  n.  2. 

Nil,  21st  sieti , 196.  . 

Numbers,  bow  expressed  in  the  text,  in- 
trod.  n. 

• 

Oblique  ascension,  equivalents  in,  of  signs 
of  ecliptic,  iii.  44?45  ; table  of  equiva- 
lents as  calculated  for  Washington, 
121;  for  Williams’  College,  313:  de- 
grees* of  oblique  oacennon,  ix.  5 n. 


850 


S&rya-Siddhdntct, 

Observations — How  far  contemplated  in!  Perigee,  perihelion,  no  name  for,  p.  63. 
Hindu  system,  vii.  18  nv  viii.  1 2 n,  :)28  -.  Perpendicular  of  a right-angled  triangle,  ii. 
anauTBCy  of  Hindu  observations,  212,11  SOn.iuld.n.  16. 

320.  UPerpendicular-Bine  = cosine,  ii.  00  n,  add. 

Oei,  28th  lieu,  184.  \\  n.  in. 

Orbit— name,  iv.  3,  xii.  '16  : orbits  of  thellFhiMgunn,  11th  or  12th  month,  i.  61  n, 

ganets,  i.  26,  xii.  73—^7 ; their  absolutcij  xiv.  3 n,  1G  n. 

mensions,  xii.  6O-0O;  how  determined.!  Phulguni,  11th  and  12tli  asterisms — iden- 
i.  27  n,  iv.  1 n,  xii.  90  n;  their  relative  tiiication  etc.,  189,  odd.  n.  26. 
dimensions  deduced  from  epicycles,  and  Phases  of  an  eclipse,  contact,  immersion, 
compared,  p.  76.  emergence,  separation,  greatest  obscu- 

Orient  celiptic-point,  iii.  46-48.  ration,  etc.— names,  iv.  16n,  17  n. 

Orient-sine,  or  sine  of  amplitude  of  orient  Pi,  2nd  siVk,  *185  ; 25th  sicn,  199. 
ecliptic-point,  v.  3.  jPingnla,  26th  year  of  JJppiter's  cycle,  i. 

; 55  n. 

Pftda,  quarter  of  a yloka,  introd.  n.  j Planet,  name.  iv.  6 n,  add.  n..22. 

Padma,  name  of  a yoga,  add.  n.  19.  Planets — names,  add.  n.  3 ; creation,  xii. 

Padma.  name  of  last  /Eon,  i.  23  n.  22-24;  general  explanation  of  motions, 

Paiica-Siddhfaitika,  i.  3 n,  add.  n.  1 . j i.  25-27,  xii.  73-77 ; point  of  comincncc- 
Par&bhavu,  14th  year  of  Jupiter's  cycle,'  ninntof motion, i. 27, p.  18;  tiraeofeom- 
i.  66  n.  j menccment,  i.  24,  p.  17, 18,  i.  44  n;  sid- 

Par&yarn,  add.  n.  1.  j creal  revolutions  in  ail  Age,  i.  29-32  ; 

Parftyara  or  Parftyara  Siddhfmta,  add.  n.  j tables  of  periods  of  sidereal  revolution, 
1 ; its  system,  add.  n.  6 ; length  of  vear,  p.  17,  20,  24,  add.  n.  5,  7 ; meal  daily 
p.  24 ; positions  of  apsides  uud  nodes,  i.  motions,  i.  26,  xii.  83  ; tables  oFllo.,  i. 
44  u.  34  n,  add.  n.  6,  7 ; mean  positions,  end 

Parallax — general  exposition  of  Hindu  of  last  (J olden  Age,  i.  57  ; do.  beginning 
view  of,  v.  1 n;  horizontal  parallax  of  of  Iron  Age,  i.  58  n,  add.  n.  0;  actual 
moon  and  sun,  iv.  1 n ; the  Mime  acc.  mean  positions,  bog.  of  Iron  Age,  p.  18  : 
to  Ptolemy,  iv.  In:  vertical  parallax  to  find  mean  longitude  for  any  given 
and  its  resolution,  v.  In;  parallax  in  time,  i.  53-67;  mean  longitude  as  found 
longitude,  name  of,  144;  mode  of  cal-!  lor  Jim.  1,  I860,  and  errors,  fc  67  n : 
culating,  in  time,  v.  3-8;  parallax  in  causes  of  irregular  motion,  ii.  1-11; 
latitude,  name  of,  144;  mode  of  ealeu-  kinds  of  motion,  ii.  12-13  : liow  to  col- 
lating, v.  10-12:  method  of  applying  eulate  true  longitudes,  ii.  29-46;  di- 
paralla^  in  determining  plmses  of  eclipse,  mensions  of  epicycles,  ii.  34-38;  equa- 
v.  9,  "13-17,  319;  general  criticism  of  t ion  of  centre,  ii.  39  ; annual  equation, 
methods  of  calculation,  156:  parallax  ii.  40-42;  calculation  of  true  rutes  of 
of  other  plancta  neglected,  vii.  23  n.  motion,  ii.  47-51 ; of  declination,  ii.  28 ; 
Paridlinvin,  20th  year  of  Jupiter's  cycle,  i.  data  for  tinding  latitude,  i.  68-70 ; mode 
66  n.  of  calculation,  ii.  6G-57 ; combination  of 

Parigha,  19th  yoga,  ii.  66  n.  latitude  and  declination,  ii.  68  : com- 

Parivatsara,  2nd  year  of  lustrum,  xiv.  parative  table  of  true  longitudes,  doily 
17  n.  " morions,  and  declinations,  for  Jan.  lf 

PArsi  asterisms,  or  28-fold  division  of  I860,  p.  87 ; apparent  diameters,  iv.  1 n, 

ecliptic,  180,  206.  vii.  13-14:  orbits,  liow  determined,  iv. 

P&rthiva,  53rd  year  of  Jupiter's  cycle,  i.  j In,  xii.  90  n ; absolute  dimensions  xii. 

65  n.  j 80-90;  relative  dimensions,  deduced 

Path  of  extremity  of  shadow,  Low  drawn  • from  epicycles,  p.  76 ; distances  from 

f on  the  dial,  iii.  41-42.  earth,  xii.  84 ; order  in  respect  to  d>s- 

Path  of  eclipsing  body,  how  drawn  in  pro-  tancc,  xii.  31 ; order  in  which  referred 

jection  of  eclipses,  vi.  14-16.  to  in  this  work,  i.  52  n : synodical  revo- 

Patriarehate,  great  chronological  period — lutions,  ii.  42  n : conjunctions  of  planets 

how  composed,  i.  18:  reckoned  as  day  with  each  other,  vii;  with  asterisms, 

of  Pruj&pati,  xiv.  21.  viii.  14-16 : heliacal  Bettings  and  risings, 

Paulastya  or  Pulastya  Siddh&nta,  odd.  n.  1 . ix.  1-H : regency  over  days,  montlis, 

Pauliya  or  Puliya  SiddhAnta,  i.  Gn,  add.  etc.,  i.  61-62,  xii.  78-79 : day  of  a plan- 

n.  1 , 6 : its  length  of  year,  p.  24.  et,  ii.  69. 

jpAuBha,  9th  or  10th  month,  i.  61  n.  xiv.  Plava,  9th  year  of  Jupiter's  cycle, 

3 b,  16  n.  * 55  n. 

Perfected,  the,  a race  of  supernatural  Ptav&nga,  16th  year  of  Jupiter’s  cycle,  L 
‘beings,  xii.  26,81,40.  55  n. 


General  Index. 


851 


t ,atltude-  *■»  how  I 

employed  in  tbw  work,  viii.  in.  ! 

ro  c-of  eartK  R4-SB  ; o£  ecliptic, 
143 ; or  prime  vertical.  U9. 
roleatara,  xii.  43 

Portion  of  an  asterism,  ii.  64,1*79, 207-10. 
Possessors  of  Knowledge,  supernatural 
beings,  xii.  31. 

Prubhava,  36th*  year  of  Jupiter's  cycle,  i. 
55  n. 

Pmjapnti— 39th  year  of  Jupiter’s  cycle,  i. 
55  n:  divinity  of  4th  asterism,  185,  viii. 
1 3 n : the  patriarchate  a day  of,  xiv. 
21 : name  of  n star  (3  Auriga:),  viii.  20 : 
name  of  a yoga,  add.  n.  19. 

Pram  .id  in,  21st  year  of  Jupiter's  cycle,  i. 
55  n.  • 


tmg  of  pfanefs,  ix.  0 n ; positions  of  ap- 
i sides  and  nodes  of  planets,  add.  n.l\. 

‘PuYi^a,  author  of  P&ulica-Siddhtata,  add. 

n.  I ; identical  with  Paulus  Alexandra  * 
1 nus?  i.  ti  n,  add.  n.  1. 

•Punarvasu,  7th  asterism  identification 
! etc.,  186. 

'Purva-asliadlia,  20th  asterism — identifica- 
| tion  etc.,  1 94. 

Purva-BhAdrapadA,  26th  asterism-riden- 
! tification  etc.,  197. 

Purva-Phalguni,  11th  asterism — identifi- 
, | cation  etc.,  189. 

: Pilshan,  divinity  of  28th  asterism,  199. 
.Pusliya,  8th  asterism— identification  etc., 
.!  187. 


Fninii'ithin,  47th  year  of  Jupiter'e  cycle,  i.  Quadrants,  odd  and  even,  ii.  29-30. 

55b  n.  i 

Pramodu,  38th  year  of  Jupiterh  cycle,  i. , Radi  us— names,  Ii,  60  n;  value  in  min- 
55  n.  j iitoa,  ii.  22. 

Prnvardha,  name  of  a yoga,  add.  n.  19.  R.ilu^  ii.  6 ; cause  of  eclipses,  ii.  8 n,  iv. 
Profession  of  the  equinoxes,  iii.  9-12  ; j 0 n. 
iJmc,  105;  statement  of,  iii.  9 ; form  Riikshasa— 23rd  year  of  Jupiter’s  cycle, 
of  theory,  a libration,  iii.  12  ii ; possible  i.  55  n ; name  of  a yoga,  add.  n.  19. 
reason,  103;  Bentley's  view  refuted,  Rnktiikslia,  32nd  year  of  Jupiter’s  cycle, 
104 ; theory  of  Biddhrinta-^iromniii,  not  i.  55  n. 

a libration,  104;  whether  precession  Ranganfitha,  commentator  on  Surya-Sid- 
taken  account  of  in  const  ruction  of  Hin-  dlifmta,  introd.  n.,  add.  □.  2. 
dii  system,  1 03,  add.  n.  20 ; position  and  Ratnavnulu,  authority  respecting  aster- 
history  in  this  treatise,  102  etc.,  add.  n.j  i-ms,  181. 

2ff ; rule  for  calculating,  iii.  9-10;  fur  Riiudra,  28  th  year  of  Jupiter's  cycle,  i. 
determining  by  observation,  iii.  11-12 : 56  n. 

(Jreek  view  of  precession,  103.  R:i'  ivfini,  Sunday,  i.  52  n. 

Prime  meridian,  i.  62.  j Regents  of  years,  months,  days,  and  hours, 

Prime  tfertical,  iii.  6 ; its  pole,  1 39 ; to  find  | i.  5 L-52,  xii.  78-79. 

hypoth.  of  shadow,  when  sun  is  on  the,  'Respiration,  measure  of  time,  i.  11. 
iii.  25-27.  .Relrngnuhition  of  the  planets — name,  ii. 

Prlti,  2nd  yoga,  ii.  65  n.  12-13:  explanation,  and  definition  of 

Progre^os  of  the  sun,  from  solstice  to  j limits,  ii.  51-55. 

• solstice,  xiv.  9.  . titevati,  2Stli  asterism — identification  etc., 

Projeciion  of  ail  eclipse,  vi ; name,  vi.  1,  8 ; j 199  ; its  last  quarter  unlucky,  xi.  21. 
scale  of,  iv.  26 ; figure  illustrating  pro-  Revolution  of  a planet,  i.  25-27 ; numbers 
jection  of  lunar  eclipse,  157.  of  revolutions  in  an  Age,  i.  29-34. 

Ptolemy — possible1  traces  of  his  name  in  Right  ascension,  equivalents  of  tho  differ- 

Jlindu  asLronoiny,  i.  6 n;  his  times  of  ent  signs  of  the  ecliptic  ill,  iii.  42-44. 

^sidereal  revolution  of  the  planets,  p.  24,  sir-RishA,  28th  unntzil,  199. 
add.  n.  10;  inclination  of  planetary  or-  Rohini,  4th  asterism — identification  eta, 
bits,  i.  70  n ; of  ecliptic,  ii.  28  n;  use  of  185 ; uatrr  logical  consequences  of  cjpl- 

clinrds,  p.  50 ; relation  of  his  chords  to  litJun  of  the  planets  with,  viii.  13. 

Hindu  sines,  add.  n.  15 ; mode  of  cal-  Rohitaka,  place  situated  o»»  prime  inerid- 
culating  equation  of  centre  of  sun  and  ian,  i.  62. 

moon,  p.6G ; of  other  planets,  together  Ilomaka,  name  o»  Rome,  i.  6 n,  xii.  39. 
with  annual  equation,  p.7  3;  his  improve-)  Roinaka-Siddhfir.tii,  add  n.  1,  i.  6 n. 
inents  of  Ureek  astronomy,  not  found  ini  Rudliirodgfirin,  31st  year  of  Jupiter's  cy- 
Hiiuhi  system,  p.  75,  33U;  •relativb  di-J  cle,  i.  55  n. 
lneiishins  and  uceentrieitics  of  planetary  Rjidra,  divinity  of  6th  asterism,  186. 
orbits,  p.  76  ; rulrograduliun  of  planets,!  * 

p.  82 ; prei!ession,  105 ; distances,  paral-j  [For  words  often  spelt  with  Sh,  S',  *9,  or 
lax,  and  dimensions  of  sun  and  inoonj  S,  see  9,  under  the  letter  C.] 

127 ; direction. of  ecliptic  in  eclipses.  Sa’d  adh-lihlbih,  22nd  manzil , 196.  . 
140;  astrology,  vii.  23  n ; heliacal  set-  Sa’d  al-Akhbiyah,  25th  «iuAut7, 197. 


852 


S&rya-Siddh&ntcfi, 


Sft'd  as-Su'ud,  24th  memsil , 197.  IISiddhlnta-SArvabMumn,  add.  n.  1 : mctli- 

Sad  Bui  a',  23rd  manzil,  19  0.  jl  od  of -observing  positions  of  asterisms, 

S&dhArafta,  18th  year  of  Jupiter's  cycle,  ! viii.  12  n;  epicycles,  add.  n.  18. 

• 1.  5$  n.  i'Siddlianta  Sundara,  add.  n.  1 ; cited  by 

- S&dhya,  22nd  yoga,  u.  65  n.  4 Biddininta-^iirvubhfiuma,  viii.  12  n. 


Samvatsara— 1 et  year  of  lustrum,  xiv.17  n . 

year  of  era  of  Vikramfiditya,  ndd.r.  12, 
Banskrit  words,  transcription  and  pronun-!l 
ciution  of,,  introd.  n. 
aB-Barfnh,  12th  m anzil,  190. 

Sarvadh&rin,  56tli  year  of  Jupiter's  cycle, 
i.  55  n. 

Sarviijit,  65th  year  of  Jupiter's  cycle,  \.\ 
55  n. 

Saturn,  names,  revolutions,  etc.,  etc.* 
Planets. 

SAubhAgya,  4th  yoga,  ii.  65  n. 

Sflumya—  17th  year  of  Jupiter's  cycle,  i. 

55  n ; name  of  a vogn,  add.  n.  19. 

Scale  of  projection  of  an  eclipse,  iv.  20. 
Seasons— >numbcr  and  names,  xiv.  ion; 
months  and  asterisms  belonging  to, 
‘them,  xiv.  16  n;  reason  of  varying 
temperature,  xii.  46,  72  n. 

Second  of  arc,  i.  28. 

Serpents,  divinities  of  9th  asterism,  188. 
Seven  Sages, 'stars  in  Ursa  Major,  xiii.  9; 

their  independent  revolution,  viii.  21  n. 
Shada^itiinukha,  solar  period,  xiv.  0-0. 
Shadow  of  earth  — diameter  on  moon  s 
orbit,  iv.  4-5 ; no  account  taken  of  pc 
nuinbra.  iv.  5 n. 

Shadow  of  gnomon — names,  iii.  5 n:  base, 
or  north  .aid  south  projection  of,  iii,  2:3- 
25  ; path  of  its  extiviniLy,  iii.  41-42 
equinoctial  shadow,  iii.  7,  12-13:  noon 
shadow,  how  calcularcd,  iii.  20-22 ; oth- 
er shadows,  iii.  28-34,  34-36 ; shadow 
cast  by  any  planet  or  star,  how  deter- 
mined awl  hud  down,  168.  172. 
ash-Shnrnt.in.  1st  inanzil , 1H3. 
a<h-Shaulah,  lOLli  untnsil,  194. 

Siddha,  21st  yoga,  ii.  65  ii. 


Siddluinhin,  27th  year  of  Jupiter's  cycle, 
i.  55  n. 

Siddhi — 16tli  yoga,  ii.  65  n;  name  of  a 

a add.  A.  19.  a 

time,  day,  year — see  Time,  Day, 

Year. 

Sieu,  28-fold  division  of  heavens  by  Chi- 
nese, 181;  comparison  with  Hindu 
asterisms  and  Arab  lunar  mansions, 
183-200  ; map  illustrating  position  and 
relations,  amL  n.  27 ; origin  of  system, 
ace.  to  Ui8t,  201. 

jSign,  twelfth  part  of  ecliptic,  i.  28;  reck- 
oned from  any  given  starting-point,  1. 
28  n,  JB  n ; table  of  names  and  symbols, 

1.  58  n. 

as-Simak,  14th  nutmil , 191. 

Sin,  ICth  nicu,  193.  i 

Bine— name,  p.  57,  add.  n.  16  ; scrieL  of 
sines,  in  minutes,  ii.  17-22 ; com paratiro 
table  of,  p.  63 ; “table  of  sine9  for  every 
degree,  with  differences,  285  ; rule  for 
developing  the  series,  ii.  15-16;  how 
derived,  p.  54-5,  add.  n.  15  ; its  falsity, 
add.  n.  15  ; Hindu  use  of  sines  earlier 
than  Arab,  p.  5G ; Arab  sines  from  Greek 
chords,  p.  56  ; whether  Hindu  sines  like- 
wise ? add.  n.  15  ; Hindu  series  how 
obtained,  p.  54,  add.  ii.  15. 
part  of  an  arc  determining  the  sine,  ii. 
29-30  : to  find  the  sine  of  a given  arc, 
or  arc  of  a given  sine,  ii.  81-33. 

[Sing,  fill]  siru,  189. 

Solar  time,  day,  month,  year,  ctcv — see . 

| Time,  Day,  Month,  Year.  i 

Solstice,  name  of,  105,  xii.  72  n.  . 


jiSoma-Siddliiinta,  add  n 1,6. 

'JSnmsivani,  Monday,  i.  52  n. 
Sidilhaiita-rirom.'iui—  dale,  authorship,  and  Splu-iv,  1-13. 
dciivathm,  add.  n.  1 ; account  of  Yeihin-  jSipmru,  iii.  5 n. 
ga-*.  i.  3 n ; planet  ary  -v^teiii.  add.  n.  6 v&lhira,  hame  of  a yoga,  add.  n.  19. 
digMiin  of  the  day,  i.  12n;  length  of  jSuhliAiiu,  51st  year  of  Jupiter’s  cyclc^i. 
yoir,  and  mean  sidereal  revolutions  of;  55  n. 


planets.  p.  21 ; po-itiniH  of  ajifiiieh  and 
fmde-s.  i.  41  n , di-imeter  and  i- iron  infer-, 
cnee  of  eurtli,  i.  6C  ii  ; prime  meridiaii. 
l.  62  n ; pn  ce^ion.  JU4  ; statement  re- 
specting preccs'.in'n  u*  taught  by  Surya-! 
Siddhfmta.  lot ; sine**  of  zenith  distance 
ami  altitude  uf  ecliptic,  v.  7 n;  defini-j 
tion  nf  piMition  of  asterisms  1 82-200 
of  fixed  stars,  viii.  12  n;  geography  uf. 
SMillmru  hemisphere,  xii.  4 4 n ; orbit  of. 
Axterisms,  xii.  90  n;  arinillai^  >plim\. 
xiii.  3 n ; descriptions  of  instruments.! 
xiii.  21  n.  22  n ; solar  day,  xiv.  3 n ; cpi-j 
cycles,  add.  H.  18.  j 


Sukarman,  7th  yoga,  ii.  G5  n. 

Sum  of  days— names,  i.  51- n ; how  found, 
i.  45-51. 

Su|i — names,  revolutions,  etc.,  etc.,  see 
Planet— -dimensions,'  iv.  1 ; mean  ap- 
parent diameter,  horizontal  parallax, 
and  distance,  iv.  1 n;  to  find  true  ap- 
parent diameter,  iv.  2-3;  biicfcr  inetn- 
*»d.  312;  solur  ecli|i«e*>,  iv,  v;  calcu- 
lation of  a Milar  oclip-o,  add.  n.  25; 
error  of  min's  motion  and  position  by 
Hindu  system,  p 22 ; adaptation  of  those 
of  other  planets  to  4t,  p.  20-3 : sun's 
revelation  of  present  treatise,  i.  2-9,  xiv. 


General  Index. 


858 


SKlStSAJ1*  f6?*10"’  *L  “-H^tarft-Bbfidraparfa,  27th  uterism-id®. 

SOrya  Siddhiuita-- professedly  repealed  by' 
tbciSmi  to  Maya,  \.  2-9  ; ascribed  by 
al-llirfini  to  liita,  i.  3n;  referred  by 


titication  etc.,  198. 
v\U ttara-Phalguni.  \2ih  asterism — ^identifi- 
cation etc.,  189. 


Bentley  to  lHli  century,  p.  21 ; refuta- 
tion of  this  conclusion,  i.  3 n,  p.  23, 328  . 
position  in  astronomical  literature  of] 
India,  in  trod,  n.,  add.  n.  1,  326 ; its  sys- 
tem compared  with  those  of  other  trea- 
tises, add.  n.  6 ; present  extent,  xiv.  27  n 
division  into  two  portions,  xi.  28  n 
commentaries  on,  add.  n.  2 ; published! 
edition,  introd.  n.,  add.  n.  1 . 

Sv&ti,  loth  asterism— -identification  etc. 
191. 

Synodical  revolutions  of  the  planets,  p.  68. 

Tables  for  finding  true  places  of  planet: 

where  given,  p.  74. 

Taitila,  5th  etc.  karana,  ii.  69  n. 
Tuittiriyu-Sanldtd  aiid  Taittiriya-Brah- 
^naiia,  names.ond  divinities  of  the  aste 
risms  according  to,  182  etc. 

Taiuinuya,  commentator  on  Surya-Sid 
dhfuita,  add.  n.  2. 

Tfirana,  52nd  year  of  Jupiter’s  cycle, 

55  n. 

ill  -Turf,  9tli  man  xii,  1 88. 

JaVva  Vivcka,  add.  n.  1. 
aTh-Thuruiy:i,  3rd  manzil , 185. 

Ti.  Mtli  situ,  192‘. 

Time — real  and  unreal,  i.  10;  different] 
modes  of  measuring  and  reckoning,  xiv 
ci\il  time  and  its  uses,  xiv.  18-19;  hi 
uar  time,  i.  13n,  xiv.  12-14;  sidereal 
time,  xiv.  16;  solar  time,  xiv.  3,  10; 

_ time  of  gods,  l’rajupati,  ami  Brahma, !| 
I*  xiv.  20-21 : mode  of  reckoning  time1 
practically  employed,  i.  13  ii:  instru- 
incuts,  for  .measuring  time,  xiii.  10,19- 
24:  to  determine  the  time  by  olwerva- 
timi  of  shadow  of  gnomon,  iii.  37-39 — 
sec  Day,  Month,  Yuar,  etc. 

Times  of  rising,  see  Ascensional  equiva- 

% lei  its. 

Tsan,  4th  »i«f,  186. 

Tsi\  3rd  «Vu,  186. 

T.-ing,  5lh  157. 

Tvnshliir.  divinity  of  14th  asterism,  190. 
Tvcho'lJrahe's  determination  of  apparent 
‘'diameter  of  planets,  vii.  14  n. 

Udravatsarn.  5tli  year  of  lustrum,  xiv.  17  n.| 
Uei,  17  th  *i*w,  194. 

Ujjavini  city  determining  position  oflj 
prime  meridian,  i.  62  n.  * 

Upimishad,  xiii.  3 n. 

Utpata,  name  of  a yoga,  add.  n.  19, 
Uiiara-Ashldhil  2 1st  asterism— identifi- 
cation etc.,  194. 


V&idlkha,  1st  or  2nd  month,  i.  51  n,  xiv. 

8 n,  16  n. 

[Vaidhrta,  pr  Viiidhrti,  name  of  a hostile 
aspect  of  sun  and  moon,  xi.  2, 4.  < 

Viiidhrti,  27  th  yoga,  ii.  65  n. 

Vajrn — 15th  yoga,  ii.  65  n;  name  of  a 
yoga,  add.  n.  19. 

V&r&ha,  name  of  current  ASon,  i.  23  n. 
y&r&ha-mihira,  astronomical  and  astro- 
logical authority,  i.  3n,  vii.  23  n,  208, 
viii.  1 3 n,  xiv.  6 u,  add.  n.  1. 
VarAha-SiddhAnta,  odd.  n.  1. 

Vuriyas,  18th  yoga,  ii.  65m. 

Varsha,  rainy  season,  xiv.  Ifrn,  16  n. 

VAruna,  divinity  of  25th  asterism,  197. 
Vasai i to,  spring,  xiv.  10n,  16  n. 

Vasislithn  or  Vdsislitlia  SiddhAnta,  add. 

n.  1,  0. 

Viisudeva,  xii.  12. 

Vasus,  divinities  of  24th  asterism,  196. 
Vatsarn,  5th  year  of  lustrum,  xiv.  17  n. 
Vedas,  xii.  17. 

Vedfingos,  i.  3 n. 

Venus  — names,  revolutions,  etc,  etc., 
see  Planets — in  conjunction  with  other 
planets,  vii.  23. 

[Versed  sine— name,  p.  57 ; how  found,  ii. 

22  ; scries  of,  for  the  quadrant,  ii.  23-27. 
Vertical  circle,  J 43. . 

Vertical  parallax,  resolution. of.  143. 
Vibluiva,  36th  year  of  Jupiter’s  cycle,  i.  # 
55  n.  t 

Vi^iLkhii,  16lh  asterism — identification 
«£«491. 

Vicrtilu.  name  of  stars  in  sting  of  Scor- 
pio, 193. 

Vii; vii vasu,  13th  year  of  Jupiter's  cycle,  i. 
55  ii. 

Vijaya,  1st  year  of  Jupiter’s  cycle,  i. 
55  ii. 

Vikarin,  7 th  year  of  Jupiter 9 Mle,  i. 

05  n.  w 

Vikramo,  48th  year  of  Jupitcr*9  cycle,  i. 

65  n.  . 

VikramAditya,  era  of.  add.  n.  1 2. 

Vikrta,  68th  ye:  r of  Jupiter's  cycle,  i. 
55  n. 

Vilainba,  6th  year  of  Jupiter’s  cycle,  i. 
65  n. 

Vinudi,  measure  of  time,  i.  11. 

Viroillmkrt,  19th  year  of  Jupiter's  cycle, 
i.  55  n. 

Vimdliiii,  67tli  year  of  Jupiter's  cydo,  i. 
55  n. 

Vishknmbha,  1st  yoga,  ii.  65  n. 

Vishnu— divinity  of  23rd  asterism/ 196; 

I original  character,  adv.  10  n. 


854  S&rya-Siddh&nta. 


Vialifyu-candm,  author  of  Vasishtha-Sid-  Yavnnas,*  Greeks  or  westerners,  referred 
dhAnta,  mid.  n.  1.  to  in  Hindu  astronomical  traditions,  i. 

Vidi^udhnnnottftni-PuHmn,  add.  n.  1.  6 u,  3 HO. 

Vishpu-Puriimi,  citations  from  and  refer-  Year — civil,  lunar,  sidereal,  and  solar,  i. 
enccs  to,  i.  9 n,  12  n,  17  n,  19  n,  21  nj.  13  n ; year«f  the  pods,  i.  14  ; yeurs  in 
23  n,  ii.  8 n,  xii.  23  n,  44  n. 


Vishti,  8tli  etc.  karana,  ii.  G9  n. 

Vortices,  or  propelling  currents,  of  the  j 
planets,  ii.  3,  xii.  73.  * l: 

Vrddhi.  11th  yogn,ii.  65  n. 

V y agitata,  13  th  yoga,  ii.  65  n. 
Vyfisa-Siddhslnta,  add.  n.  1. 

Vyatipata— 17th  yoga,  ii.  63  n,  xi.  20: 
name  of  a hostile  aspect  of  suu  and 
moon,  xi.  2, 4. 

Vyaya,  54tli  year  of  Jupiter's  cycle,  i.: 
55  n.  i 


practical  ivw  in  India,  i.  13  n;  sketch  of 
solar  and  limi-solar  calendar,  for  year 
1 859-60,  i.  51  n : length  of  sidereal  solar 
year,  ucc.  to  different  authorities,  p.  24  : 
years  of  enyi  of  ^aliviihana  and  Vikra- 


miiditya,  character  and  names  of,  add. 
n.  12;  years  of  Jupiter's  cycle,  names 
of,  i.  55  n ; years  of  lustrum,  names  of, 
xiv.  17  n. 

Ycllaya,  commentator  on  Surya-Siddhfiu- 
la,  add.  n.  2. 

Yoga,  period  of  time — name  whence  de- 
ls rived,  add.  n.  19  ; two  systems,  names 
Warren's  K&la  Sankalita,  references  toj  and  character  of.  ii.  65  n,  add.  n.  19. 
and  citations  from,  ihtrod.  n.t  i.  13  n.  Yojana,  measure' of  length,  its  siihdivUiun 
34  n,  48  n,  55 n,  02  n,  p. 74,  xiv.  3n,  17  n,'j  and  value,  i.  60  n,  add.  n.  13. 
add.  n.  12.  1.9.  # i-Yuvan,  *13rd  year  of  Jupiter's  cycle,  i. 

Weber,  references  to  and  extracts  from1  55  n.  • 

his  works  and  essays,  i.  3 n,  6 n,  ii.  8 n.'i  ^ 

vii.  23  n,  204,  xiv.  6 n,  odd.  n.  1,  3,  26.,  Zenith,  name  of,  ▼.  1 n. 

28.  | Zenith-distance — on  the  meridian,  iii.  1-1- 

Wcek — not  an  original  or  ancient  Hindu  : 15  ; elsewhere,  iii.  33;  sun's  zenith-dis- 

institiuiun,  i.  52  n,  xii.  79  n;  whence 
brought  to  India,  i.  52  n ; names  of  its. 
days,  i.  52  n;  how  determined,  i.  52  n ;!, 
when  they  liegin,  i.  0G. 


Wilson — his  catalogue  of  Mackenzie  Col-i 
lection  referred  to,  add.  n.  1,  2 ; hi 
Vishnu- Parana,  sec  Ykhnu-Purana. 

Y,  10th  »>ii,  190. 

■ Yam  a,  divinity  of  2nd  asturism,  184. 
Yamakoti,  city,  xii.  38, 


tanre  on  circles  of  intermediate  direc- 
tion, how  found,  iii.  28-34 ; to  find  the 
same  elsewhere,  iii.  31-36;  how  found 
from  shadow,  iii.  14-15,  37  : instrument- 
for  obtaining  sun’s  zenith-distance  iy 
observation,  xiii.  21  n. 

Zodiac — name,  iii.  12  n signs  of,  see 
Signs. 

Zones  of  the  earth,  xii.  59-69. 
jaz-Zuhiinan,  16th  manzilft  192. 
az-Zubrali,  11th  manzil,  190. 


ERRATA. 


'■  4 p.  4, 11.  2,  3 from  below — exchange  the  words  former  and  latter. 

& p.  12, 1.  28 — for  plants  read  planets . 

p.  13)  1.  25 — for  *73-89  read  80-90.  h h 

p.  24,  table,  3rd  colnmu  ( Ptolemy),  1.  1 — for  36  read  6. 

p.  29, 1.  34 — for  Ward  rend  Warreti. 

p.  32, 1.  20— for  81-88  rend  31. 

p.  39, 1.  41— for  5059.556  rend  5059.64. 

p.  47,  L 22 — for  day-sine  rend  earth- sine. 

^•^p.  120, 1.  4 — for  sines  rend  si  (jus. 

p.  123, 1.  20 — for  longitude  of  rend  of  longitude. 
p.  190,1.  12 — for  as  Sarfah  read  as-Sarfah. 
p.  191,1.  15 — for  fourteenth  rend  thirteenth. 
p.  283, 1.  2 from  below — for  1952nd  read  1917th. 

References  mode  in  the  notes  on  the  earlier  chapters  to  the  latter  portion  of 
chapter  xii  are  in  ceveral  instances  wroire  by  one  verse,  owing  to  an  error  of  thes 
manuscript  consulted.  ' \ f 


