vedanga jyotish of sage lagdha

8/7/2019 Vedanga Jyotish of Sage Lagdha

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VEDANGA JYOTISA OF LAGADHAIN ITS ~K AND YAJUS RECENSIONS

WITH THE TRANSLATION AND NOTES OFPROF. T. S. KUPPANNA SASTRY

Critically edited byK. V. SARMA

INDIAN NATIONAL SCIENCE ACADEMYNEW DELHI


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VEDANGA JYOTISA OF LAGADHAIN ITS ]pC. AND YAIUS RECENSIONS

WITH THE TRANSLATION AND NOTES OFPROF. T. S. KUPPANNA SASTRY

Critically edited byK . V. S ARMA

INDIAN NATIONAL SCIENCE ACADEMYNEWDBLm


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Published forTHE NATIONAL COMMISSION FOR THB COMPILATION

OF HISTORY 0," SCIENCES IN INDIA

byINDlAN NATIONAL SCIENCE ACADEMYBahadur Shah Zafar Marg. New Delhi

e1985Indian National Science AcademyPrice Rs. 25 00S 8;-00

Pnnted at Sree Sa raswa tY Press Limlted(A Govt of W est BensaI Undertaking)32 A..P.C. RoadJ, Calcutta 700009


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FOREWORDThe Vedanga Jyl)ti~a o f sage L agadha is highly significant in the h isto ry o f sciencin India, in the sense that it is the ear lie st f ull . ..fledged treatise on Indian astronomjAs an adjunct to the Vedic lore, it forms a manual for the determination of rituals ansacrifices by the V edic priest and for the preparation of a bandy calendar for socisand religious events. The work is current in two r ec en sion s, one in 36 ver se s r ela teto th e lJgveda and the other in 43 verses related to the Yaiurveda , mos t of the versein the two texts b ein g common ,Several attempts have been m ade earlier to edit and interpret this popular texHowever , the fact that the work was but a manual and not self-contained, and th athere was much to be learnt from tradition and practice towards a co rrect u nd erstanding and interpretation of this cryptic text has made all the earlier attemptsuffe r fr om some inherent limitation or the other.As such, it IS a matter for gratification that tho late Prof. T . S. Kuppanna Sastrtook up tho task of preparing a textual study and rational mterpretation of the workH e com bined in him self em dition inV edic tradition, know ledge of Indian astronomand equipped in modem m athem atics . The draft he had left before he Passel

away in 1978 required to be edited and made p res s-w o rth y. M o reo ver, the Sanskr itext needed to be critically edited from original manuscripts, and the necessari nd ices e tc , prepared, to make the pub li ca ti on academica ll y acceptable, This additionawork has been done in a s ch ola rly manner by Dr, K . V . S arma of the Kuppuswar rSastri Research In stitu te . M adras ,In placing before d isce rn ing scho la rs of Sanskrit and Science the ancient text 0Vedat iga Jyotisa, Ihave great pleasure in recording my sincere tbanks to the sons 0late Prof. Sastry fo r making available their father's erudite work for publication bthe Indian National S cience A cademy and to Dr. K, Vt Sarma fo r p re pa rin g t h . ischolarly edition.

Indian National Science AcademyN ew D elhi S .. K t MUKHBR JEBVice..Cha irmanNational Commission for thCompilation of History 0Sc iences . in India


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CONTENTS

FOREWORD . . . . .. . . . . It III CoNTENTSPREFACE

.. . t . .. o il . . .. . . . .. . . .. .

Page357

INTR ODUCTION . t .. oil ~ 111.Astronomy of the Vedic Sambitas- 2 Datable Vedic passages- 3 t Textof Veddnga Jyotisa (VJ)--4. Date of VJ-S. Verification of the date ofLagadha~, Contents of the VJ-7... Accuracy of the VI-S.Modem studies on VJ-9. Acknowledgements

PAl lT A : T E x T OF VHD xN "OA JYOnsA . . . II t ,,I. AItCA-JY~M-aGVEDA VEDANGA JYOTI~An. YAl 'V lA..JYOTI$AM- YA JURVBDA VEDANGA JYOTI~ to

PART B: RB . ARRANOED TEXT OF VI W ITH TR A NSLA 'IlON A ND NOTES to

S N . I I > B EN ED IC TIO N AND VA LEDICTION . ~1~Introduction . .2. Importance of A stronomy ~ I>3 t B e n e d i c t i o n I > . .4" Valediction

t t II .. + t It II

., . .. . I > SN. i L MBASUI lES 0' T I M E , ASTBIUSMS ETC.1...Time measures ..

2" A ste ri sms--Presiding deitie s . .3. R ule of Three ..

. .,. 1 t ... . . I >

SN . iii. FuNDAMENTAL AND DERIVED1. Yuga and Its elements2. Lagnas in the Yuga3. Day-time

YUGA CONSTANTS t ..... .,.r ~t . .

.. t . . . .SN . iv. TITH!, NAK$A.TRA Erc. O F C im .T A IN SPECIAL DA YS ~ .1. The fiv e-year Yuga . . . . ~~2. Commencem ent of the Yuga .. , ..3 . N a ks atr as at the beg inning o f the Ayanas ..4. The Y(nna ~. t ~ 1

S t . 8 t u s in a Yuga 1 ~t ..6 1 Par t of the day at which Pat11Q ends .. . t It7 rI Current year of the Yuga ~~ 1 t

t . . .. . o il o il

oil tt

oil

III

21232 73535353536363737394041414 2444444454 6464 748S O


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6 'V BDA i rG A JYOT I~Page

SN i t v. DA ILY Tn'HI, NAK$ATRA ETC . 51~ . III .. II1. Introductory . . . !I- 5l2 . Computation of Parvar id ! . . . . . 513. Asterismal parts . . .. . . II .. 524. . Bh t iJ r Ija or Nak~atra-parts II .. . . 535 4 ' Hour-angle a n d Lagna 4 ' . . S46..Naksatra at any Parva . . .. ... .. .. . . 5 67. Kalas for M oon 's Naksatra . . S88 .. Tithi-ntJk$atra in the Ji iyadi series .. . . . . . 5 99. BhO.danakaJas . . . . 6010. T im e of the day: P o sitio n o f the S un 61II. Sun's Naksatra at any time . . .. . . . . 6 212.. Day's parts at the beginning o f the Naksatra 4 ' It .. 6313. Corrections for the Sidereal day .. . . . II . . . 6414. Corrections fo r th e Yuga .. . . . . . . . . . 6S15. ~tuJtla: Ti this yet to elapse in a ~tu. . "" .. . .. 651 6 , Day-tim e at any Parva I ..

-II .. . . . 6617~ U p O V a 3 Q . t h a and In te rc ala ry days t 'II .. . . 6 6BmLIOGI tAPHY . . .. . . . . 6 8i..Text e ditio ns a nd T ran sla tio ns . . !I- 41 'II ~ 68ii. Studies . . ~ .. . . III It . .. . 6 8

. .. .VERSE (Pada) INDEX " . 6 9. . . . . . . G BNER A L IN DEX . 7 3... . . . ... . . . .. . .. . . . . .


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PREFACEVedonga Jyoti~a (VJ), 'the astronomical au xiliary of the Vedas', of which a c rit ic aleditio n w ith translatio n and detailed ex po sitio n is being is su ed th ro ugh th is p ub lic atio n,is th e e arlie st In dra n te xt d evoted ex clusively to the treatm ent o f astronomy .. T he w ork

is traced back to the teachings of sage Lagadha (c. 1180 B. c.) and is current in tworecen sio ns ex hib itin g b ut minor d iff er en ce s, one pe rta in ing to the Bgveda (R..VJ) andth e other to th e Ya jurveda (f:V J) a nd c alle d, respectively, Arca . .Jyoti~a and Ydjtqa-Jyo t i sa . The work had, p rimarily, b een in te nd ed as a manu al fo r th e determination ofthe tim es fo r rituals and allied pu rp oses, for the use of th e Vedic p rie st s who supple-mented it, as n eed ed , with the concepts and practices Im bibed by them by tradition"This latter as pect) co up led w ith th e fact that the work is only a handbook and not afull-fledged self-co ntained treatise o n th e s ub je ct, h as rendered the correct understand-ing of several pas sa ge s in it difficult, fo r things not specifically defined in the tex t haveto be known through traditional knowledge and prac tic e, Particularly for thls reason,the present translation and detailed ex positio n o f the work with ample applicationof modern a stronomy, by late Prof T . S , Kuppanna Sastry should be welcome, for hecombined in h im s elf th ree q ualitie s essential for the task , v iz. sound sch olarsh ip InSanskrit, good knowledge of W e stern astro nomy and full understanding of theconcepts and practices of traditional H indu astro nomy .

The B haratiya V idya B havan provided P rof S astry w ith a pro per fo rum fo r placinghis exposltion befo re sch olars for their adjudgement, The B havan organised in B om bay,on M arch 24-25, 1979, a 'W orkshop on A ncient A s tro nomy' under it s project on-A ncient Insights and M o dern Discoveries', a project which had been envisaged bythem as a co -operativ e n ational endeavour to explore the pos sib ilitie s o f a meaningfulcorrelation of ancient Indian insig hts and thoughts and the mode rn scientific dis-coveries and technical achievem ents. In fact, the Veda s , the Upa n i 3 ads, th e l'tdW}asand several other works o n vario us subjects inancient languages would now seem tostand up to the more critical inquiry and exam ination of a modern sc ien tific mind,as m ore and m ore discoveries of m odern tim es arc found to have r ele vant parallelreferences inthe teachings of early Indian sages, The subject has been, for quite sometime now. eng aging the attentio n o f scientists with a S ansk rit background and Sans-kritists with a scient if ic background to make a m eaningful correlation betw een the two.Tow ards the achievem ent of this laudable obiective, the Bhavan has taken severals teps in cluding the establishm ent of contacts with scholars of th e type mentionedabove ; in stitu tion o f stu dies an d researches of an inter-disciplinary nature and org anisa ..tion o f s em inar s and work sho ps tow ards p ro viding a fo rum for d is cu ss io ns and mutualexchange of ideas inthe diffemtt disciplines. It is p ertin en t to record that VediiftgaJyot i la and it s present exposition w as set out on the occasion of the first Workshopon A nc ien t Ind ian A s tronomy organ is ed by the Bhavan under its auspices as a part ofits p ro je ct noticed above, In fact, l a te r . .P rof Sastry had ex pressed a desire to have hiswork published by th e Bhavan , and the latter had included it in its public ation p ro . .gramme~ It was subsequt'.1t1y felt that it would be befitting if this w ork w e r e to be


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8 VEO.AJ : IGA JYOTI$Aissued through the Indian National Science A cadem y, for two reasons, first, onaccount of this being a work on a scientific discipline and secondly the current year]984-85 being the Jubilee Year of the Academy, a suggestion made on behalf of theAcademy and accepted by the Bhavan, It is to be hoped that this decision would beacclaimed by the scholarly world.

The VedaiJ.ga Jyot isa, being just a handbook, does not present its contents alwaysina systematically arranged manner as is the case 'Wi th later texts on astronomy. As aresult, topics on the same subject often find themselves distributed in different p lacesin the work and vice versa ..In order to enable the understanding of the astronomicalknowledge contained in the work m a compact way~the Text, Translation and Exposi-tion in this publication are presented in the undermentioned manner.In Part A, the lJk and Yajur recensions, R..VJ and Y-VJ, of the Vedanga Jyot isahave been separately edited from a critical point of view on the basis of 20manu scrip ts inclu ding th ose w ho se read in gs are recorded by A .. W eber in his 'O ber denYedakelendar, namens Iyotisham', (Abh . Ber l iner Ak, der Wiss! ' 1862, 1-130).. Thecorruptness of certain passages have necessitated emendations which have been socouched as to suit the available lettering in the manuscripts, the context and themeaning ..and have been placed within brackets The justification of the emendationshave been made later in t he expos it ion of the v erses in Put B of this publication.The undennentioned maauscripts have been collated towards constituting theCritical Text of VJ given in Pt. At The abbreviations used herein are: DNg.==Deva-

DigaI\ Gr.=Grantha, Te1=Telugu; Pt=Palmleaf; Pr~=Paper;and Cm ..=Complete,}j.k- Vedanga Jyoti$a

A and B .. No. lS05~ Verse ichn is s der Ski, und. Pkt, Hand . der Konig. Bibl. zuBerlin, by A- Weber. Ng. Prt Cm , 8 ff~C. No. 372! op. cit. Nglt Pr. Cm , 4 ff~Dated S am .. 1 834 (A.D~ 1779).D~ Wilson 503 in CataIog i Cod , Man . .BJb l . Bodle iane, by T; Aufrecht, Ng. Pr, Cm .

Dated S 2 . Q l . . 1 8 4 9 (A .D . 1793)..E. No, 373, inWeber . op, cit, Ngt Pr.. e m . 4 if.F " Modem copy procured. by A. Weber and used inhis edition.G. N o , D . .1 C Y 2 7of t h e Govt, O r . Ms s , Lib., Madras (GOML), Gr..P I . . Cm .. 4 :ff~H. No. R-6018(b) of GaML. Gr. Pl~Cm. 2 :It1. No. D -1 8126 of GOML. ra Pr~Cm , 5 pages,1.. No ..D-14097 of G01dL~ TeL P I . . Cm. 3 Jr .K. No. D..1028 ofOOML. Tet Pl. e m . . 3.if.L. No. R-4082(d) ofGOML" Tel Pt Cm. 3 if.M~No. D-1788f) of OO}dL~ Tel. PI. Cm, 2 pages,N. N o, 6 7034 of the Adyar uorary and Res . Centre, M adras . Tel. P I a e m . 2 if.


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PREFACE 9Ya ju r- V e da ng a J yo ti$ aA~ No .. 1 50 5, We ber, o p. cit. , with the commentary of S om akara . . N g, P r. e m .78 if.B. N o. 374, W eber" op, cit. Ng, Pr. e m . 5 ff : numbered 4 to 8 ..e l f No~375,Weber~Opt cit. Ng. Pr~e m . 6 ff. numbered 4 to 9tD..No ..W ilso n SOba" A u frecht, Opt cit.. Ng, PCI Cm , Dated S am . 1696 (AILD. 1639)"E-F t M odern co pies p ro cu red by Weber and used in his editiont

Part B is devoted to the Translation and the Exposit ion of the VJ and to th ed emon str atio n o ftb e principles and prac ti ces involved by means o f wo rk ed ou t examples.H erein tho VJ v ers es h av e been classified into five S ectio ns acco rding to the topicsdealt w ith by th em . . S i nc e mos t of the verses in the two recensions are common, bothare t ranslated and expla in ed together. T hus against the common verses w ould be givenboth the R- V J and Y-VJ r ef er ence s, wh ile ver se s OCCUlTing in only one o f t he r ecensionsw ill h ave the r ef er ence s on ly to th e r espe ctiv e r ec en sion. The following are th e s ec tionsunder which the v erses h av e been c la ss ifie d: (1) B en edictio n an d VaIedia tion ; (ti)M easures of T ime ; A s terism s etc .; (iii) Fundamenta l and derived Yuga constants; (Iv)Tithi,Naksatra etc. of certain special days; and (v) Daily Titrn and Naksatra and theirrisings and settings" T he rules fo r the calcu latio n o f th e days, parvas , daily ti this andnaksatras included.in the last section are not very obvious and the term s u sed are mostlyundefined that these verses have been most difficult to understand. Successivescholars who have attem pted to unravel the meaning a n d application o f these versoshave been successful in different degrees and most of them have left several of theverses as incomprehensible. T he length to w hich som e scholars, especially from th eW est, have been baffled as to have expressed them selves in a mos t unb ecom ing manner,with ig no ra nc e tu rned to anger and anguish , rm ght be illus trated from a statement ofD. W . W h itn ey , w h en he says: "And when we come to a d d that th e J yo tis ha (V.T)has no definable place in Sanskr i t literature, or relation to the Vedic cerem onial .. . Awes hall see that this fam ous datum " w hich has seem ed to prom ise so much, has cau sed somuch labo ur and discussion , and is even yet clung to by som e scho lars as th e s heet-anchor of ancient Hindu ch ro no lo gy, is no th ing but a. delusive phantom," (cf: h isO r ien ta l a nd L in gu is tz c S tudies , S econd S eries, N ew York, 1874, PI 384). M ay be,Prof. Sastry's rational interpretation of these enigmatic verses would induce thisWestern Onental ist turn in his g rave . .It goes to the credit o f P ro f. Sastry to have ta ck ledtb e VI in its entirety and to have b een ab le to give satisfactory- interpretations to allits verses, w hich, perhaps, is the most convincing of wh a t have been given thus far byscho lars w ho have attem pted the task.

I m ight close this Preface with a personal no te. It would seem that a w is h ex pres sedby Prof. Sastry; more than five years ago, finds fruition at this momen t In a let terdated March 3, 1919, he wrote to me: "Deer S harma, . o r . ~ Regarding the Vedanga.editio n, D r. A b raham (o f the C hris tian College, M adras) and Dr, A nsari (o f the A . M .U niversity A ligarh), asked m e to get it published by the Bharatiya V idya B havan .. t O therw ise, I w ould have wished It to be done by you, because if 1 s imply send t I i e manus-


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10cript to )'OU~ you wou ld have don e e ve ry th in g e ls e? H aving the highest regard fo rProf, Sastry and appreciation for th o confidence that he had been placing on meduring our c lo s e a ca dem ic r ela tio n sh ip for nearly 30 years. I am happy that my associa-tion which he had wished for in th e edition and publication of the Vedanga Jyot i$ahas ultimately b een fu lfilled , th ou gh u nder circumstances not envisaged by hirn,

The present Translation and Notes of Yedanga Jyot isa has been prepared on thebasis of the draft thereof and the related papers left by Prof. Sastry with his son Dr ..T. K. Balsubramanian, Scientist, BARe; Bombay, who placed them in my hands, fortheir edition and publication through a common friend, Shri S. Hariharan, ExecutiveDirector, Uc, Bombay, who, bes id es , was an admirer of Prof. Sastry . I am . thankfulto both these friends inthe matter. M y thanks are due also to the Bharatiya VidyaBhavan and the Indian National Science Academy , the former for agreeing to publishth e book, in the first instance, and the latter for a ctu ally p ub lIs hing th e work under theirauspices during their Golden Jubilee Year.

Adyar Library and Research Centre, Madras ,Sriiv tl lJ.a-pijr1:l ima, The Sanskrit Day~Augus t 1 1, 1 98 4K. V. SARMA


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INTRODUCTIONI. Ast ronomy of th e Vedic Sll t fIhitas

The Vedanga-Jyoti1a (Vl)be1ongs to th e late Vedic age. Even during the time of theearly m t I 1 J . d a l a s of the J . ! . . g v e d a astronom ical Info rm ation necessary for the day to da ylife o f the people, hke the knowledge of the s eas on s fo r s ow in g, reap ing etc.., had beenacqu ired, as among all ancient peop le s. In fo rma tion req uired fo r the r elig iou s lif e ofthe peo ple, like the tim es of full and new m oons, the last disappearance of the moonand its first appearance etc., necessary fo r the m onthly rites like the DarsapiJrnamasaand seaso nal rites lik e Caturmasya, had a ls o b een a cquire d. ' The nam es of the moon 'sasterisms (27) were known and used to indicate days.1 There are v estig es In theshape of the Vedic legends and nam es of asterisms to show the antiquity o f partreularmant ras . Fo r in sta nc e, Agrah5Y t lVa , an old name for the asterism MrgaSir$a, meaning'b eg inning o f th e year', points to th e f ou rth mi llenn ium B c. when the sun was th ere atthe vernal equino x. The Rohin i legends po int to a time in the late ~edic periodwhen the po int shifted to the asterism R o h i l J . r ~ a T he later sacrificial session caIledGavamayana was especial ly desig ned fo r th e daily o bserv atio n o f the movements of thesun and of the disappearance of the m oon, and this must have given t he p rie sts suffi . .c ie ntly p rec is e know ledge about the astronomical elements, We have evidence to showthat even knowledge of a special kind, lik e th e saros of the G reeks, fo r predicting thesolar eclipse, was poss es sed by the priests of th e Atr i family, 4 .

The above type o f knowledge impro ved with t ime, so that in the Yajurveda periodwe can say wi th cer ta in ty that th e fo llow in g w as well known: The solar year w as knownto have 365 days and a f ract ion more" though it w a s roughly spoken of as having 360days, consisting of 12 m onths of 30 days each .. Evidence for this is found in the K!ma-Yajurveda: Taittirfya Saqlhz to (TS) 7.2t6; where the extra 11 days over the 12 lunarmonths, Caitra, Vaiakha etc., totalling 354 days, is mentioned to complete the rlusby the perform ance of the EkadoJar l i t ra or eleven-day sacnfice ..& TS 7.1.10 says that5 days more were required over the Savana year of 360 days to comp lete the seasons,addlng that 4 days are too short and 6 days to o lo ng .' F urther, five years w ere fo undto form a yuga , the nam es of the years th er eo f being Samvat sara , Parivassara, ldavatsara,Anuvatsa,a and ldvatst l la. ' This )'Uga was used to reckon time, as seen from suchstatemen ts as 'D lrg hatamas, son of M am ata, becam e old even in his tenth yuga, Le,between the age of 45 and SO.8Even ear lie r, the tw o intercalary months , called ~pati and Samsarpo, required to complete th e yuga, were known, as seen from th e state-ment veda mlisa dhrtavrato dYadaiapr aja vatlib /v eia y a upa jiiy a te ll (RV 1 .2 5.8 ).

The six rtus in the solar year, wi th the names of the twelv e tr op ica l month s, a regiven by the s ta temen t:

MatlJzuJca Madhavaica Vasantikav[tU! Sukrafca SuciJca Gra 4mOv rtU , N a bh aS caNahhasyaJca V5r$ikavrtU, Isaica ' O r j a J c a saradavrtU, S ah aS ca S ah asya icaHaimant iktnl tU J T apa sca T apa sya ica SaiSiravrtf i . (T S 4.4.11tl; VOjasaney iScJ t tth1t ii (VS) 13.14).


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12It might also be seen that th e sacr if ic ia l year commenced w ith Vasanta (spring).It had also been noted that th e shortest da y was at winter solstice when the seasonalyear SiSira began with Uttardyana (Ka~itaki Brahmll1).o,19.3) and rose to a maximum

at the summer solstice"2 Datable Ved ic pa ss ag esIt was observed that the moon came b ack to th e same position in the zodiac oncein about 27 days and that each da y was m ark ed by th e asterism or asterismal group(nak1a tra) near w hich the moon was seen , result ing in callmg' the asterism as the day'snaksatra; from which the 27 astensmal segments of the zodiac came into use. Thenam es of these with t he ir p re sid ing derties are enumerated in the Yajurveda, beginningwith Krttikot w here the spring eq uino x w as situated at that period. The thirteen and ahalf naksatras ending with ViJtikM, situated 10 the northern hemisphere, were calleddevanaksatras; while the thirteen and a half others ending w ith Bhara~i were calledyamanaksa t ras , as seen from the passage: Krttikah prathamam, V iJa kne u t t amam ,t ti n i deva-na lqa t rl ir ) i. Anu ra dh ab pra th am am , ApabharQ~ f r u t tamam, tan i yama-naksar 5 J : J . i (Taitt. Br~, 1. .5..2.7). Incidentally, this would give the age of the observationas c. 2300 B..C.

Another statement about the Krttfkiis points to even an earlier period: Vide thepassage = e ta (Krttikfl) ha va i p rlic ya i diJo na cyltJJante~ sarva:u. i ha l'ai anyiini l laksatrQ1;) . ipro.cyai d i J a J cyavante (S dta pa th a B rB hm an a, 2.1.2.3)4 This means that the asterismalgroup Krttika never sw erve from the east, while the others do" The meanin g is confirmedby SiYaQ.a 's comm entary . T his po ints to c . 2950 B.C"

A fa r later observation is reported in the MaitraYalJiya Bri ihmana-Upanisad,6..14; to the effect that the winter so lstic e w as at the m id-point of the S r a v i 3 1 h . ase gmen t a nd the summer solstice at th e b eg inning o f Magha~Th is poin ts to c. 1660 B,CJ;a little before the period of the Vet ldnga Jyotisa.E ven regular astronom ers are mentioned by expressions like prajfianaya naksatra-dtuJam (YV-Vajasaneyj S Q 1 ] 7 h J t a , 30..10; Tait ..Br. 3~4t4.1),and y a d t J s e ganakam (YV~

VO j. S lJ 1!l, 30 . .20; Taitt Br.~3..4 .154 '1 ). A Na'lqatra-vidya (S cience of the stars) ismentioned in the Ch iin do gy a Upa ni$ ad , 7.1.2.4; 2..1; 7.1..These references would givean idea of the astronomical knowledge w hich had been acquired before th e time ofYJ, on the basis of which the P 'I has to be adjudged ..3 . Text of the Vedanga Jyotisaor th e extant Indian astro nomical tex ts, th e VI is the earliest, The astronomicalmatter forming the basis of th e work is of one Lagadha, but the c la ss ic al languageemployed inthe work as current now would indicate that the original must have beenredacted by a later person belonging to the last centuries B.C. The same system asmentio ned in the YJ is seen in th e MaMhMra t a , th e ear lie r ast ronomical samhit i is likethat of Ga rga etc.,. and the P a i t l i m a F t a Siddhdnta condensed by Varihamihira (VM)inhis PaiicasiddlJantika (PS)4 The VJhas com e down in tw o recensions, one belonging


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INTROnUcnoN 13to the &veda (R..VJ) and the other, which is later, larger and more advanced in itsmethods , to the Yqnuveda (Y-VJ)" though their basic content is almost the same.Later than these came the Atharvava Jyaut isa , attached to the Atharva V eda , called sojust for the sake of uniformity ..While the first two are astronomical, the third dealswith the Muhiata branch of astrology", %11e the first two purport to be based onLagadha's science, the AtharvaJ;Ul says that it was taught by Pitamaha to Kasyapa ,4 1 1 Date o f th e Vedi i l iga JyotisaVerses 6j 7 and 8 of the Yajur-Vedanga Jyotisa (Y ...VJ) show that at the tim e ofLagadha the W Inter so lstice was at the beginning of the asterism $ravis lha (Delphim)segm ent and that the summer so lstice w as at the mid-point of the Asle~ segment. Itcan be seen that this is th e same as was alluded to by Variha.m.ihira in hIS Pai icas iddhdn-tiled and B rhat sa r ph ita ...Since VM has stated that JD. his own time the summer solsticewas at Punarvasu i,and the winter solstice at Uttar~arj.hli - I " there had been a preces-sion of 11 s te lla r s egment s; i.e. 230 20" . From th is we can compute that Lagadha's tunewas 72x23 1/3=1680 years earlier that VM~s time (c. A.D. 530), i.e, c. 1150 B.C.If, instead of the segment, the group Itself is meant; which is about 3Q withm it,Lagadha's time would be c. 1370 B~C.5 . . Ve r if ic a ti on of the date of LagadhaThe date arrived at as above can be confirmed by the Si l ryas iddhan ta and theSiddhiin ta S i r o m t J J : l i which give 290~polar longitude and 360 polar latitude to Sraivl lha .F rom this, the actual longitude of Sravi$!ha got is 2960 151 S ince the siddhdntas use thefixed zodiac beginning with the vernal equinox of c. 550 A~D " " and the winter solsticeof this is 270, there has been a precession of 2960 15' minus 270Q=:26 15'~ Smce26ix 72== 1890 years, the wanted time is 1890 years, befo re A.D .. 550, i.e, c, 1340 n.c.,being the same as the above. the small difference being observational ...

We can also calculate the tim e directly by com paring the position of Sravi i lha(Q D elphm i) at the time when the w inter so lstice w as 270 , With its position in 1940 AID~(Rt, as . . 2Qh 36m 519=309 13', and declinatio n 15 4 2 J N) ..ln th e fig ure : The obliquityis about 23 40', r is the vernal equinox, S is Sravi l lha and R its Rt. as, position.s

ts42'A ~ ~ - - ~ ~ - - - - - - - - ~ ~ ~ - - r - ~ ~ - - - - ~


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14Rr=360C--Rt ..as..~50 47'. RS is the declination =150 42/~ R S is the continuation ofSR up to the ecliptic. Now: ~

( z ) From the rt. angled spherical triangle RrS, it can be calculated that RS= 180461; 8,=530 13!t;and angle 8=75 17'..

(ti) From the rt. angled spherical triangle SSS", SS" =90 53 J3 " J $ 1 1 being the celes..tial longitude of S m A ..D- 1940. It was 2700 at the time required ..Therefore, the preces ...sion is 3600-530 13'-270+90: 53' =:46 40 ' ..Multiplymg by 72, the t ime i s . 3360yearsbefore A.D..1940, i..e..c. 1400 B.C. If th e beginning of the segment is mean t and $ravi~lhais about 30 Inside, it is c. 1180 B.C..Since all these is subject to small errors of 0bserva-tion, itwould be noted that we have got from all almost the same date for VJ . .One may wonder why so much trouble is taken to prove this. It is because that

late L.D. Swamikannu Pillai has f ixed the date c. 850 B.C~, after a lot of argument,in his Indian Ephemer i s , vol. . I,Pt. i. p p . . 444 . .45 . . Trusnng in the so-called Drk-gaJ.lzttaPaiicQAga of the K um bhakonam M u tt, in South India., h e has accepted the precessionin 1916 as about 22f, with the spring equino x of about A D. 550 as the first point of thefixed zodiac. This would give 22iX72=;=:1620 years earlier than 1916 for the springequinox of VM~s time, i.e, c. A.D. 300 . . Th is d if fe rence of about 250 years is taken bySwamikannu Pillai as VM's observational error, since he ha s taken that VM' s date iscorrectly A.D ..550. .Proceeding from this, he argues that in about 1600 years there is anobservational error of 250 Years, and "allowing the same proportion of error for theprevious epochs, the antiquity of Vedii i tga Jyotisa observation, ..... may also be reducedby 2 S0/1620 !p i.e, by 2/13; in o th er w ords, from 3300 years before DO W to 2792 yearsb efo re now, Le.. from B.C. 1400 to B.C 850." ( ib . ., p. 445) .

Note here the strange lapse on the part of PIIJai, taking that th e error of observa-tion depends upon the time elapsed. On th e other hand, it depends on the instrumentsused and the 'personal equation', and not "proportiontate' to th e time elapsed. Hehas confused this with the error in th e cycles derived from previous observations"which error alone can accumulate with time.

Further, VM 's observation was remarkably good. The vern al e qu in ox was at thefirs t p oin t of the Tndial l zodiac , defined as being about 10 1 east of the 'Junction star"of Revott , which, from its c o-o rd in ates g iv en by the s idahiintaJ, must be identifiedwith Zeta Piscinm A ll s iddMntos) explicitly or implicitly, take the precession to bezero at about this period and the vema! equinox was s i tuated here at thts period. Sothere w a s very little error of observation on the part of VM, which is a remarkablething. If so, the precession at 1916 should be about 19Q since (1916-550)+72=19 ..How, then, has this 22 i0 precession arisen in the T am il Drk. almanac, it may be asked.This ishow it has happened. All Hindu s i i l d I r a n t a s give a s iderea l year intheneighbour-hood of 365-15...31-30 days, which is about 8, v I n a t / i s more than the correct siderealperiod ofthc Sun .. S i nce the S un is tak en to return to th e first point of th e H indu Z odiacafter each sidereal year, the first point of the Hindu zodiac itself ~ a precessional


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INTRODUCTION 15movement (though taken to be fixed), and, reckoned from this point} the rate of preces-sion would be not the rea150H .. 25~but 50".25 plus 8". 5 ; : ; ; ; ; : : : a b o u t 59H This error of 894 5has accumulated up to the trrne of the appearance of the Tamil Drk almanacs at theend of the last century, and when the Kumbhakonam Mutt Piicanga originated abou ta hundred years ago, the error had accumulated to more than 3. In order to fall Inlrne witb the s iddhi innc new year day and thus avoid popular outcry If the correct c..19 precession were to be adopted, in which case the new year would have to be begunthree days earlier, and also to avord certain difficulties WIth the dharmaids t ras , thisDrk Paiiciiilga tacitly adopted a precession of 19 plus 3=22, to hide the fact thatthe Drk system was an innovation and to create the Impression that It ha d been inexistence from time immemorial. This had led Pillai to this error In judging the periodof the VJ.96~Con ten t s of the Vedanga Jyot isa

The system of the VJ IS the same as that taught in the GargasaT]!hi ta of theS Q ' I 1 2 h i t a period, being the immediate centuries before Christ and the next following,Paitdmaha S iddhan ta condensed in the PS and the Jam works like Jyotisakarandaand Suryapraj i iapt i , . The only difference is that the Paitiimaha gives a rule for thoVyatfpiita-yoga and the Jain works have brought down the winter solstice fromSravilfha to S ra V C O J O . , and included A,bhij l t (Vega) as closrng the zodiac, giving it asmall segment at the end, All give the five. . .year yuga of 1830 days WIth 62 synodicmonths in it. Everything else, like the 67 lunar sidereal periods etc., can follow fromthese three given Item s, The Pa i t amaha instructs that the naksatras and tithis are tobe calculated from the days elapsed in the yuga using the unitary method ..The Jainworks give the days and the naksa t ras in a parva , from which they are to be calculatedfor the other parvas and days.

The VJ states in detail that in the yuga there are 5 solar years, 67 lunar siderealcycles, 1830days, 1835 SIdereal days, 62 synodic months, 1860 tithis, 135 solar naksa t ras ,1809 lunar naksa t ras and 1768 risings of the Moon, all derivable from any threeprincipal elements. It also mentions that there are 10 ayanas and visuvas and 30 rtusor seasons, and the naksa t ras and t i this of these are enumerated, their number beingsmall. But the other things sought to be given, hke the daily llaksatras and t i this Wi t htheir ending moments , the hour-angle of the Sun at the ends of the parvas and tithis,the hour ...angle of Sravil lhd with the lagnas , which are too numerous to be enumerated,have bocn given by ingenious rules that enable them to be calculated mentally dayby day, as we want them. It is these rules that have baffled interpreters, since theya r e couched in archaic, technical and terse language, and the purpose of each cannotbe seen easlly and the terms used are not generally defined. The day is divided into124 bMgll3 or parts, so that the ending momen ts of the parvas and t t thts can be giveninwhole units. Tbe da}!' is again. divided into 603 units called kalds; so that the dura-tion of the lunar naksa t ras is given in whole units as 610 kDiiis4 The naksa t ra IS dividedinto 124 a w J ( l S so that the naksa t ras passed at the ends of the parvas may b e ex pressedin whole amJas . .A table of the division of time is given, beginning from gurvak ,ara


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16or the double matra or long syllable, to the day, passing on to the yuga . The practicalway of measuring time is mentioned as the trme taken by a specified quantity ofwater to flow through the onfice of a specified clepsydra, as one nutjik& or 60th partof a day,7 .. A ccu ra cy o f the V e d aitg a J yo tis aWe shall DOW proceed to ex am rne the accuracy of the system, a much discussedaffafr. The VI says that there are 1830 civil days in the yuga , in which there are fivesolar sidereal years and 62 lunar synodic months. This gives 366 days for the yea rwhile It is really 3651 days; known in the Vedic period before; as we have seen. Also,it must have been known, even at that penod that 62 synodic months take almost aday more than the 1830 given, because even at the end of one yuga; the amav5sy i i(new moon) must have been observed to occur on the da y next to the 183Oth. .Obse rva . ..non at the end of the next yuga would have shown this unmistakably, since on thelast day of the yuga the Moon would have been observed to be well up in the skyat sunrise, showing the day to be ca turdas i or even t rayoda i t ; so that the ami iv i i syawould occur one or even two days latet.10 The p ries ts " whose duty It was to observethe last disappearance of the old Moon and the :first appearance of the new Moon,could never have failed to nonce this, for there was priiyaScit ta (penalty propitiatoryrites) for transgression either w ay (see below, verse 12 and notes thereon).

Then, why this apparently absurd system? The answer is that it was meant pri-marily to pro vide a civil calen dar, w here co nven ien ce o f d ivisio n and ease of calculationis Important. The 1830 days period is dIvisible by 5, giving 366 days for the year.This is divisible by 6, giving 61 days for each rtu (season), The ayana has 183 days,The two intercalary months, over the 60 normal months can come, one at the end ofthe 5th ayana and the other at the end of the 10th. The difference from actuality isalready there, because only the computation of the Mean Moon and the Mean Sunwas known, which itself could give an error of more than half a day, So the rules forcomputing the various Items like naksaua can give only approximate results. Butthe religious calendar required correct results, and this Civil calendar Intended forthe day to da y life of the people could serve only as a frame-work to guide the religiouscalendar .. Certainly the priests must have framed rules by long observation to gettolerably correct positions, 50 as to avoid the penalty laid down by tho jQ.3tras~ asmentioned above. For one thing, a day could have been tacitly added to the yugaafter its end, as suggested by many. (even as we do evt:zy fourth.year to get the leapyear), and not counted in the calculanon, to make up the 62 synodic months, 80 thatthe most patent discrepancy could be avoided. H~ Krishna Sastry Godbole, writingabout the Vedic c a. Ie ndar in 1884, s ugge ste d th is . As this would amount to allowingthe error to accumulate to one da y before correction, some suggest that the uncountedda y might have been placed at the end of the 5th ayana , Le. after the first intercalarymonth. Tilak suggests that it was done at the end of the 93rd parva and addsibat it is actually instructed by verse 12. I think he is not correct (cf" theverse).


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INTRODUCTION 17But there is another type of error that will accumulate in course of time. 62synodrc months 18 ex actly 1 830 8 96 5 days. So, the correct Mean S un would be 454'in advance of Srav i~ /ha , each yuga, It will accumulate to 30" In 30...;.-4-54 yugas~Tobring the Sun and the Moon back to 8ravfJ lha, one intercalary month will have to be

dropped after 6 yugas and another intercalary month after 7 yugas , and this has tobe repeated. The priests could have found this rule by experience and used it. Butit must be noted that it is not even necessary to know this rule to drop the intercala-bon, because mere observation of the Moon in the Sravi3tha region of the sky wouldhave shown this, for this must have been the rule during the Vedic times (as theMuslims do even today, by observing the crescent M oon) to find the need for an inter-calation, for thrs IS independent of the knowledge of the exact periods of cycles.

But" still, in course of time; the winter solstice itself would move from SrQvi l lhato SravtlTJa and so on, at the rate of about one naksatra in 100 0 years, owing to theprecession of the equinoxes; and this correction must be done to know the correctseasons. It has already been mentioned that the SUryapToj i iapt i and other worksactually placed the winter solstice at the beginning of $ravQ/;latt But one thing iscertain. Long after the time of Lagadha, the system of the VJ was followed in Indiaas seen from the Mahabharata , the Ar thaSas t r a~ GargasQl1fhi ta and the pQj tamahaS iddhan ta , first inall parts, and then at least in some parts, for almanac making, andthat is why it is described in the PSas one of the systems. m vogue, though crude. Butby then it had come to be linked Vl i tb the luni..solar year to prevent accumulation oferror; as we have already mentioned ..8 . M odern s tu d ie s on Vediinga JyotisaThe above discussion would show how wrong and unjustified W hitney was,when he remarked: "The s o-c alled Vedic a str onomical manual (VJ) whose first objectseemingly ought to be to give roles on such points (as amiivasya etc.) is mostly filledwith un-intelligible rubbish, and leaves us m the lurch as regards valuable information."This remark is born of frustration, for, i f un-in te lligible, how does he decide It isrubbish?

The V]attracted the attention of the early Indologists like SirWilliam Jones andColebrooke, especially the two verses placing the winter solstice at S r a v i J J h Q J whichcould help in determining VedIC chronology. Later, Capt. Jervis, who was investigatingthe Indian measurement of time, noticed it in 1834. Prof. A Weber was the first tobring out an edition of both the recensions of VI with the different readings from.the manuscripts available to him, But excepting for a few simple verses in th e Firstand Second Sections of the edition presented her embe1ow, few could interpret themain body of the verses. It was in 1877 that Thibaut in his article entitled, "Contri-butions to the explanation of the Jyotisha Vedanga' published in tho Journal 0/ theAsiatic SOCie ty of Benga l (47J.411..37) could decipher a few of the difficult verses,l~ out several verses, including 11; 13-17, 19-23t25-27 and 41 of the y.VI UD-touched, His knowledge of astronomy and adequate knowledge of Sanskrit helped. .


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18 VEDANGA JYOTI~to interpret the o ther verses, in spite of the obscure t e rms and the apothegmaticIanguage, because th e meaning of these could be guessed if what they are driving atis known, Then, in 1884, H..K. Godbole tried to tackle the problem of the correctreligious calendar to be got from the approximate civil one, Next, S~B~Dikshit,in his Bhdratiya JYDtisa-ids tra in M arathi (P oena, 1896 ) brought his excellent know . .. .ledge o f H indu astro nomy to bear on the VJ and interpreted s ome mo re unin te rp re te dve rses " , Bu t the more important verses were left untouched by him. In 1907t LalaChore Lal, Execunve Engineer; W ..P .; brought out a full-fledged edition, adoptingthe pseudonym "Bhhaspatya', giving his ow n interpretanon to all the verses, re-printing them from the Hindus than Review, wherein they had a pp ea re d s erially .H ow ever, in m any places his m eaning is not clear in spite of his long explanations ..Neither ha s he mentioned wha t was being done nor bas he given examples . .At aboutthe sam e tune, M. M. S udhakara D vivedi of the Q ueen's College, B anaras, w hohad edited the PS in c olla bo ra tion with G . . Th ib au t, edited the V J with an oldS a ns krit c ommenta ry by Somaka.r~ in which he noticed m any o f th e in te rp re ta tion sof "Birh.aspatya', some of them as corrected by h im . H ow ever, his p eculiar V/ayofemending the verses drastically has affected this edition. Then again_, hIS p re sump .. .tion of the use of bhii tasaizkhyii is u nw arran ted . . But even where he agreed, he hastried to show off his superior lm ow ledge of S anskrit by giving hIs own 'better'interpretation. These exasperated 'B lirh as pa ty a' to such an extent, that he issuedan A p pendix criticising Sudhakara Dvivedi right and left One very good servicethat 'Barhaspatya' ha s done is to ap pen d a critical edmon of both th e recensio ns o fthe VJ, to his edition of the work .

The renowned Indian patrio t and freedom fighter, B .G ~ Tilak w rote his 'Noteson the interpretat ion a/ th e Vedanga Jyot isa . . C r itic tsm s a n d sugges t ions ' in 1914while he w a s . lodged in jail in M andalay, B urm a 11 H e took for criticism y...YJ 15 ,]9~27 (with i ts variat ion R-VJI3)~ 21,20,25,26,12, 14 and R..VJ 19. Of these y . .VJ15~20~ 21, 25 and 26 h av e b een dealt correctly by him , po intIng o ut the defects andmistakes in the interpretations of 'Blrhaspatya' and Sudhaka.ra Dvtvedi, but inY-VJ 19 he committed th e s imp le m i st ak e of taking udvapet to m ean 'should beadded', instead of ' should be taken away' .. By this he missed the meaning of theverse and, to make up for the error in th e rule created thus" he had to misinterprety: .VJ 27 and R~VJ13 a . s well as to suppIement it. Still, h is in te rp re ta tion is onlyapprox im ate, as he himself bas owned . . Thus a perfect ru le w as spoiled by a smaIlmistake1' The involved interpretation, requiring sev eral p ag es o f ex plan atio n, shoulditself have told him that he was going on the wrong track. Idisagree with his inter-pretation also of y..VJ~12and 14 which he takes as p ro vid in g fo r th e one day to beleft out o f count, to correct the system to keep in step with reality~ Y-VJ 27 deals

with lagna, about the meaning of which he is no t sure, In th e present edition allt he se po in ts have been dealt with convincingly"W e have already seen that, at about 1916, Swamikannu PiIlai took certainpoints in the V J for discussion (vide his In d ia n Ep ht1 n 6 ls , vol, I, pt. i,ppll 443-56;


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INraODUCTlON 19'The Vedanga Jyotisha calendar'). In 1936 , R . S ham asastry, R e td, Curato r, O rientalLIbrary, and D Irector o f th e A rchaeological R esearches in Mysore brought out anedition of the Y- VJ, WIth his ow n Sanskrit commentary and Bnglish translation andnotes, It is not a c ritic al edition and in spite o f the good interpretations of scholarsbefore him he has misinterpreted almost all the verses included in th e FJftb Sectionof th e present edition. He has quoted from the Jain works, but exhibits ignorancenot only of their meanmg but also of their purpose. F or instance, in order to getthe parva . .n a k s a t r a s and O 1 ( l J a s , th e number of naksatra and a J p i a s moved in oneparva (which I S . grven as a constant) are m ultiplied by th e number of p a r v a s . Thiscannot be done mentally and, so y..VJ 15 and 18 give simple rules to get Itt ButShamasastry interprets that th e said tw o verses give the days no t fit fo r dariapw-' (U lmQsa sacnfices and, ev en that, using hIS own pecul ia r criterion for the same. A sfo r getting th e parva-1U1lqatras an d a t r z $ a s , he asks us to add to those of the previousparva, the motion for one parva, and this too In kaltis~ mostly fract ional I His inter-pretatio n o f y . . VI 13 is a monument for his capacity, A n d, the m ost ridiculous as-pect IS that he criticises th e earlier interpreters, who a re by far h is superiors. Stilllater, D r. Satya P rakash o ffered a detailed treatm ent of the topics dealt With in theVJ in th e chap ter en titled 'Lagadha: The first to rational ize astronomy' in his bookFounders of Sciences in Ancient India, (N ew D elhi, 196 5,. pp. 455~512)1but he takeshis t rans la tions verbatim from Sb amasastry and in th e explanations also fo llowshim w hich m akes his treatm ent liable to the s e v e r e lim itations o f his source-book .9. A cknowled gem entsI have the satisfaction now that what I began in 1960 and worked off and onhas been duly brought to a completion, I think of all those who have helped me inth e publication of this edition, especially to the B haratiya V idya B havan, Bom baywho provided a forum for my expounding th e sub ject in detail in the Workshopon Ancient insights and mode rn d i s c o v e r i e s organised by them. M y thanks are due toevery one who has devoted his attention to the 'VI, irrespective of whether he hasdone w ell or ill, for I have benefited from his work in some way or other, I cherishw ith g ra titude the m emory of my tw o friends who enthused me in the work, firstthe Vedic and Vedanta scholar, Malma Narashimachariar, a respected preceptorof th e Mumtrayam S ect, who learnt the Sidyasiddhanta and th e y a j u l a - J ' " e d d i 1 g aJyoti3a from m e, and second, S rinivasa Iyengar of P eriakulam , R etired Head M aster,a Vijasaneyin and a man of many parts with a fund of knowledge who d iscu ssedmany problems with me and gave me his copy o fT ila k's p aper on the subject.

T~ 8 1 1 K U PPA NN'A S A S TllY


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2 0 VEDXNGA JY~REFERENCES

J . C f 4 BKveda 1 .16 4 48 :Ila. . _ ' ' ' ' ' e d

ifcfiq " a u ' " . . ; ; fIf.;.mN4 CdI. fa_ 1m ; : r 1!1,i1Wtdi:II f b a A IQ'T "'''' lIQ: uCf~also Bgveao. 1 .94 . .4 :

.. (11(_ liIfI!iNt


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PART A

CRITICAL EDITION OFVEDANGA lYOTI~A

I. ~GVEDA.VEDA.NGA-JYOTI~AII, YAJURVEDA-VEDANGA-JYOTI~A


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I. S 1 l \ i ~ f a ' t + l (R-VJ)"f .t l S A ! 4 6 'C ( U ( f f l i \'1 m r~ 5 (G j r q f t r l O ( If~if t4:q'1+ e M I'!l f O l R( ftmrl ~; J [ 1 1 1S I ' J I4 f i n II 411{1Z i t f'fl4'l iI ( f q a1"( I~ 'U n pi ' S J i I ' ~ r f l t it~r e l ~ :q i l l e + l1 1 : J t " I ltRi1Fa t ! t [qij'; ,,


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24(mrr) U ' k I 4 " l l i


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2 5li$d {t4J4'1aT ;rff ~-; ;t i S ~ ~ f e : tu r d lSl("'f~ t~ (ift) ~ r FsTi f c { $ I a t f f

t r a r r m ~ I~ fqq~~f1Jr+( II~~ H( ~ ) ~ f f . t r t 11F i rr~ ij"U t ( q r u t q'rul r~~. g ~ ~ 1is:rrlf ~q'U[(+( n~~n!iq[4ij~~ltPr 1firs (~ ) Si'6~41 rfill(f(ftr);rarur(~) f4'1f~ * ' H i (I r o - ( ; ; r ) n,)(Uqfi;f; 5 : l G l 1 4fi:r; ~l+n ~s fe ;r ti4~~~ J

~ f t t & ~ ~ f t rWi llif d~!fEtq i t 1 1 T - ' 4 ' S f ( II + T 1 1if II~~ r r F e n ) , ~ 1 S2 I 1 "f I I Q O Q i \ : " a fi. , 1 f ir e f ~ = t r f~ f i r . i f d ( I tt l ~t i l t ! t 4 - 1 "1'~C f ~ II~~1 tf. t~ 4 Q c i l u n s;r ~ql c t ; ; N c r !if I'4 f t ! ;& '4 t'd f l O " T" f 4 1 l i ! f i 1 . ' lPf ~ "if J 1 ' : ( ~ n; r e a w 4 q ~ r t J : ( I TlfGtm~ lJItd.,i;I

~(j'I~ l i ; , rif i l l r;:r lH a G i f ' l i : 1 l ( r J ~ ~ It

~ (if) :q ffiq l S I ' f o l i ~m:qtrifull '( [f((ifcc4l['14Iijt'i & t Ilr(~) ~fit~ II~til

; rT~V l 1 5 4 , ff (~) r f ( 1 S t t i~~1 f 4 '9 : ITttll Q &EFcf4(~ ) ' 6 T t ! 1 w P i S f i i l i f l 3 " n~~Il~ i f 4 l f f ~ t 0 1 1 o i f l t f t ( ~ Q l r r i j t r ) )~ = i f fif,}:rpt s r ) i ' r aR ( 1 f t " ) ~ ~ ~ I I~~ II'ifwi"q~:Jftqij~T ~ ~ f ( i = l ' ~ f a o q r l t + i I: I~ ~1!f&1lf t;41T ~ ~ e R t S S l~ t ~ 6 I I N 2 h 1 + ( 1t~)(1 r1 j t I j T " P i T ~ f ' l l t ' 1 1 ' I 1 # 1i 'T O [ t i t ~ J" , { q < { 1 t f c n W f t~ , 61i


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26 vmAilOA lYOTijAM~ i t : ififr4'ff\l5tifflr:*M]1~i rqf~IQ~ ~r; ~a f ' i 1 l f ~ ,mc fa'Mlill'(d;ft G t t l F C ' t ~ ~ ~ ~ r 1 " \ u~ \ .IIlf r G 4 1 r a ~ ~~ ~ ~ " I f " ~ l i ( r I

qs; f f la j t 'Q


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YArnlA1Y~ 2722. (c) All mss.m ql!\ff; P.~ ..23" Ca ) C.E ..P.G-N. ( f ' { ; C.D 'd'. (d) A.B. 4'6LI4T~ C..D B..fl-CllI2 4 1 > (a) C..B. qtIN (b ) All ross. ~4.1scil;:j ;C.E '3 l~ (c) All mss ufilr; A."B .. f(fl't W f t" d 1 1 { ,

L. m!Afmi'(; aU other mss, ml'l'ttRlll'( (d) C.E q~;qij' t all mss. ~2S I (6) NqlillR f i J : . (c)G. ij1q1"rid'f!Ai{26. (6) N. "Ilftti ca. f1rit2S t (a) AtB.Br t n n " . (t:) G.II [Eel,,":29.. (a) All mss ~m: G.. c ; ( ' & i f U l , (b) G ~. (d) All mss, 8 ! f f C l f r d ; (0) Wllifsy30. AlI IllSS ~ (N ~); aU IDSS. "iffuit (G q - r o rJ K .. GifW). (h) All mss m L ~ (A. , . " I " I ~ . .

D . ;il4 d1 l B.G.K. Ait, L W ICfil),H~K . qfutdl(~ N. l T r w m t (c) All mss, w l f t ;all mss ...fw (G. 'Ifut. K. " f f < t l l ) . (4) G..fim~ frfOi6 . .

31. (a) C.E. ii114l ~. (6) (x) "'l i lT;;; CB. ""i(';r''{..(e) C.F. IIUfldt (tl) All mss, ~; N rtlq.ij~(.32. (a) G . liiNfl; all mss, ~~. (b) N. f l+i INUr", (c) C . Eo.~ ~33 4 (b) AU nus. ~ 4 I L t Q f t l J : . . (c)H. ~ = i f ; A.B . f c : r . F t F J C .D .E loF,.L. fit,! a t i. (d) A ll mss . I I (~r :q'ro. 'I


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28 VEDANGA JYOllf.AMJfPf! lJ:%!I I t N t ~

'= "mt 6Ojij"l r f i J 'l : ,

~ f ? f : s 1 fi t 3t-tftfl d 1 1 X n~1l!64d l+ r r q l- t ~ m ~ ~4lttcn I~['i'j


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29'$rtti 11ill [&!4f1fT;r ~T Q ! ti Iitr e t ~ f tT . ,a;ifNt~ ( f t : r ) ~a~ ([~qcf) I I , tilfa N t 4 1 1 1 : J U f R f 1 *,'jfq~W( " q W 1 ~ t{ i i i '4 i fImt J I ( ~q a!'lIf i 1 f 'f rJ ~ i j(:q 1f':!tl q : r 1 ' = { 0 u

f~ ;:a~ ~ n r~ ! @ f lw f ~~ltij( Jtm'r ~!f ~ fdftr: : g o f ~ ' " f 4 1i~;Ip\ ~ II

t f C F 1 r M ' t f ; ; . . o ~ N i ~qi a a tf~ffiflittl' s : 1 0 f lR f . ~ ~ If q { f ~ r q ~ ; f ~&qtg ~I : t (dit r p g tflllfltg ~ ! I C + { I0 1 ~ II~:II

(~ ) 1 lit~ f~i!iIi{IWI~t i f g d O Q F l t " l : f f 1 4 i f t 4 " ~ f'ITiM ;nftr w 'RTsit;:I~tlli i t \ i $ I ? f i f i ' ((q) II,\!It

\i'(qr iI1~~ I E 4 r~",(If i n ; ( '!)q : s :a q , : IiJj(~Ifl'd~(t.iE 2 '1 ,f ; i j lM (i)~~Uj 1'( II~trI


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30 VBDANGA .TYamAM

~tlr N 6 G T S 8 I " ' C f P f t ~ . ., , , ; f t f iw r ~ ~ ~~ f i t 4 F a ([til ~ 1 4 l!41(C:t - t f ! f = I f n ~~~If~"l~ql ~ a f t S G l ' 1%11& 6 l l q : o r I~~T ~ t r l 1 t q . " . lI+r ~ ';f H~Yn% w l e r a r lP m l ( i , l fqqfi4i~ I. . . .l(\JI~ l fl TQ i l# l : ;n;r ;;&iQla) ~~ II~~II\fl4 J V C tr A i ~ ~ ~ ftfAll & I I I C f ' l I l S l f d l fti r' { { T fV r ~ ~r ( \ < t (tf!) v l f ~ l ~ 1I~ ~ I IHI I( ilJ;i f~ ftz" '4 ( 'i ~ ~ ~qu111lRtidlf1~lqa. ~s; i j " " l f s t I + a C f 1 1 n ~\3114+U q ~rqitll '(41\ (i) "liM i f r f i 4 1 r,,(~)~ dNiIi1I'11 2 : * ,e:_ 8dt Q 4f! 4~ 1 ~ 1I~~11~ " 'd E t i ~ ~ : ~ ~ Q 1 t i l C ; : Q T I(ijijijIf;r) g q & E f F Q f = i3f)166f tf&ll r ft~ f ~ II q tr r

lf$~ (~llI*'fft i r f f ' E Z I T -(:;)~ ~


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31' 1 ' + { w i ~ i 4 r i fCllr1 ~(q~ I '1 + R A 4 ~ " 'i t f ( d ~ ~ ~ 1"afC''( U)(~u

~ ~ ;q ..afa+( IItf~:q:aqt~< (m~) I fi:f E .,. ii, C it'lL~. (b) B.C.D ..R ~ P. N~; B..C.D B. ~;

A .F i f : i " l : q T j B.C .D .E .F . B ' J ' i I " . (c) A 4 ~l{*!fT, B ~J o.urlIS,F . A T 4i4lctl; aU m a s 'Plf(d) D . lw T lS M

19. (a) C,. 'IEIII' (h) A.B .C . ~;r (c) A ll mBS . & ( I ' d f e r (d)AE.F ~ ~*'tIAt i(J B.C~D~ 64"(1 A f 4~(~.)

20 . (b) B q3:i(q, 421. (b) F. i E t t t f i J . 1 I J T , F 4 ftr1\; (c) AU mss, ~Qijl('dml22. (b) AlI m s s . it f F I u r t . (d) B ~D t M 6 6 i2 3 4 (b) ltD4 ",)44 (d) B. ~i A . t1dtt:


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32 VEDA NG A JYOTI~A M24.. (0) A ~ '! .d 1 M j D.P25. (a) A. = { ~ f 4 ' = t B.C D.F~ f d l i 4 y I 1 . . F..f;{1:fW!;ALm; A vm : (b) A. ~!fi"~'{. (c) B . ' l=lIr:v;r; C. qUil)(tl) A.B.D ff 'i('q1C.m..(d) All IDS$,. ' t d : r : t l t " '28. (a) A.BD E. f~l!l~l. (h) E. C(~qd 4 T (cd)A ~ (for ~) i~~ (d) A. ltaT:J D.F. ~29.. (a) A~-qmq~: (b) All mss ~ for ij', A ~~J B q - : ; ; ; o ~ . (c) A. ~ql1~f~~~ (d) All mss.

,qiM(A. w)30. (a) B.c. . qs::qf!iI[. (c) E"F ~a r t~ A.E . . ~.q'Jfr. (d) B D tfqiif;l: ~~31. (a) A-E. ~fta+tI~Tijt" F~~r (6) A. ~; m,B.C.D.F ~, E. m (c) A.B..D.E. 1 1 : f f ; C f ll c r : . ~c. l 1 f a ! l i l ~ J A. (4rwt j ~ IB D..F. ~rr4'1fl!Ia :1c. ~'EFt tmi:j E. ' I [ a t tl'tij Iti~(d) A~D. = v ; c 1 W . 1 U[ iJ

F. \4'R!ij i j32. (a) B . . - s r~ ; tlq fd33 . . (c) B..CD~om . t34. (a) A rB .D . add in the beg. ilJr. (b-c) A. vftsf~.q4 ~ IlR t t if ;i :: j[ 'd ! lfT ~ (c-d) A~E.F" ~'nE4;fr35, . (0) RF . ~ t t a T36. . (b) B.C.D.E.F ~~ a : o n . (c) A ll mss . t ' 6 t If a ' :37. (ll) All m s s . ~if~ (b) Ar ~; B-F q Z q o r : , (c) A ii~J F lfi~~ (d) C. lf~38 . . (a) B.C,D.lTr~lU;F. f~~rr. (b) A.E.F. ~lftIJ B. ~ fir~C"D~~ 1 1 : , p~~. (c) . ,!rii41~,

B.F~Rrf!ll({. (d)c~, E ~mrTi A~~ C f a l , B ?lff~, c~J D~~~ ..39. ALE.F ..~. (b) A ~R r (c) All mss, 'iilOfrtfi for ; : r . : : n n R ; A.E :q r for (j40. (a) F. i1Ti)4if'm. (b) F !!~ for 6 " t t T . (c) All russ ~ ~ A~N~) F. f~ i : f d " .41. . (a) B"CD r 446R i 1 . . (d) A T ~ , u . . .F. - i j . t'l(; B t r & f U r42.. (4) A .B . F. :ufu~ A. t f ~ - e r r " L r B.C.E.P. r m P t~~1> D. i f R I P l1 H " T l , (d) B-F . ' * m r r , B ..E. (tr~

42rO~ (a) c.~. (4) B.CD alflm; All mss, ? I t ( f e n .43. (a) A. iPr~i all mss , MAf~. (c) IU 1 m ss, ~ ~. (d) A m ~1 B.C.D. ~~d


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PART BRE~ARRANGED TEXT, TRANSLATION AND NOTES

SEctION I. BENEDICnoN AND VALEDICTIONSECTION I I . IvIEA sU R ES O F T I M E , A S T .B R . IS M S E r c .SECTION m~FUNDA M ENTA L A ND DB lUVED YUGA CONSTANTSSECTION IV. T I n n , . NAK~TRA ETC . QP CER TA IN S PECIA L DAYSSBCTION V. DAILY TlTHt" NAK . ~ATRA ETC.


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RE-ARRANGED TEXT OF VEDANGA JYOTISAillSECTION I

B EN ED ICTION AND V A LED ICTION1. INTRODUCTTON

Text Ipa i i casamva tsa ramayam y u g o d h y a k g Q 1 1 Z prajapatim/d tn a rtva y an amd s iis g am p rll'( lom y a slrasa SucihIIR . .V J 1; y:VIIjyo tf l8m ayanam punyam pravaksyamyanupurvaSab/sammatam b r a h m a n e n d r W : t a l T l yaJ i iaka lar th l ls iddhaye lJR~VJ 3; Y - V I 2prasamya sirasa kalam abhrvadya sarasvattmlkaJaj i iQnam prayak$yOmi Lagadhasya mahatmanah/ fR. . .VJ 2Purify in g my self and saluting with bent head Prajipat.1, the embodiment andpresider over the five-year-yuga and who bas for his lrm bs tim e-segm ents lrk ethe day, month, seasons and courses of the S un (ayalUl ) , I shall write syste-matically about the effect on tim e of th e movement of the luminaries, meri-torious by Itself and accepted by learned b r a h m Q 1 ) Q S t fo r the purpose of deter-m ining the p ro per tim e for th e d if fe rent s ac rif ices . (R - V I I, 3; Y- V J 1-2)

Arca-lyot i$a or Eg ve d a-V e tIa .n g a-J yo t~ a (R ..V I) has a different s econd vers e,which completes the first, thus:

And, having saluted Tim e with bent head, as also Goddess Sarasvatl , I shallw rrte on the lore of Time" as enunciated by sage L ag ad ha. C R -VI 2)2 .. IM POR TA NCE OF A STR ONOM Y'

Text 2veda hi yajMrtham abhipravrt tahkaJDnupUrvya vihitdi ca yajiiabltasrniid J d a m kaIavltihanwiistra1ltyo jyo tisam veda sa veda yajiian I I y.VI 3

The vedas have inde ed been revealed for the sake o r the performance of thes ac rif ic es . Bu t these s ac rif ices a re dependent on the (various segm ents of) tim e.Therefore, only he who knows the lore of time, viz..Jyot isa , understands theperf ormance ~o f the sacrifices (fully). (Y -VI 3)


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36 VEDA&GA JYOTJSAyatM jikhU. mayi i r t i 6Qf /1 l l i i gonom mavayo yathtijtadvat! vedangaSustra,;i i / ' f l jyoti1aln miadhan: s t h it aml /R ..VJ 35; y. .VJ 4Like ' the combs of the peacocks and the crest . . .jew els o f the serpents, so doesth e lore of Jyo t i sa stand at the head of all the lares fo rmmg the au xiliaries o fthe Vedas . (R..VJ 35; Y-VJ 4)

Note 1. GQ1)ita, a variant reading fo r ]yotiva m eans 'com putation ' w hich is theessence o f th is science.

Note 2 . The Im portance of every kind of lo re is stressed by being praised in them anner done here by the w riters on that lore.

3 . BENEDICTIONText 3

somas ur ya strca ritO JfZ v id vd n v ed avid a sn u te ]somasi iryas trcart tam lokam loke ca santatun!!R- VJ 30; y~VJ 43One learned in the Vedas who ha s also learnt th is lo re o f the movem ent o fthe Moon, the S un and the stars \ViIIenjoy, after death, sojourn in th e worldwherein the M oon, the S un and the stars have their being, bes ides having, inth is world, an unending Im e of progeny. (R. .VJ 30; y-V J 43 )

Note 1 DIfferent deities o r groups o f d eitie s have their own worlds , where theirdevo tees go and enjoy happiness after death .

4 VALEDlcrIONText 4

ity e vam m i is avaY Im ; tim muhUrtodayaparvr.mQm/dina rtvaya11Gmiistingam( 'lniim} yyiikhyfina1J1 Lagadho 'bravft/I(Y..VJ, unnum bered verse after 43)Thus did the sage Lagadha speak In detail of the (synodic) months ; the year,th e muhUr tas , the ris ing s, the syzygies, the days, the ( six ) se as on s and th ecourses of the S un w ith the (so lar) months. (Y-VJ, unnumbered verse after 43)

Note 1. In W eber's :firs t and critical edition, th is verse appears u nnumberedbefore the last verse 43 of th e y .. V/t It is not found in 1 l h e R VJ. The verse enumeratesa n item s c ompute d in the work, with the nam-e of the source , VIZ. the w ork of L agadha.Perhaps , it is a later addrtion, to supply th is need. S ham a S astry , in h is h ig hly un-critical edition o f VI, numbers th is as 431 and the last v e r s e as 44~


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SECTION IIM EA SUR ES OF TIM E, A STER ISM S ETC .

I. TrnE MEASURESText 5

palam paiicdaaJad apam dhrtiini ta d a dh akam dronam ata/l prameyam!t rl hh ir v ih in am kudavais tu ki iryam f a n ni id ikayas tu bh av et p r o u z m . z a m l l y:VJ 24A vessel w hich ho ld s (ex actly ) 50 palas of water is th e measu re called adhaka .F rom this is derived th e drona measu re (w hich is four times th e adhaka). Tinslessened by three kudava measures (i.e, th ree-six teenth s o f an adhaka) is th evo lum e m easured (in the clepsydra) fo r the length of one nii.{iika of time. (Y - V I24)

Note 1 1 According to th e d ictum that ultimately some term s w ill have to be leftundefined, and taken from usage, the weight and relation betw een the w eight andvolume measures alone are m entioned, just as we say 1 gram of pure water au 4Cis 1 ce. The clepsydra also is not descnbed here 4 There are several types of this, des--cribed in astronomical works.

Note 2. R . .V I 17 gives a substitute for this verse:Text 6

nadike dve muhiir tas tu . paiicasat pa/arn.Qjakam (? i idhakam} fmasa(? at jha )kii t kumbhdco droflah kutapair vardhate tnbhib/ /R ..V I 17Two na(l ikas are one muhnrta, The o c J h a K ; a is fifty palas. From the a f / h a k a ,kumbhaka or dror;a increases by three kutapas. (R,..VJ 17)

Note 1.. Kuiapa seem s to be the sam e as kudava as current in some parts of India.N one o f the th ings m entioned are related to one ano ther or the n a r J i k a 4 Indeed, funda-m entally the lacuna is to be supphed from usage. But here IS lacu na w ith a vengeance.

Text 7ka la daSa s a v U r z J a s}lid d ve m uh urta 3ya n i i r / . z k e Idvf( ? dyu) stri1 f7 Jat ta t hali inl im tu ~ a!c ch a ti tr ya d hik a b ha v etllk : ..VJ 16 ; y.. VI 38The n a t l l k a (m entioned In the previous verse) is ten plus a twentie th kalds oftim e. T wo nd(ii/cas make one muhUr t a . T hirty tim es the muhUrta is a day whichis equal to 603 ka liis . (R ~V J 16; y..VJ 38 )


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38 VEDA&GA JYOTl~AText 8

_.. pddas trimsat tu saikikii!(Y ..VJ 12b).. -kG /lh anam caiva tfib kaltib!( y:. V J 30d)

31 kasthas make one pi ida. (Y-VS 12b). . (Four pfidas) (equal to 124) ka$/hiismake one kala. (Y-VJ 3Od)

Note 1. The word t a b here refers to the four pddas given in the t t 1 1 r d foot of theverse as cafuspodi . being a compound of catumdm piiddnam samiiharab. The wordpada itself means the number 31 by the statement, pallas trimiat tu saikikd (Y-VJ 12b) .The word pdda in thrs verse also signifies 31..

Note 2~ The reason fo r adopting the above . .s ai d s ign if icance js that the day isdivided into 124 bhagas or parts .. Since a quarter ( p a d t J ) of this IS 31, the word padaIS used to sigrufy the number 31 . Similar ly , the asterismal segment also IS divided into124 parts called a m J a s or b h O m a s .

Text 9ka$IM pai icaksara bhav et] Y - V I 39d

One k~fhii is equal to five aksaras (letters of double matras) . (y-VI 39d)Note 1~ The aksara mentioned here IS the length of time called guryalqara, equalto two 1)1dtriis o f tim e.

Text 10ardhapai icamabhas tvrtu{.J!(R~VJ 9d; Y- VJ lOd)

Four and a half asterismal segm ents is one rtu. (R~VI 9d; Y - 'V J IOd)Note 1~ The period of the Sun or Moon moving through 4j segments is a rlurelated to it, i..e. the Sun's flu or the Moon's rtu But the popular rtu or seasons isonly the Sun's. (cr. the Vedic statement. MadkuJ ca Madhavas ca Vasant ikav rtil!

SukraJ ca Sucii ClJ Grail'ndv r tU/Nabhai ca Nabhasyai ca varjikalJ r tu /llaS ca uQ asca S a r a d d v rtil/SaW ca Sakasyai ca Ha iman id v r til/T a pa s ca Tapasyaa ca SaisirliVrtilJ(Vaj. S am . 1325; Tait S am . 4~4+11~1)~Text 11

t r iSatyahniim 9 a s . 4 1 1 i r abdab ~al car/avo 'yane!rnQs l i d~adaAa s U r y t ib " c ta t paRcoguqutm y u g t tm . ! ! y.YJ 28


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U. M EA SUR ES OF TThfB ETCt 39T hree h un dred and srxty-six days form the so lar year. In the year there areSlX rtus and two ayanas (Sun's courses). In the year there are twelve Bo la rmonths, F iv e years make a yuga . (Y - V J 28 )

Note 1~Thus we have th e table:5 gurvaksaras or 10 mat rQs1 2 4 f c Q s lh a s10 1/20 kaliis2 na ikas30 lnUhidtas366 days

5 s ola r y ea rs

.::= 1 klis{ hiilkalii:=1niidlkii~=1muhia ta=1~day (i.e the civil day)=12 so la r month s or 6 rtus o r 2 ayanas or 1 solaryear~ J yuga

Note 2 .. The nad lk i i IS thus connected In tw o ways, first WIth the speech ormusical m easure of miitrQt and second with the flow of water in the clepsydra of 50palas of pure water, measuring an a{ihaka.Note 3. YuglJ mean s 'jo in ing or coming together ', t echnica lly the coming togethero f two or more of the Sun , th e M oon, the star . .planets, their nodes and the apogees,at the sam e place in the zodiacal circle m arked by the asterisms, The five-year yugamentioned here is the period when th e SUD and the M oon meet in. the s ame a ste rismal

positron In the zodiac, discovered in the Ved ic p err od rtself, and which is roughlycorrect. The Vedas have a name for each of the years o f th is y ug a: S at}'J va tJQTab,Parivatsarait, Jda( {la)l1atsara(1, Anuvatsarah1 Id (Ud)va t sarab (Va). S a m . 2 7~ 5), w ithsom e variants in certain places.2 , . ASIERlS)rs: PRBS ID1NG DEITIES

Text 12agn ib prajapatiJ) $0010 rudro 'duir brhaspatl( t/sarpaJ ca pitara S ca iva bhagas ca iydryamap i ca l Jsavl td t V t 1 1 1 d t h a vdyuS cendr i igni mura eva ca lin dr o n ir rtir Opo va l viivedevQst ta thaiva callvi~ur va sa vo v~ ' jaekapat ta tbaiva ca la hirbu dh ny as ta th a pUla aivino yama eva ca llnaksatradevata. hy eta etlibhir yaj f iakarmar.uyajamt inasya sOstrajfl.ailt n a m a n aksa tra ia m sm (tim /!(R . .VJ25-28; Y-VJ 32-35)

The presiding deines o f the a ste rism s ( be gin nin g f rom Krt t ikah) a re , re sp ec -tively: Agni, Prajtipati , S om a , Bud ra , A dtti, B rha spa ti, S erpen ts , P urs (M anes),Bhaga , Aryaman , Sa v i t a , T V t l I t a , V fiy u , In d ra g n l; Mitra , Indra, Nlrrt i , Waters J


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40 VEoAAGA JYOTijAV is ve d ev a s, V q ~ Vasus , V~~ AjaeRapf id , Ahi rbudhnya , Piqan, Asv lns andYama The people learned in the religious lores say that these deity ...namesare to be substituted for their own names in the (sankalptJ of) the yaga (ofthe person on whose behalf the sacrifice IS performed, VIZ.) ~ ya jaUlJ ina .(R- VJ 25-28; y..VJ 32..35)

Note 1+While naming a child, it was the custom in ancient times to choose aname the first letter of which is appropriate to the usterism under which the childwas born. A set of letters is associated with the asterisms. Even now, conversely, whena person's naksatra is not known, he is given a naksat ra appropriate to th e first letterof hrs name, for religious rites or horary predictions In ordinary religious rites, It 15declared in the introductory resolution (sai ika/pa) . 'I, bearing this name and bornunder tlus asiensm, am going to perform thrs rite.' But when he happens to be theya jami i na in aYQga, in the place of his own name and astensm, the derty of the asterismis to be substituted, the idea being that he is now one with the deity and the deityitself is perform ing the yaga, as" say, 'AJaekapad yajate', mean in g, "A J aek ap ad per-forms this yaga~'

Text 13ugriil}Y i i rdri i ca citra c a v iS likh a s r a vano "8vayuk IkrUrQ1:li tu magha svdt! jyes/hi i midam y amasy a yat] I Y - V J 36

The asterisms Ardra, Oi t ro , Vliakhd, S r a v C l 1 ) 4 and Aivini are fierce. Magha JSvat i , Jye~thii,Millam and Bhafa1} . i are c r u e l asterrsms, ( Y - f V I 36)Note 1 4 These arc mentioaed here as an exception to the previous verse, andthe nam es cfthe deitie s o f th es e should not be used for th e purpose mentioned. F urther ~these should be avoided in choosmg the tune for the performance of auspicious ntes

like mamage.Note 2. The R. . . .V J does not have this verse.

3. RULB OF T H R E EText 14

ity u pa ya samudd eJ alt b hiiy o 'py a J r n a I J prakalpayet ljifeyarQiigatablryarta (? tam) v ibhaje t jMna ra Jin iil lR ..YJ 24; y..VI 42

The fo llow ing is 'the rule of three' (for obtaining th e desired result), This ruleof three is to be applied aga lD and again .to the day. (using the fundamentaland derived constants grven in tho work, in order to get the various computa-tional rules and results given in tile work). Tht. rule is; The known result isto be multiplied by the quantity for Which the result is wanted, Iand dividedby the qnantity for which the known reswt is given. (R-VJ 24; Y-VI42)


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ill. YU GA CONS TA NTS 41Note 1~ The instruction is concise and looks like an aphorism. There are fouritems in a proportion, three known and one unknown, which is obtained from the

three knowns, Hence the rule to get this is called the 'Rule of three'. The fonr itemsare = (a) If for so much quantity, (b) so much result is got, (c ) for this much quantrtyg iven now, (d ) how m uch is the result that w ill be got? The firs.t two a re c alle d jf la . ta . .rasis and the next two are called jiieya-rw, The application of the rule is: Take theknown result, i.e, (b) , multiply It by the quantlty (c) for which the result is to beknown,' and divide by the quantity (a) for which the result is given; thus the result

I to be known, i.e. (rl)~ is got. Though the verbal description of the rule is long, it issimple and known to every school boy . .SECTION ill

PUNDA M ENTA L A ND DER IVED YUGA CONSTANTS1. YUGA AND ITS ELEMENTS

Text 15uda ya v a s r a vasya syu( t thnarasib sapaficalaJb./rs er d viS ll$1 1h fn am syod vimiatya s aL ko yii s tr ~/! y .. V J 2~p a i i c a t r u n S a m s a t a m p a U S 1 J .am ekonam ayanany r $ e h lp a r v c o ; t 5 J ] 1 s yad catuiplido 4 ., I I y..vJ 30 a-csi ivanenaus trmdsiindt t t ~a$Il/) saikadvlsapt tki i]dyutriJrziat s v a n a s y o r t l h a b s u r y a ! z s t r ! Z o m sa paryayab l lY-VJ 31sasaptakam bhayuk . somab s i iryo dyftnl trayodasalnavam dm tu paiicahnab ~.. , 4 fiR ...V I ISa-c: Y - VI 39"a..c

Note 1, The p res en t section co ntinu es from verse Y...V J 28; given in the previousSection II, Text II" and it s meaning should be understood here, viz. the 366 daysform the year and that in the year, there are ,6 r tus , 2 ayanar and 12 solar months,FIve yea r s make the yuga. ;

. .' ...The num ber of rtsrngs of the asterism Sravi l lha in the yuga is the number of4 a , y s , 1 J lu s j f i V ~ p C i r q l , 183Q+5,Tl&15)~~~Thelnumber~qf flsings p i the Moon is 'thedays m m u s 62 , O . . e . , 1830~62~i 768)t , T h e toial of eaoh of the MOOB'S 27asterisms coming round 67 times in the yuga is the number of the d a y s . minus21 (i.e, 1830-21:=1809). G y . . VJ 29)In the same way, the total of the astensms of the Sun (which comes round 5times) IS 135. There are one less (i.e, 134) ayanas of the Moon (i.e.. its north ..ward and southward courses), There are 4 padas (i.e. 4X31=124) parvas (orpaksas, or their ends, i.e, bright and dark fortnights) In the yuga~... (Y-VJ30 a-c) -


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In. YOG A CONS TA NTS 43U sing the rismgs of Sravi$thii in the yuga ( viz. 1 835), w hich are also the num berof its Orient E c lip tic pomts (prag...lagna)~a.nd multiplying it by th e nwnber inthe g roup (here, of asterisms, viz. 27), we get 1lItetotal number of l agnas in theyuga (viz. 1835 x27=49, ,545). Multiplying the sidereal revolutions of the Moonin the yuga by 6, we get the total number of lunar rtus (viz 67X 6=402).[Considering the mandatory verb in the first half of the verse, one can translateit also as; USlng the distance of SravisthO. from the rising point (i.e. its hourangle), and multiplying it by 27~ w e get the l agna , in asterism s and parts)1*(R-VJ19)

Note 1. In th e yugat the S un m akes five round's forwards in the zodiac, whichitself is rotating rapidly backwards round the earth , S ince the time of the motion ofthe S u n re lativ e to the earth 19 the civil day, and there are 1830 civil days In the yuga,the zodiac itself rotates round th e earth 1835 (1830+5) t imes in the yugaJ the tImeof one rotation being called a sidereal day.

Note 2. A single or a group of asterism s of asterism al segm ents, being fixed In thezodiac, m akes the same number of rotations. Lagna , a s u su ally used, is th e point of theecliptic rising on the eastern horizon S ometim es the word pri ig ..lagna is used to distin-guish it from the Occident (W est) E chptic point and Meridian Ecliptic point (dt lJama-lagna) . Now ...a-days lagrta is mentioned only in connection with the riiiia. In those daysthere was no division into rasia, but there was the division of 1 ! h . e zodiac into naksatrasegm ents. W e do not know whether the lagna~ in those days, was of th e asterismsthem selves or the asterism al segm ents. The exact tim e of the rising of any point can becalculated from its distance from the diurnal circle, the whole mandala representmg6 03 '" 'lO s or 124 parts of time, (See also S ection V . . 4, below.)

Note 3. In the text the syllable g U o has been emended iato ga , making gU{ f l J intog Q f 1 a by me. Dikshit has takengWul to mean 3~aeeording to the bhUtasa i lkhya notation,but this notation does not seem to have been in vogue at such an early period. In thewhole of the work w e do not find Itused anywhere else. But Barhaspatya commits aworse mistake by interpreting gu:{lQ as 8 in the bhiltasankhyii , wh ich tr an sg re ss es allco nventio ns. T his kind of transg ressio n w ill resu lt in ambiguity, while the requirementis that the numbers are precise"

Note 4. The Sun or Moon's ayanas is spoken of as beginning from their situationat the first point of&Sravisth~ segment or midpoint of the A s lesa segment, repsec-tively (See Y~VJ7 in S e ctio n IV. 2~below). The ayanas have 3 rtus each. T he siderealp erio d c on ta in in g 2 ayanas have 6 Ih4. In the yuga, having 6 7 s id ere al periods of theMOOD:t the rtus are 67 ~ 6==402 . . It is noted that while the names of th e rtus Sisira,V asanta e~ . beginning with 1be S ' u m at rg~t\ lA are signifioau,t' as referring to realseasons, in' the 08Stf of !he MOODl they ~o simply Domina!.

I Note,jrr L.II!ve emended lftinto! sta, making it staryiin w Inch m eang ~pertarning to"iar&r~tTy,;-rJw.ok~bb!te Vedic word narya ,ls in ce the word stery is an uncommon


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44 VED.A .MOA JYOTISAword, it is easily mistaken to be surya in the copying of manuscripts. But the Iun~rrtus cannot be related to the solar months, as it t ransgresses the statement ardhapan-cam abh as tv rtu1)t which justifies the emendation. Rgvedms pronounce even o la ss ro al(fa as la as in the Veda itself.

3..DAy ...TJMET e . : r t 17

g Ju rrma vrd dh ir a pQ l]1 prasthab lqapahrasa udaggatau/t lak3i1 )e tau viparyasalz $QJ)muhiirtyayanena t u I I R . .VJ7; Y-VJ 8During the northward course of the Sun, the increase of day-time per day isthe sam e equivalent o f one prasiha (o f w ater used in the clepsydra) The nightdecreases at the sam e rate and vice versa during the southward course. Duongthe whole course (aya1 ta) the increase or decrease amounts of 6 muhi ir tas(=12 nadikli3)~(R-VJ7; Y-VJ 8)

Not e 1.. The time when the courses begm and end is given in the next Section.From the given data the duration o f the course can be calcu la ted to be 183 days, andthe increase per day, which is given as one prastha; can be calculated from the data Inthe previous Sect ion to be 4/6 1 ~ . F or the whole course of 18 .3 days, th e In cr ea seis 183~ 4{61=12 niijikas or 6 muhib ' tas .Note 2. The rate of increase given here is the average per day, It is very crude,Actaal ly , for the first and sixth m onths of the course it is approximately a sixth or thetotal, for the second and fifth it is a third, and for the third and fourth it is half.Not e 3.. The total increase is not the sam e in all latitudes ..It is proportionate to

tan declination x tan latitude. The latrtude corresponding to the total given here is3SO t in the extreme north of India.. The Vasiffha S iddMnta of the PaiicasiddM:tt t ikaof Varihamihira gives the same total mcrease , not to speak o f the crude Pai tWzahaSn1dlt i inta,SECTION IV

TITInJ' NAKSATRA ETC .. OF CERTAIN SPEC IAL DAYSTRB FJ ~ YEAR YUGA

rniighaul:JJaprapartnasya Pf lU1a/q lfUlSatniipitltiifyugasya pll i lcaYar$aSya ka/ajiiiiltatn p ra c lc :a ia fe //R ..YJ 32; Y-VJ S

M en @ . ik e the respected Lagaclha) give the details aboun the jimt's of variousi tems in the five-year yuga whtch begins with the bright lort.nlsht 0f the JUDn1lk


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IV" TITHI, NAK~ATRA Ere. 45of Map and ends with the dark fortnight of the month of Pausa, (R-VJ 32;Y-VJ5)~

Note I .. This g iv es the epoch , nec es sa ry for calculatmg any item, US1ng the rule ofth ree g iv en in S e ctio n 1 1. 3.Note 2. The plural verb needs the understanding of a plural subject.

2. COMMENCEMENT OF THE YUGAText 19

svar akram ete so zn iirkau yadii s a k a m savi isavau]syi i t t addd t yugam mi ighab tapab suk lo ' yanam hy udalc l ]prapadyete Jrav~ tMdau s f1ryacandramasav udak ]sarpardhe dak$i1)arkas tu m.aghal ravf I?Iayol ) s a d o f f(R-VJ 5..6; Y-VJ 6-1)

When the Sun and the Moon occupy the same region of the zodiac togetherwith the asterism Sravi l l / za , at that nme begins the yuga, and the (synodic)month of M agha, the (solar seasonal) month called T apas, the bright fortnight(of the synodic month, here Magha), and their northward course ( u t t t : U a ' f J 7 .ayanam)t (R-VJ 5; y..YJ 6)., . .When situated at the beginning of the Srav i s (M segm ent, the S un and the Moonbegin to move north ..When they reach the midpoint of the Asle$6 segment,they begin moving south. In the case of the Sun, this happens always in themonth of Magha and Sravana, respectively. (R . .VJ 6; Y - V J 1)

..\Note 1. The VJs y s t em . ha s simplified the various periods as the 5 sidereal revolu-tions of the S un in the yuga of 1830 da]l'~ 67 sidereal revolutions of the Moon in thesam e perio d, etc. ThIS is done for CIVll calendrical purposes, which demand suchsim plificatio n, ju st as, In m odern tim es, the yea r is ta ke n by us now to have 365 days,ordinarily, with one day m ore once in fo ur years, callin g it leap year, with its own .furth er ex ceptio ns, T his serves only as a fram ework fo r a relig ious clalendar, S o , theyuga cannot begin exactly at the first point of S ravi$ thi segm en t g enerally, unlesscotrected .. FUrther, the given cycle-days are mean, wlnle the actual courses dependu p o n the true S un and Moon} affected b Y the equations o f the centre .. So, only theregion marked by the asterism Srav"ItM can be specified. The exact points of thesegm ents w here the courses begin were determined by simple c alc ula tio ns b as ed onin sp ectio n o f the sky. For details seeIntroduction, The words i idau and ardhe in Y - VJ7signify that th e ex act point of the segm ents are m eant, o f course, fo r the civil calendar.

;

Note 2 ' 1 1 Prapadyete here means 'move', not s im p l y 'reach' and ayanam means'movemens' , primarily. The ~ Imeaning is "the period of 'O\oyel'liOnt'. . Onlythe Spb'~Zl~~~~ly ~ t

I


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46Note 3. The beginning of the no rthw ard m ovem ent o f the Sun at Srav i l lha andthe m entio n aftb .e day-tim e to be least here (see S n . m~3,Y-YJ 8) shows that this is

the tIm e o f the w inter so ls tice . .F rom this, the tim e w hen the o rigm al w ork o f L agadhaw as w ritte n can be determined .. (S ee In troduction),Note 4+ There is a corrupt reading dinam tyaja!t for ayanam hyudak. This is mademuch of by some . (See Introduction).

3 . NAK ~ A T R A S AT nm BEGINNING OF THE A Y A NA SText 20

prathamtllfJ saptamam ci ihur a y a n a d y t J 1 f Z t rayodasam!caturt/uutJ da iama tn caiva ~?cadvifJ)yug oW dy am ba bule 'py r fau/ / (R-VJ 8; YVJ 9)VQ$US tV4Jld bhavo la S ca m itra s sa rpo ' sv inauja iam/dMta kai cayanadyQs syulJ (RV19a-c; Y ..VJ 10 a-c)

The first, seventh, and thirteenth tithis of the bright for tnight and the fourthand tenth of the dark for tmghr are at the beginnings. of the first five ayanas .T hese occur twice, ( i . .e..these fiv e a re to be repeated fo r the nex t five ayanas).(R-VJ 8; Y-VJ9)The naksatras at the beginning of the ayanas are STavir lM, Oitra, Ardrii~PiJrvapro$lhapadii , buradhii. AJJe~ii~ AYir t i , Pflrviild(llrD, Uttaraphalgunf andRohilJi. (R- VJ 8a-c; Y-VJ 9a-c)

Note 1. W M l is actually given is 'the beginnings in the even t f tJris, 4 th and Iflth ,are in the dark fortnight', In the ayana there are 6 synodic months and 6 tithis morebecause the yu .ga=62 s yn odic mon th s= 10 ayanas, a lre ad y g iv en , So, every seventhcomes as the b eginning .lJ ,.tu m eans 'a repeating period', here, th e fortnightNote 2 . Since inth e ayanathere are s ix SIdereal re vo lu tio n s o f the Moon and laX 9

more naksatras, e ve ry n in ete en th beginning from Sravi l tha. occurs as an ayana-n a k4 atr a .. DMtii is used as a . B y n o J + y m for A ryam an. Note 3.. I have emended caiva into ca dslh , omitting the useless Word eva" whichis better than Birhaspatya's explanation that the last foot w ith rune sy llables is a IJar,a-prayoga,.

. 4 . + " T a E VISUV.AText 21

~pam ~ dvablry f i l t ' rU paJ ,l It a llJ ~tu ~/yal laht lham t a m parvUl)i tathardhvtml (1tatharifJrmn) Iii., l:IIIa:MtflR=VI3L


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IV~TrrHI~NAIa lATRA ETC~ 47viJuvantam lvir a bhy as ta m rilp on am ladgwJ.lkrtan/palqa yadar iham pakiavatn iithis sa v iju va n smrtabll Y-VJ 23trtiydm navami in caiva pauJ 'V llma s irn tr ay oda sim (? masim athdsite] IIll1 th im ca l 'iJuYan proktall dvadaJyOm (?daS fm) ca samam bhavet] fR ..V J 33

Double the ordmal number of the visuve (or equinoctial pain1!) and subtract one,M ultiply this by 6 . The parvas gone are got, Halve this number. The tith! atthe end of which the v i 3 U V t Z occurs is got. (R-VJ 3 1 )Take the ordinal number of the viJuva and multiply by 2 Subtract one ..Multiplyby 6. What has been obtained are the number of parVQS gone. Half of this IS thenthi at the end of which the v~uya occurs. (Y- VI 23)The visuva is declared to occur in the bright fortnight, at the end of the tlthisTrt iya) N a l ' Q . J 1 7 i , Full Moo n , and in the dark fortnight, at $asJhi and Dvadasf .This is repeated once again. (R- VI 33)

Note I. The v isuvas , being equinoxes, occur at th e middle of each of the tenayanas . The interval between the visuvas IS 124/10 parvas= 12 parvas and 6 tithis. So,the time gone at the nth vi$Uva=(n-l) (12P 6 t}=(2n-l) (6p 3t)=(2n-I)X 6 parvasand half that of t t th is.

Note 2. There is no verse in either R-VJ or Y-Vl giving the naksatra of thesepoints ..Note 3. R...VJ means the same as Y~VJ23~Also R-VJ is only an enumeration of

the result of R..VJ31.Note 4 .. t rayodaa , meaning the 13th tithit In R-VJ 33 is wrong" and seems to havefound a place here by correspondence to the word t rayodasam inR...VJ 8. In that verseit IS proper since the beginmng ti thia are gt~en for the ayana points. But! here the endsof tho ti this are given and there is dvada i im , which IS correct ..dvadaiyQm in the latter

half of the verse is to be emended to dvada3 l tn , to fall in line with the other adverbialaccusatives.~t l. tTPS ~ A YUGA

Text 22Ie kOn ta r e t.~ mt1se ca piirvfm. krt~' ...dir (!m) uttarah/ardhayo(z paiictn arP Jiim m rdu (? rdu) pai fcadaa, ;amel l Y-VJ 11~

} IIn each of the two halves o f _ five-ye.ar-yuga, in the altetnating petioQ.s I Iof ODe s yn od ic ! l1Onth . aad tithi, the next rtu o ccu rs after the previous one, ( ; I Q .~ w o r t i B . t ~.the consecutive rtlU o ccur at intervals of two syeodic mon~ ~


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48 VEDANGA JYO ' I i SAtwo t i this because 30 rtus make up 62 synodic months), Regarding the eighthrtu; the 15th tithi com es as the beginning t i thi . (Y ..VJ 11 )Note 1.. The first rtu of the yuga is SrJira, as can be seen from the statement thatthe first flu month is. Tapas (vide R-VI7; y...VI 6), Tapas and Tapasya being the monthsof Sihra (err Tapai ca Tapa3yaJ ca SaiJuQv rtu, Vaj. Sam. 13,2~;Taitt. Sam. 4 .4 .11 .1 ) . .The next flu Vasan ta begins two synodic months and two tithis later, i.e.. on Cai t ra . .. .Sukia Trt iyB, Sis i ra having begun In the Mdgha-Suk la Pra thamd . This continues fo r

the rest ..Note 2~ The 15th tithi mentioned as the beginning of the 8th rtu is pur1) imd. Ihave emended mrdu as rlu and have taken It to m ean a co ntractio n for r tu-dyu.

6.. P A A T DE THE DA Y A T WHICH PllVA ENDSText 23

du (?dyu) heyam parvQ ce t pade , ...bhi igi i tmanl i ~paYriy iUpSan ntrdised adhtko y ad i] / Y -VJ 12 a.c-d

If the end of th e s yzygy o cc urs w ith in the first pada ( i e. 31 parts of the day),that t i thi 1S to be omitted from the reckonmg, If the parts are more than 31;the parva whose t t th: IS to be omttted is to be found by subtracting the numberof parts that has to be lessened fo r the elap sin g o f one parva each. (Y- VJ 12a, c-d)

Note 1. 31 parts is a quarter of the day which is divided into 124 parts. S o, lessthan 31 parts m - e a n s 'before mid..day' ..Note 2. Even todag, the syzygy falling before or after nud-day IS crucial til deci~iug the day for the performance of iii/~ though the tithi IS tsken now as true tjtltif,~Not e 3. The parts of the day, at which the end o f each successrve parva occurs,is 30 parts less and le ss e ach parva , s in ce th e dur ation of each parva~days In the yugadivided by 124= 15 days minus 30 parts~ This ltltJdns 2, parts less fo r each tlthi.Note 4. The verse. however, takes fo r granted that the parts of the day at whichthe parva ends is known, for then alone can w e know in 'Yhich pdtla of the day theporva-end falls. This can be learnt' only. .by unplieatLon froril.l 'the seCond half of thisver se , s in ce nowhere else inl the worlJ t ias it been ga:tenl W &. ean \ "p~ taking th esuccessive lS--day periods m the yuga , s ub tra ctin g 3 0 parts. fo r each, to get th e en d of the

successive parvas, This IS given in the verse. But this is 1 ! h e same as 1rL1r lng the parvanumber and subtracting 31 parts, or one p _ for each'l1lJr.'Vttr8ince we " \ V a n t onlythe ~ and can neglect wholeJ days accumulated, and., ~ 4 jriitfas mtke a full


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IV~ TITHJ, NAK $.A T R A B rC. 49tday, we can cast our fours, take the remainder and subtract one, NO or three padasfor th e remainders 1, 2 or 3. O r" w hich is the sam e, we can add 3 padas or 94 parts,add 2 padas or 62 parts, or add one pQ4a or 31 parts to the number of the parvas forthe remainde rs 1,2~ 3 respectively, interpreting bhagatl1lanO to m ean pai Ia-bhagatmani i .

Thus We get the simple rule implied by the second half of th e verse: Take th e ordinalnumber of tbe parva. Cast out fours and get the remainder, If 1 remains, add 93;if 2 remains, add 62; and if 3 remains, add 31. . If there is no remainder, t ake thenum ber alone" W e get the parts at w hich the parva ends.Ex am ple" Fin d the parts o f th e day ending: (z ? 37 , (ii) 43" (iii) 54 and (iv) 68 pa r vas..C i ) Casting out fours from 37~I, r ema in s . .So, 93+37+124=130/124=6 (module

1 2 4 ) , L SO, 6 IS the number of parts of the day at which the 37thparva ends. Verl f icat ion:37x 1830 -;. -124=546 6}124 days and the 37 thparvQ ends.

(ii) Casting out fours from 431 remamder is 3. So, 43+31=74 is the number ofparts endmg 43 parvas . Verif ication: 43 X 1830-;-124=-=634 74/124J which gives 74 p arts )neglecting full days.

(iil) Casting out fours from 54, 2 r ema in s . . SO:J 62+54=116 parts at the end of54 parvas. Verif ica t ion: 54x 1830-:-124=796 116/124 days, whioh gives 116 parts,neglecting full days.(iv) Cas tin g o ut fours. from 68, zero rem ains. S o , 6& itself is the number of partsof the day at the end of the 68th parva. Verif ication: 6 8X 183 0.-;-1 24 =1 00 3 6 8/1 24 ,w hich gives 68 parts at the end of 68 parvas , n eg le ctin g fu ll d ay s.Note 5..For the sake of convenience, the CIVIl calendar requires the reckoningof days from 1 to 15, c on se cu tiv ely , ta kin g the

vedanga jyotish of sage lagdha

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