Vedanga_Jyotisa_Lagadha

OF LAGADHA IN TIS Laks mente YAJUS RECENSIONS

OF

Edited by K.V. SARMA ## Page 3

VEDANGA JYOTISA OF LAGADHA

IN ITS RK AND YAJUS RECENSIONS

WITH THE TRANSLATION AND NOTES OF

Critically edited by K. V. SARMA

INDIAN NATIONAL SCIENCE ACADEMY

## Page 4

THE NATIONAL COMMISSION FOR THE COMPILATION OF HISTORY OF SCIENCES IN INDIA by INDIAN NATIONAL SCIENCE ACADEMY Bahadur Shah Zafar Marg. New Delhi © 1985

Printed at Sree Saraswaty Press Limited (A Govt of West Bengal Undertaking) 32 A.P.C. Road, Calcutta 700 009 ## Page 5

VEDANGA JYOTISA OF LAGADHA

## Page 6 FOREWORD The Veddnga Jyotisa of sage Lagadha is highly significant in the history of scienc in India, in the sense that it is the earliest full-fledged treatise on Indian astronom; As an adjunct to the Vedic lore, it forms a manual for the determination of rituals an sacrifices by the Vedic priest and for the preparation of a handy calendar for sociz and religious events. The work is current in two recensions, one in 36 verses relate to the Reveda and the other in 43 verses related to the Yajurveda, most of the verse in the two texts being common. Several attempts have been made earlier to edit and interpret this popular tex However, the fact that the work was but a manual and not self-contained, and tha there was much to be learnt from tradition and practice towards a correct under standing and interpretation of this cryptic text has made all the earlier attempt suffer from some inherent limitation or the other. As such, it 1s a matter for gratification that the late Prof. T. S. Kuppanna Sastr took up the task of preparing a textual study and rational interpretation of the work He combined in himself erudition in Vedic tradition, knowledge of Indian astronom, and equipped in modern mathematics. The draft he had left before he passe: away in 1978 required to be edited and made press-worthy. Moreover, the Sanskri text needed to be critically edited from original manuscripts, and the necessar indices etc. prepared, to make the publication academically acceptable. This additionz work has been done in a scholarly manner by Dr. K. V. Sarma of the Kuppuswar Sastri Research Institute, Madras. In placing before discerning scholars of Sanskrit and Science the ancient text o Vedanga Jyotisa, I have great pleasure in recording my sincere thanks to the sons a late Prof. Sastry for making available their father’s erudite work for publication b the Indian National Science Academy and to Dr. K. V. Sarma for preparing thi scholarly edition. Indian National Science Academy S. K. MUKHERJEE New Delhi Vice-Chairman National Commission for th Compilation of History o Sciences in India ## Page 7 CONTENTS Page

CONTENTS . a . . . . 5

INTRODUCTION o 11 1. Astronomy of the Vedic ‘Sambitas— 2 Datable Vedic passages— 3. Text of Vedanga Jyotisa (VJ)—4. Date of VJ—S. Verification of the date of Lagadha—6. Contents of the WJ—7. Accuracy of the VJ-—8. Modern studies on VJ—9. Acknowledgements Part A: TEXT OF VEDANGA Jyorisa . - a 21 I. Arca-JyorigaM—RGVEDA VEDANGA JyorIsa . a 23 IL. YAsuga-JYOTISAM—YAJURVEDA VEDANGA JYOTISA . . 27 Part B: REARRANGED TEXT OF VJ WITH TRANSLATION AND NOTES an 35 SN. i. BENEDICTION AND VALEDICTION.. Bo oe Do 35 1, Introduction . 00 . Bd 35 2. Importance of Astronomy .. . . oe 35 3. Benediction . . . 36 4. Valediction os . . 00 36 SN. ii. MEASURES OF Time, ASTERISMS ETC. . . 37 1. Time measures . . Bo 37 2. Asterisms—Presiding deities .. . . . 39 3. Rule of Three . Bo o . «=—40 SN. iii, FUNDAMENTAL AND DERIVED YUGA CONSTANTS no . 41 1. Yuga and its elements . . . 41 2. Lagnas in the Yuga Oo . Bo Bo 42 3. Day-time . . . a 44 Sn. iv. TITHI, NAKSATRA Etc. oF CERTAIN SPECIAL Days .. . «644 1. The five-year Yuga . oe . 44 2. Commencement of the Yuga . . 45 3. Naksatras at the aa of the Ayanas D0 no 46 4. The Visuva oe 50 46 5. Rtus in a Yuga . Bo od 47 6. Part of the day at which Parva ends .. . . 48 7, Current year of the Yuga .. oo a0 _ 50 ## Page 8 6 VEDANGA JYOTISA Page Sn. v. Datty TITHI, NAKSATRA Etc. . . te 51 1. Introductory Oo Bp Oo 51 2. Computation of Parvardsi . . an 31 3. Asterismal parts od od oe 52 4, Bhamsa or Naksatra-parts . . D0 53 5. Hour-angle and Lagna . . . 54 6. Naksatra at any Parva . BG BO 56 7. Kalas for Moon’s Naksatra BG BG o 58 8. Tithi-naksatra in the Javadi series we . oe 59 9. Bhadanakalas . . . 60 10. Time of the day: Position of the Sun... . o 61 11. Sun’s Naksatra at any time . OG 62 12. Day’s parts at the beginning of the Naksatra o D0 63 13. Corrections for the Sidereal day ae . oO 64 14. Corrections for the Yuga Oa Bo Bo 65 15. Rtusesa: Tithis yet to elapseina Riu .. . . 65 16. Day-time at any Parva . . Bo 66 17. Upavasatha and Intercalary days . . o 66 BIBLIOGRAPHY a . o 68 i. Text editions and Translations . 50 Do 68 ii. Studies BG . . . . 68 Verse (Pada) INDEX . on a o 69 ## Page 9 PREFACE Vedanga Jyotisa (VJ), ‘the astronomical auxiliary of the Vedas’, of which a critical edition with translation and detailed exposition is being issued through this publication, is the earliest Indian text devoted exclusively to the treatment of astronomy. The work is traced back to the teachings of sage Lagadha (c. 1180 8. c.) and is current in two recensions exhibiting but minor differences, one pertaining to the Rgveda (R-VJ) and the other to the Yajurveda (Y-VJ) and called, respectively, Arca-Jyotisa and Yajusa- Jyotisa, The work had, primarily, been intended as a manual for the determination of the times for rituals and allied purposes, for the use of the Vedic priests who supple- mented it, as needed, with the concepts and practices imbibed by them by tradition. This latter aspect, coupled with the fact that the work is only a handbook and not a full-fledged self-contained treatise on the subject, has rendered the correct understand- ing of several passages in it difficult, for things not specifically defined in the text have to be known through traditional knowledge and practice. Particularly for this reason, the present translation and detailed exposition of the work with ample application of modern astronomy, by late Prof. T. S. Kuppanna Sastry should be welcome, for he combined in himself three qualities essential for the task, viz. sound scholarship mn Sanskrit, good knowledge of Western astronomy and full understanding of the concepts and practices of traditional Hindu astronomy. The Bharatiya Vidya Bhavan provided Prof. Sastry with a proper forum for placing his exposition before scholars for their adjudgement. The Bhavan organised in Bombay, on March 24-25, 1979, a ‘Workshop on Ancient Astronomy’ under its project on ‘Ancient Insights and Modern Discoveries’, a project which had been envisaged by them as a co-operative national endeavour to explore the possibilities of a meaningful correlation of ancient Indian insights and thoughts and the modern scientific dis- coveries and technical achievements. In fact, the Vedas, the Upanigads, the Puranas and several other works on various subjects in ancient languages would now seem to stand up to the more critical inquiry and examination of a modern scientific mind, as more and more discoveries of modern times are found to have relevant parallel references in the teachings of early Indian sages. The subject has been, for quite some time now, engaging the attention of scientists with a Sanskrit background and Sans- kritists with a scientific background to make a meaningful correlation between the two. Towards the achievement of this laudable objective, the Bhavan has taken several steps including the establishment of contacts with scholars of the type mentioned above, institution of studies and researches of an inter-disciplinary nature and organisa- tion of seminars and workshops towards providing a forum for discussions and mutual exchange of ideas in the different disciplines. It is pertinent to record that Vedanga Jyotisa and its present exposition was set out on the occasion of the first Workshop on Ancient Indian Astronomy organised by the Bhavan under its auspices as a part of its project noticed above. In fact, later, Prof. Sastry had expressed a desire to have his work published by the Bhavan, and the latter had included it in its publication pro- gramme, It was subsequently felt that it would be befitting if this work were to be ## Page 10

issued through the Indian National Science Academy, for two reasons, first, on account of this being a work on a scientific discipline and secondly the current year 1984-85 being the Jubilee Year of the Academy, a suggestion made on behalf of the Academy and accepted by the Bhavan. It is to be hoped that this decision would be acclaimed by the scholarly world. The Vedanga Jyotisa, being just a handbook, does not present its contents always in a systematically arranged manner as is the case with later texts on astronomy. As a result, topics on the same subject often find themselves distributed in different places in the work and vice versa. In order to enable the understanding of the astronomical knowledge 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 Rk and Yajur recensions, R-VJ and Y-VJ, of the Vedanga Jyotisa have been separately edited from a critical point of view on the basis of 20 manuscripts including those whose readings are recorded by A. Weber in his ‘Uber den Vedakalendar, namens Jyotisham’, (Abh. Berliner Ak. der Wiss, 1862, 1-130). The corruptness of certain passages have necessitated emendations which have been so couched as to suit the available lettering in the manuscripts, the context and the meaning, and have been placed within brackets The justification of the emendations have been made later in the exposition of the verses in Part B of this publication. The undermentioned manuscripts have been collated towards constituting the Critical Text of VJ given in Pt, A. The abbreviations used herein are: DNg.=Deva- nagari, Gr.=Grantha, Tel.=Telugu; Pl. Palmleaf; Pr.—Paper; and Cm.—Complete. Rk-Vedanga Jyotisa A and B. No. 1505, Verseichniss der Skt. und. Pkt. Hand. der Konig. Bibl. zu Berlin, by A. Weber. Ng. Pr. Cm. 8 ff. No. 372, op. cit. Ng. Pr. Cm. 4 ff. Dated Sam. 1834 (ap. 1779). Wilson 503 in Catalogi Cod. Man. Bibl. Bodleiane, by T. Aufrecht. Ng. Pr. Cm, Dated Sam. 1849 (a.p. 1793). . No. 373, in Weber, op. cit. Ng. Pr. Cm. 4 ff. . Modern copy procured by A. Weber and used in his edition. . No. D-1027 of the Govt. Or. Mss. Lib., Madras (GOML), Gr. Pl. Cm. 4 ff. . No, R-6018(6) of GOML. Gr. Pl. Cm. 2 ff. No. D-18726 of GOML. Tel. Pr. Cm. 5 pages, No. D-14097 of GOML. Tel. Pl. Cm. 3 ff. ~ No, D-1028 of GOML. Tel. Pl. Cm. 3 f& . No. R-4082(d) of GOML. Tel. Pl. Cm. 3 ff. M. No. D-17880 of GOML. Tel. PL. Cm. 2 pages. N. No. 67034 of the Adyar Library and Res. Centre, Madras, Tel. Pl. Cm, 2

PASS boss ba ## Page 11

Yajur-Vedanga Jyotisa A. No. 1505, Weber, op. cit., with the commentary of Somakara. Ng. Pr. Cm. 78 ff. B. No. 374, Weber, op. cit. Ng. Pr. Cm. 5 ff. numbered 4 to 8. C. No. 375, Weber, op. cit. Ng. Pr. Cm. 6 ff. numbered 4 to 9. D. No. Wilson 502-a, Aufiecht, op. cit. Ng. Pr. Cm. Dated Sam. 1696 (A.D. 1639). E-F, Modern copies procured by Weber and used in his edition. Part B is devoted to the Translation and the Exposition of the VJ and to the demonstration of the principles and practices involved by means of worked out examples. Herein the VJ verses have been classified into five Sections according to the topics dealt with by them. Since most of the verses in the two recensions are common, both are translated and explained together. Thus against the common verses would be given both the R-VJ and Y-VJ references, while verses occurring in only one of the recensions will have the references only to the respective recension. The following are the sections under which the verses have been classified: (1) Benediction and Valediction; (i) Measures of Time, Asterisms etc.; (iii) Fundamental and derived Yuga constants; (iv) Tithi, Naksatra etc. of certain special days; and (v) Daily Tithi and Naksatra and their risings and settings. The rules for the calculation of the days, parvas, daily tithis and naksatras included in the last section are not very obvious and the terms used are mostly undefined that these verses have been most difficult to understand. Successive scholars who have attempted to unravel the meaning and application of these verses have been successful in different degrees and most of them have left several of the verses as incomprehensible. The length to which some scholars, especially from the West, have been baffled as to have expressed themselves in a most unbecoming manner, with ignorance turned to anger and anguish, mught be illustrated from a statement of D. W. Whitney, when he says: “‘And when we come to add that the Jyotisha (VJ) has no definable place in Sanskrit literature, or relation to the Vedic ceremonial . ..we shall see that this famous datum, which has seemed to promise so much, has caused so much labour and discussion, and is even yet clung to by some scholars as the sheet- anchor of ancient Hindu chronology, is nothing but a delusive phantom.” (cf. his Oriental and Linguistic Studies, Second Series, New York, 1874, p. 384). May be, Prof. Sastry’s rational interpretation of these enigmatic verses would induce this Western Onentalist turn in his grave. It goes to the credit of Prof. Sastry to have tackled the VJ in its entirety and to have been able to give satisfactory interpretations to all its verses, which, perhaps, is the most convincing of what have been given thus far by scholars who have attempted the task. I might close this Preface with a personal note. It would seem that a wish expressed by Prof. Sastry, more than five years ago, finds fruition at this moment. In a letter dated March 3, 1979, he wrote to me: “‘Dear Sharma, .... Regarding the Vedanga edition, Dr. Abraham (of the Christian College, Madras) and Dr. Ansari (of the A. M. University Aligarh), asked me to get it published by the Bharatiya Vidya Bhavan.... Otherwise, I would have wished it to be done by you, because if I simply send the manus- ## Page 12 10 VEDANGA JYOTISA cript to you, you would have done everything else.’ Having the highest regard for Prof. Sastry and appreciation for the confidence that he had been placing on me during our close academic relationship for nearly 30 years, J am happy that my associa- tion which he had wished for in the edition and publication of the Vedanga Jyotisa has ultimately been fulfilled, though under circumstances not envisaged by him. The present Translation and Notes of Vedariga Jyotisa has been prepared on the basis of the draft thereof and the related papers left by Prof. Sastry with his son Dr. T. K. Balsubramanian, Scientist, BARC, Bombay, who placed them in my hands, for their edition and publication through a common friend, Shri S. Hariharan, Executive Director, LIC, Bombay, who, besides, was an admirer of Prof. Sastry. I am thankful to both these friends in the matter. My thanks are due also to the Bharatiya Vidya Bhavan and the Indian National Science Academy, the former for agreeing to publish the book, in the first instance, and the latter for actually publishing the work under their auspices during their Golden Jubilee Year. Adyar Library and Research Centre, Madras, K. V. SARMA Sravana-pirrnima, The Sanskrit Day, August 11, 1984 ## Page 13 INTRODUCTION 1, Astronomy of the Vedic Samhitas The Vedanga-Jyotisa (VJ) belongs to the late Vedic age. Even during the time of the early mandalas of the Rgveda astronomical information necessary for the day to day life of the people, like the knowledge of the seasons for sowing, reaping etc., had been acquired, as among all ancient peoples. Information required for the religious life of the people, like the times of full and new moons, the last disappearance of the moon and its first appearance etc., necessary for the monthly rites like the Darsapiirnamasa and seasonal rites like Caturmasya, had also been acquired. The names of the moon’s asterisms (27) were known and used to indicate days.2 There are vestiges in the shape of the Vedic legends and names of asterisms to show the antiquity of particular mantras. For instance, Agrahdyana, an old name for the asterism Mrgasirsa, meaning ‘beginning of the year’, points to the fourth millennium B c. when the sun was there at the vernal equinox. The Rohini legends point to a time in the late Rgvedic period when the point shifted to the asterism Rohini.2 The later sacrificial session called Gavamayana was especially designed for the daily observation of the movements of the sun and of the disappearance of the moon, and this must have given the priests suffi- ciently precise knowledge about the astronomical elements. We have evidence to show that even knowledge of a special kind, like the saros of the Greeks, for predicting the solar eclipse, was possessed by the priests of the Atri family.‘ The above type of knowledge improved with time, so that in the Yajurveda period we can say with certainty that the following was well known: The solar year was known to have 365 days and a fraction more, though it was roughly spoken of as having 360 days, consisting of 12 months of 30 days each. Evidence for this is found in the Kysna- Yajurveda: Taittirtya Samhita (TS) 7.2.6, where the extra 11 days over the 12 lunar months, Caitra, Vaisakha etc., totalling 354 days, is mentioned to complete the rtus by the performance of the EkddaSardtra or eleven-day sacrifice.’ TS 7.1.10 says that 5 days more were required over the Savana year of 360 days to complete the seasons, adding that 4 days are too short and 6 days too long.* Further, five years were found to form a yuga, the names of the years thereof being Samvatsara, Parivatsara, Idavatsara, Anuyatsara and Idvatsara.” This yuga was used to reckon time, as seen from such statements as ‘Dirghatamas, son of Mamata, became old even in his tenth yuga’, ie. between the age of 45 and 50.8 Even earlier, the two intercalary months, called Amhas- pati and Samsarpa, required to complete the yuga, were known, as seen from the state- ment vedo masa dhrtavrato dvadaSa prajavatah|veda ya upajdyate]] (RV 1.25.8). The six rtus in the solar year, with the names of the twelve tropical months, are given by the statement: Madhu§ca Madhavasca Vasantikavrti, Sukrasca Sucifca Graismavrti, Nabhasca Nabhasyasca Vargikavrtii, Isasca Urjasca Saradavrtit, Sahasca Sahasyasca Haimantikavrti, Tapasca Tapasyasca Saifiravpti (TS 4.4.11.1; Vajasaneyi Samhita (VS) 13.14). ## Page 14 12 VEDANGA JYOTISA It might also be seen that the sacrificial year commenced with Vasanta (spring). It bad also been noted that the shortest day was at winter solstice when the seasonal year Sisira began with Uttardyana (Kausitaki Brahmane, 19.3) and rose to a maximum at the summer solstice. 2. Datable Vedic passages It was observed that the moon came back to the same position in the zodiac once in about 27 days and that each day was marked by the asterism or asterismal group (naksatra) near which the moon was seen, resulting in calling the asterism as the day’s naksatra, from which the 27 asterismal segments of the zodiac came into use. The names of these with their presiding deities are enumerated in the Yajurveda, beginning with Krttika, where the spring equinox was situated at that period. The thirteen and a half naksatras ending with Visakhd, situated n the northern hemisphere, were called devanaksatras, while the thirteen and a half others ending with Bharani were called yamanaksatras, as seen from the passage: Krttikah prathamam, Visakhe uttamam, tani deva-naksatrani. Anuradhah prathamam, Apabharonir uttamam, tani yama-naksat- rani (Taitt. Brahmana, 1.5.2.7). Incidentally, this would give the age of the observation as c. 2300 B.c. Another statement about the Kyttikas points to even an earlier period: Vide the passage: etd (Krttikd) ha vai pracyai digo na cyavante, sarvani ha vai anyani naksatrani pracyai difa§ cyavante (Satapatha Brahmana, 2.1.2.3). This means that the asterismal group Kyttikd never swerve from the east, while the others do. The meaning is confirmed by Sayana’s commentary. This points to c. 2950 B.c. A far later observation is reported in the Maitrdyaniya Brahmana-Upanisad, 6.14, to the effect that the winter solstice was at the mid-point of the Sravistha segment and the summer solstice at the beginning of Maghd. This points to c. 1660 B.c., a little before the period of the Vedanga Jyotisa. Even regular astronomers are mentioned by expressions like prajfiandya naksatra- dargam (YV-Vajasaneyi Samhita, 30.10; Tait. Br., 3.4.4.1), and yadase ganakam (YV- Vaj. Sam, 30.20; Taitt. Br., 3.4.15.1). A Naksatra-vidya (Science of the stars) is mentioned in the Chandogya Upanisad, 7.1.2.4; 2.1; 7.1. These references would give an idea of the astronomical knowledge which had been acquired before the time of VJ, on the basis of which the VJ has to be adjudged. 3. Text of the Vedinga Jyotisa Of the extant Indian astronomical texts, the VJ is the earliest. The astronomical matter forming the basis of the work is of one Lagadha, but the classical language employed in the work as current now would indicate that the original must have been redacted by a later person belonging to the last centuries B.c. The same system as mentioned in the ¥/ is seen in the Mahabharata, the earlier astronomical samhitas like that of Garga etc., and the Paitimaha Siddhanta condensed by Varahamihira (VM) in his Paficasiddhantika (PS). The VJ has come down in two recensions, one belonging ## Page 15

to the Reveda (R-VJ) and the other, which is later, larger and more advanced in its methods, to the Yayurveda (Y-VJ), though their basic content is almost the same. Later than these came the Atharvana Jyautisa, attached to the Atharva Veda, called so just for the sake of uniformity. While the first two are astronomical, the third deals with the Muhirta branch of astrology. While the first two purport to be based on Lagadha’s science, the Atharvana says that it was taught by Pitamaha to Kasyapa. 4. Date of the Vedanga Jyotisa Verses 6, 7 and 8 of the Yajur-Vedanga Jyotisa (Y-VJ) show that at the time of Lagadha the winter solstice was at the beginning of the asterism Sravisthad (Delphini) segment and that the summer solstice was at the mid-point of the Aslesd segment. It can be seen that this is the same as was alluded to by Varahamihira in his Paficasiddhan- tika and Brhatsamhita. Since VM has stated that 1n his own time the summer solstice was at Punarvasu 2, and the winter solstice at Uttardsaghd }, there had been a preces- sion of 1} stellar segments, i.e. 23° 20”. From this we can compute that Lagadha’s time was 72X23 1/3=1680 years earlier that VM’s time (c. A.D. 530), ie. c. 1150 B.C. If, instead of the segment, the group itself is meant, which is about 3° within it, Lagadha’s time would be c. 1370 B.c. 5. Verification of the date of Lagadha The date arrived at as above can be confirmed by the Saryasiddhdnta and the Siddhdnta Siromani which give 290° polar longitude and 36° polar latitude to Sraivstha. From this, the actual longitude of Sravisthd got is 296° 15’. Since the siddhantas use the fixed zodiac beginning with the vernal equinox of c. 550 A.D., and the winter solstice of this is 270°, there has been a precession of 296° 15’ minus 270°=26° 15’. Smce 264 x 72=1890 years, the wanted time is 1890 years, before A.D. 550, i.e. c. 1340 B.c., being the same as the above, the small difference being observational. We can also calculate the time directly by comparing the position of Sravisthd (Q Delphini) at the time when the winter solstice was 270°, with its position in 1940 A.D. (Rt. as. 204 36m 518=309° 13’, and declination 15° 42’ N). In the figure: The obliquity is about 23° 40’, r is the vernal equinox, S is Sravisthd and R its Rt. as. position. ## Page 16 14 VEDANGA JYOTISA Rr=360°—Rt. as.=50° 47’. RS is the declination=15° 42’. RS is the continuation of SR up to the ecliptic. Now: () From the rt, angled spherical triangle RrS, it can be calculated that RS=18° 46’; Sr=53° 13’; and angle S=75° 17’. Gi) From the rt. angled spherical triangle SSS", SS”"=9° 533”, S” being the celes- tial longitude of Sm A.D. 1940. It was 270° at the time required. Therefore, the preces- sion is 360°—53° 13’—270°+9° 53’ =46° 40’. Multiplying by 72, the time is 3360 years before A.D. 1940, i.e. c. 1400 z.c. If the beginning of the segment is meant and Sravistha is about 3° inside, it is c. 1180 B.c. Since all these is subject to small errors of observa- tion, it would 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 fixed the date c. 850 B.c., after a lot of argument, in his Indian Ephemeris, vol. I, Pt. i. pp. 444-45. Trusting in the so-called Drk-ganita Paficdnga of the Kumbhakonam Mutt, in South India, he has accepted the precession in 1916 as about 224, with the spring equinox of about A D. 550 as the first point of the fixed zodiac. This would give 224721620 years earlier than 1916 for the spring equinox of VM’s time, i.e. c. A.D. 300. This difference of about 250 years is taken by Swamikannu Pillai as VM’s observational error, since he has taken that VM’s date is correctly A.D. 550. Proceeding from this, he argues that in about 1600 years there is an observational error of 250 years, and “allowing the same proportion of error for the previous epochs, the antiquity of Vedanga Jyotisa observation, .. . . may also be reduced by 250/1620, ic. by 2/13; in other words, from 3300 years before now to 2792 years before now, i.e. from B.c. 1400 to B.c. 850.” (ib., p. 445). Note here the strange lapse on the part of Pillai, taking that the error of observa- tion depends upon the time elapsed. On the other hand, it depends on the instruments used and the ‘personal equation’, and not “proportiontate” to the time elapsed. He has confused this with the error in the cycles derived from previous observations, which error alone can accumulate with tume. Further, VM’s observation was remarkably good. The vernal equinox was at the first point of the Indian zodiac, defined as being about 10’ east of the ‘Junction star’ of Revati, which, from its co-ordinates given by the siddhantas, must be identified with Zeta Piscium. All siddhdntas, explicitly or implicitly, take the precession to be zero at about this period and the vernal equinox was situated here at this period. So there was very little error of observation on the part of VM, which is a remarkable thing. If so, the precession at 1916 should be about 19° since (1916—550)--72=19. How, then, has this 223° precession arisen in the Tamil Drk almanac, it may be asked. This is how it has happened. All Hindu siddhdntas give a sidereal year in the neighbour- hood of 365-15-31-30 days, which is about 8} vinddis more than the correct sidereal period of the Sun. Since the Sun is taken to return to the first point of the Hindu Zodiac after each sidereal year, the first point of the Hindu zodiac itself has a precessional ## Page 17

movement (though taken to be fixed), and, reckoned from this point, the rate of preces- sion would be not the real 50”. 25, but 50”. 25 plus 8”. 5=about 59”. This error of 8”.5 has accumulated up to the time of the appearance of the Tamil Drk almanacs at the end of the last century, and when the Kumbhakonam Mutt Paficdnga originated about a hundred years ago, the error had accumulated to more than 3°. In order to fall in line with the siddhdntic 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 begun three days earlier, and also to avoid certain difficulties with the dharmasastras, this Drk Paficanga tacitly adopted a precession of 19° plus 3°=22°, to hide the fact that the Drk system was an innovation and to create the impression that :t had been in existence from time immemorial. This had led Pillai to this error in judging the period of the VJ. 6. Contents of the Vedanga Jyotisa The system of the VJ 1s the same as that taught in the Gargasamhita of the Samhita period, being the immediate centuries before Christ and the next following, Paitamaha Siddhanta condensed in the PS and the Jain works like Jyotisakaranda and Suryaprajfiapti. The only difference is that the Paitdmaha gives a rule for the Vyatipata-yoga and the Jain works have brought down the winter solstice from Sravistha to Sravana, and included Abhijit (Vega) as closing the zodiac, giving it a small segment at the end. All give the five-year yuga of 1830 days with 62 synodic months in it. Everything else, like the 67 lunar sidereal periods etc., can follow from these three given items. The Paitamaha instructs that the naksatras and tithis are to be calculated from the days elapsed in the yuga using the unitary method. The Jain works give the days and the naksatras in a parva, from which they are to be calculated for the other parvas and days. The VJ states in detail that in the yuga there are 5 solar years, 67 lunar sidereal cycles, 1830 days, 1835 sidereal days, 62 synodic months, 1860 tithis, 135 solar naksatras, 1809 lunar naksatras and 1768 risings of the Moon, all derivable from any three principal elements. It also mentions that there are 10 ayanas and visuvas and 30 rtus or seasons, and the naksatras and tithis of these are enumerated, their number being small. But the other things sought to be given, like the daily naksatras and tithis with their ending moments, the hour-angle of the Sun at the ends of the parvas and tithis, the hour-angle of Sravisthd with the lagnas, which are too numerous to be enumerated, have been given by ingenious rules that enable them to be calculated mentally day by day, as we want them. It is these rules that have baffled interpreters, since they are couched in archaic, technical and terse language, and the purpose of each cannot be seen easily and the terms used are not generally defined. The day is divided into 124 bhagas or parts, so that the ending moments of the parvas and tithis can be given in whole units. The day is again divided into 603 units called kalas, so that the dura- tion of the lunar naksatras is given in whole units as 610 kalds. The naksatra 1s divided into 124 ampgas so that the nakgatras passed at the ends of the parvas may be expressed in whole amSas. A table of the division of time is given, beginning from gurvaksara ## Page 18 16 VEDANGA JYOTISA or the double matra or long syllable, to the day, passing on to the yuga. The practical way of measuring time is mentioned as the time taken by a specified quantity of water to flow through the ortfice of a specified clepsydra, as one nddika or 60th part of a day. 7. Accuracy of the Vedanga Jyotisa We shall now proceed to examme the accuracy of the system, a much discussed affair. The VJ says that there are 1830 civil days in the yuga, in which there are five solar sidereal years and 62 lunar synodic months. This gives 366 days for the year while it is really 365} days, known in the Vedic period before, as we have seen. Also, it must have been known, even at that period that 62 synodic months take almost a day more than the 1830 given, because even at the end of one yuga, the amavasya (new moon) must have been observed to occur on the day next to the 1830th. Observa- tion at the end of the next yuga would have shown this unmistakably, since on the last day of the yuga the Moon would have been observed to be well up in the sky at sunrise, showing the day to be caturdasi or even trayodasi, so that the amavasya would occur one or even two days later.!° The priests, whose duty 1t was to observe the last disappearance of the old Moon and the first appearance of the new Moon, could never have failed to notice this, for there was prdyascitta (penalty propitiatory rites) for transgression either way (see below, verse 12 and notes thereon). Then, why this apparently absurd system? The answer is that it was meant pri- marily to provide a civil calendar, where convenience of division and ease of calculation is umportant. 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 of the 5th ayana and the other at the end of the 10th. The difference from actuality is already there, because only the computation of the Mean Moon and the Mean Sun was known, which itself could give an error of more than half a day. So the rules for computing the various items like naksatras can give only approximate results. But the religious calendar required correct results, and this civil calendar intended for the day to day life of the people could serve only as a frame-work to guide the religious calendar. Certainly the priests must have framed rules by long observation to get tolerably correct positions, so as to avoid the penalty laid down by the Sastras, as mentioned above. For one thing, a day could have been tacitly added to the yuga after its end, as suggested by many, (even as we do every fourth.year to get the leap year), and not counted in the calculation, to make up the 62 synodic months, so that the most patent discrepancy could be avoided. H. Krishna Sastry Godbole, writing about the Vedic calendar in 1884, suggested this. As this would amount to allowing the error to accumulate to one day before correction, some suggest that the uncounted. day might have been placed at the end of the 5th ayana, i.e. after the first intercalary month. Tilak suggests that it was done at the end of the 93rd parva and adds that it is actually instructed by verse 12, I think he is not correct (cf. the verse), ## Page 19

But there is another type of error that will accumulate in course of time. 62 synodic months 1s exactly 1830-8965 days. So, the correct Mean Sun would be 4°54’ in advance of Sravisthd, each yuga. It will accumulate to 30° in 30--4-54 yugas. To bring the Sun and the Moon back to Sravisthd, one intercalary month will have to be dropped after 6 yugas and another intercalary month after 7 yugas, and this has to be repeated. The priests could have found this rule by experience and used it. But it must be noted that it is not even necessary to know this rule to drop the intercala- tion, because mere observation of the Moon in the Sravisthd region of the sky would have shown this, for this must have been the rule during the Vedic times (as the Muslims do even today, by observing the crescent Moon) to find the need for an inter- calation, for this 1s independent of the knowledge of the exact periods of cycles. But, still, in course of time, the winter solstice itself would move from Sravisthd to Sravana and so on, at the rate of about one nakgatra in 1000 years, owing to the precession of the equinoxes, and this correction must be done to know the correct seasons. It has already been mentioned that the Séryaprajfiapti and other works actually placed the winter solstice at the beginning of Sravana. But one thing is certain. Long after the time of Lagadha, the system of the VJ was followed in India as seen from the Mahabharata, the Arthasastra, Gargasamhitad and the Paitémaha Siddhanta, first in all parts, and then at least in some parts, for almanac making, and that is why it is described in the PS as one of the systems in vogue, though crude. But by then it had come to be linked with the luni-solar year to prevent accumulation of error, as we have already mentioned. 8. Modern studies on Vedanga Jyotisa The above discussion would show how wrong and unjustified Whitney was, when he remarked: “The so-called Vedic astronomical manual (VJ) whose first object seemingly ought to be to give rules on such points (as amdvdsyd etc.) is mostly filled with un-intelligible rubbish, and leaves us in the lurch as regards valuable information.” This remark is born of frustration, for, if un-intelligible, how does he decide it is rubbish? The VJ attracted the attention of the early Indologists like Sir William Jones and Colebrooke, especially the two verses placing the winter solstice at Sravisthd, which could help in determining Vedic chronology. Later, Capt. Jervis, who was investigating the Indian measurement of time, noticed it in 1834. Prof. A Weber was the first to bring out an edition of both the recensions of VJ with the different readings from the manuscripts available to him. But excepting for a few simple verses in the First and Second Sections of the edition presented hereinbelow, few could interpret the main 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 the Journal of the Asiatic Society of Bengal (47.i.411-37) could decipher a few of the difficult verses, leaving out several verses, including 11, 13-17, 19-23, 25-27 and 41 of the Y-WJ un- touched. His knowledge of astronomy and adequate knowledge of Sanskrit helped ## Page 20 18 VEDANGA JYOTISA to interpret the other verses, in spite of the obscure terms and the apotkegmatic language, because the meaning of these could be guessed if what they are driving at is known. Then, in 1884, H. K. Godbole tried to tackle the problem of the correct religious calendar to be got from the approximate civil one. Next, S. B. Dukshit, in his Bharatiya Jyotisa-Sastra in Marathi (Poona, 1896) brought his excellent know- ledge of Hindu astronomy to bear on the VJ and interpreted some more uninterpreted verses. But the more important verses were left untouched by him. In 1907, Lala Chote Lal, Executive Engineer, W.P., brought out a full-fledged edition, adopting the pseudonym ‘Barhaspatya’, giving his own interpretation to all the verses, re- printing them from the Hindusthan Review, wherein they had appeared serially. However, in many places his meanmg is not clear in spite of his long explanations. Neither has he mentioned what was being done nor has he given examples. At about the same time, M. M. Sudhakara Dvivedi of the Queen’s College, Banaras, who had edited the PS in collaboration with G. Thibaut, edited the WJ with an old Sanskrit commentary by Somakara, in which he noticed many of the interpretations of ‘Barhaspatya’, some of them as corrected by him. However, his peculiar way of emending the verses drastically has affected this edition. Then again, his presump- tion of the use of bhitasankhyd is wawarranted. But even where he agreed, he has tried to show off his superior knowledge of Sanskrit by giving his own ‘better’ interpretation. These exasperated ‘Barhaspatya’ to such an extent, that he issued an Appendix criticising Sudhakara Dvivedi right and left. One very good service that ‘Barhaspatya’ has done is to append a critical edition of both the recensions of the VJ, to his edition of the work. The renowned Indian patriot and freedom fighter, B.G. Tilak wrote his ‘Notes on the interpretation of the Vedanga Jyotisa: Criticisms and suggestions’ in 1914 while he was lodged in jail in Mandalay, Burma ™ He took for criticism Y-VJ 15, 19, 27 (with its variation R-VJ 13), 21, 20, 25, 26, 12, 14 and R-VJ 19, Of these ¥-VJ 15, 20, 21, 25 and 26 have been dealt correctly by him, pointing out the defects and mistakes in the interpretations of ‘Barhaspatya’ and Sudhakara Dvivedi, but in ¥-VJ 19 he committed the simple mistake of taking udvapet to mean ‘should be added’, instead of ‘should be taken away’. By this he missed the meaning of the verse and, to make up for the error in the rule created thus, he had to misinterpret Y-VI 27 and R-VJ 13 as well as to supplement it. Still, his interpretation is only approximate, as he himself has owned. Thus a perfect rule was spoiled by a small mistake. The involved interpretation, requiring several pages of explanation, should itself have told him that he was going on the wrong track. I disagree with his inter- pretation also of Y-VJ12 and 14 which he takes as providing for the one day to be left out of count, to correct the system to keep in step with reality. ¥-VJ 27 deals with lagna, about the meaning of which he is not sure. In the present edition all these points have been dealt with convincingly. ; We have already seen that, at about 1916, Swamikannu Pillai took certain points in the VJ for discussion (vide his Indian Ephemeris, vol. I, pt. i, pp. 443-56; ## Page 21

‘The Vedanga Jyotisha calendar’). In 1936, R. Shamasastry, Retd, Curator, Oriental Library, and Director of the Archaeological Researches in Mysore brought out an edition of the Y-J, with his own Sanskrit commentary and English translation and notes. It is not a critical edition and in spite of the good interpretations of scholars before him he has misinterpreted almost all the verses included in the Fifth Section of the present edition. He has quoted from the Jain works, but exhibits ignorance not only of ther meaning but also of their purpose. For instance, in order to get the parva-naksatras and amsas, the number of naksatras and amsas moved in one parva (which 1s given as a constant) are multiplied by the number of parvas. This cannot be done mentally and, so Y-VJ 15 and 18 give simple rules to get it. But Shamasastry interprets that the said two verses give the days not fit for darsapiir- namdsa sacrifices and, even that, using his own peculiar criterion for the same. As for getting the parva-naksatras and améas, he asks us to add to those of the previous parva, the motion for one parva, and this too in Kalas, mostly fractional ! His inter- pretation of Y-VJ 13 is a monument for his capacity. And, the most ridiculous as- pect 1s that he criticises the earlier interpreters, who are by far his superiors. Still later, Dr. Satya Prakash offered a detailed treatment of the topics dealt with in the VJ in the chapter entitled ‘Lagadha: The first to rationalize astronomy’ in his book Founders of Sciences in Ancient India, (New Delhi, 1965, pp. 455-512), but he takes his translations verbatim from Shamasastry and in the explanations also follows him which makes his treatment liable to the severe limitations of his source-book. 9. Acknowledgements T have the satisfaction now that what I began in 1960 and worked off and on has been duly brought to a completion. I think of all those who have helped me in the publication of this edition, especially to the Bharatiya Vidya Bhavan, Bombay who provided a forum for my expounding the subject in detail in the Workshop on Ancient insights and modern discoveries organised by them. My thanks are due to every one who has devoted his attention to the VJ, irrespective of whether he has done well or ill, for I have benefited from his work in some way or other. I cherish with gratitude the memory of my two friends who enthused me in the work, first the Vedic and Vedanta scholar, Malma Narashimachariar, a respected preceptor of the Munitrayam Sect, who learnt the Siiryasiddhdnta and the Ydjusa-Vedanga Jyotisa from me, and second, Srinivasa Iyengar of Periakulam, Retired Head Master, a Vajasaneyin and a man of many parts with a fund of knowledge who discussed many problems with me and gave me his copy of Tilak’s paper on the subject.

## Page 22 20 VEDANGA JYOTISA REFERENCES ICf. Reveda 1.164 48: 3For a detailed exposition, see B. G. Tilak, Orion, (Bombay, 1893). See esp. ch. IV. Agrahdyana, pp. 61-95. “Cf Reveda 5.40.5-6, 9: 5See Taitt. Sam. (Krsna- Yajurveda), 7.2.6: seme & (wererrert) Ut rerreerererreey b TeTECT | Aer... CTE ATETANY See Taitt. Sam. 7.1.10: Ss UECraSTaT ON arf aa TE Tet Tot fart ward Tae) "See Vaj. Sam., 27.25; Satapatha Brahmana 8.1.48; Taitt. Br. 3.10.4.1; Tait. Aranyaka 419.1 Aerecisfer tferercisfit garrercsfa aqwertisf, eeerdtsfir | See Reveda 1.158.6: dhiat art qaait wae qh *The problem of the Hindu precession has been dealt with elaborately by me (i) in the Introduction to my critical edition of the Mahabhaskariyam (Madras, 1957), (ii) the Introd. to the Vakyakaranam (Madras, 1962) and (iit) my paper entitled ‘Main characteristics of Hindu Astronomy’, Indian J. Hist. Sc., 9 (1974) 31-34, WAlluding to this point Swamikannu Pillai makes the mistake of stating that the Moon would be observed to be “three days old” on the last day of the yuga, meaning that the new moon would have gone already. “Included in the posthumous collection of his papers, published under the title, Vedic chronolo, and Vedanga Jyotisha, (Poona City, 1925), pp. 43-108. ui ed ## Page 23 ParRT A CRITICAL EDITION OF VEDANGA JYOTISA I. RGVEDA-VEDANGA-JYOTISA II. YAJURVEDA-VEDANGA-JYOTISA ## Page 25 Fa TAATA I. arisatfarr (R-VJ) eT areas ITCRA | fencdaaarars rer farcear qa: ug sore farce areafraresr aTeay | stead waeatht cee WET UR fart gerd TR AREA UR pre fet fit if )

equaad oatarat oer ate Aareat ear carla at ATTETT: Yat (Sa WTR) UI sree osfssret = qatrararqea | arid afiaraeg aTesramat: war ei i Set: aITETT TaeTT at facata: wager g tell Note: 14 manuscripts, numbered A to N, have been collated to determine the critical text edited here, the unaccepted readings being relegated to the footnotes.The text is corrupt at places. In such cases, if at least one manuscript gives a correct and sensible reading, that is adopted in the ‘Edited’ text. Where, however, no manuscript gives a satisfactory text, emendations are suggested in brackets (and also explained in the Notes below), all mss. readings being given in the footnotes. The variant ings are noted under the indication of the relevant verse and pada numbers, a, b c dd. (See page 26). ## Page 26 24

fat age aaa ( is a) feetraret a ust ageaer aaisora fia: aatfiaett ery | STAT | BRATTATENTAT AIHA (7) ETT: 111 aia: eyeeat: ara: RTM ATTA: \ waren (st)a: grasa’ deat ate gor! arat siiarse (a) cart Her Tarafearerfe: | aaert = (fa) ara (frq) ster: 19911 (iat) wast feaaterara- wagan(raraia) «fire rasta (aT aa Tist) CC COOCCC@ILEGT| qorauredted TaTaT att PAT | wafmeqerete: ergtaeaeet TUG ot at a: S eg st AIT fat yy a: (GAT ETM) 1 - RAT: EAT STS FT: F AT St sor eget fg. ger wart: owt fang arated Sag (Agee) sent amnrar yo aa (a) fear afet (a) fam soon § weer ae a ash afes 2 ugdeg Tarra (s) aT | (sre) are HEAT AT: Heddy fafa: qo (waas) aq (aT) aie sfasorat (T)orereart siPaerary fatifeai (ea) ait Arar Sore frereararTAry ts iiqan arefterstart (72) mea ay WETATTT oe aT: fara (oq) TRY Frererertaet: aT: RGU ## Page 27

agaeearrrat 1a ae wer J aq cfaodsreT ae (m) eee feet fret ware tang PRARTATTL RRM (a)ad ferarmat war safer wf) megTy Fae free Fert TTA NR weagert | es(oTe_) HET! sae (far) water (et) frasig srrererfar(at) uu afi: sorefe: att etisteferagerta: | aaier frrota oo waetariarfs RH afant ererr agers fra wt +1 wal frafreit ¢ fardtarenta TREN freee TST HITT steerer et qr ster al oat Te aeaeeat var warfisrdtir 1 aero meaty | Aaa | SYTTT RSI meastor «= ageifeardory ee ee sare (#) aren arg (FF (Fe) Ts s wea oon 8 — Fafreege Ngo faqa qayt aeoee er atin (et ae) eRe agi ilk ak atest: alls Brea aaa 11280 qret qt vat ta ctetardt (aerfarr) 1 edt o fagars aR are (at) TAA AAT BB agarqraaseran wag salted fenqafer AAT: | Tepe eat afessrat a arity ayn wer fire wget arat Aoat wear aqag, aarqareaTt Aes yeh ferTy RR ## Page 28

aero fe «= aaretafasqar: eer Fee ara faarararedt Srnfe de @ oe mary UR aw wifes Fa 1 aa FATT I beh osschsll ali UT AGS Naas (wit 99) 1 BRT TTT (RAT 9G) I ar: TS (wet 29) 1 fray (wet Re) 1 age (we 9) | TT U ef arienfest ware ariwnfrr (R-VJ) : VARIANT READINGS 1. © 1. xem repeated. (d) M. arreret 4. © G. faq. @ G. ufrpery 5. @ A.B. D. F. a; C.E. aaet; G. H. eras; all mss, 3% (G. 32). @ All mss. eet fet aT: 1 6. () G. aH 7. @AC. GH set: (6) CE. same. (6) J. eft; G. at faq; ACEHIIK.LM. faatet. @ CE. uget; G. agd; N. agat 8. (@) All mss. si for fai; G. om. aera. (c) All mss. 4a for 4. (@) N. faqrr; G. eye. 9. ® M. frat; L. af, @ All mss. Tat 10. (©) All mss. quai: (G. er). 11. @ All mss. seprear® (6) N. war’ a. (c) All mss. fiz for fiz. (c-d) All mss. aeardtreatg. (d) G. afearet: 12. @ A.B.CE, farieft, D. fart, GHK.M eeu, 1 angst, J. eet; CE. wit, K MN. ete (Na: BY), K. aieerart. (6) All mss. read: derereqyeftafinry. (c) G. ard st 3; All mss. arf Tit. @) N ata; G. way. 13. ® G. agaatate 14. @N. at a: HG. sz; @ AL mss. stares: G. sara). © G. % q; HLL. er for er @ G. yrrrat, N. yea 15. @ All mss, agit; G. ad; GL. gf yl at gq; © HJ. wart 16. (@) All mss. 4 for , all mss. fart for fara. (6) All mss. fg for 2, GH. qgdeg. (c) All mss. feferarg; G. wat. @) G. veagelfing 17. @) All mss. aTaRy (G. ywe). (6) All mss. aNETE (G. Fea); G. Fer, LK.M. Fen:, @G. ¥ea: 18. (@) All mss. qaray; all mss. git: (N.wqRerr:). (6) all mss. qatent Os. TTAIT:, @N. arr 19. @ H.LJK. wfaesr; all mss err (N. wre). (c) All mss. qatq. @A.B.D.F. frararx, CE. fermen 20. (a) All mss. arty (G. art g). (6) CE. wtetfimt; M. araaq 21. © sfatq wareq (K. Fae, N. Her). @ CD.EH. wert: ## Page 29

22. (c) All mss, ata sseut; F. farted. 23. @) CEF.GN. a; CD vf. @ AB. gua, CD E. dara 24. @) C.B. agar (6) All mss. yas; CE steer (c) All mss ufit; A.B. THT] ART, L. waiserearq; all other mss. warexeary (d) C.E 4 Giver, all mss. afirg 25. ©) N wenrenft:. (¢) G. aatetarrte 26. (6) N. sarfia; CE. fireit 28. (a) A.B.E. @at. (c) Great: 29. @ Allmss giaeret, G. aaifit. (6) G ofr. @) All mss. eqreant; (G) arise 30. All mss yifea (N Gafa); all mss. afedt (G afer, K. aft). (6) All mss atanq (A. eer, D. wary, BGK. eat, L site), HK. aftney, N. aferan. (0) All mss. qifta; all mss =fadt G. afer. K. afait). @) G. frarta fragt. 31. @ CE. aveat ef. () (g) Start; CE. wayerg. (c) C.F. aeeted, (@) All mss. aeited; N farted. 32. @ G. aragg; all mss. wqereg, (6) N. wafer, (c) C. B. grey 33. (6) All mss. art aaitanity. (c) H. asst at; A.B. fava, C.D.E.F.L. fargar. (@) All mss. greet ¥ GG. arewaraa); G. araq; N. TaTAT. 34. @ G. qraaaencr. (4) G. aaitfadt; GH. qf. (©) N. eafgs; N. gat @ E. wfteor; G. cera; N. atasqartarry. 35. @ C.E. feafiry II. araasatfavr (Y-VJ) MT ATMS ITTTT | qaqa «= rere fexctarmrarg Serer fircar afa: ian safrarrad TATATTAT: | arn wert waa AST WRN srarggeat fafgaret | aart: t wenrfad apretfaarererreet WD fet ae T Fz AMT URI wer fran at avrat Awa za! wag aargreant afore aif ferry ivi qeerteat \ te ree (yar ae @ tae I¥-o1t (un-numbered verse in mss.) Note: 6 manuscripts, A to F, form the basis of the critical text presented here. For the metho- dology adopted in recording the variants, see Note to Arca Jyotisam (R-V9), (p. 23). For variant readings of Ydjusajyotisam, see p. 31. ## Page 30

ALATA TT ATH OTAT TT: | qrer comaer | area | TAT IMI eaqceene aarat ger are aarat! waraerfe at WTSI WAR NGI sat | sifrsaret |= qataeaneraaa | arta aferoraeg ATeaTamat: | AAT tel! mighacat Tarra | Tee ot fei: wegen Gist wey ae aTgeaaTeh aaa wet cud (4 fe) fret ages nen geese: watsora fire: atisteaat SH | ate REATTATETT: AISA ATT: 119011 waretstg are a gate searfe(q) at: | ada: cSaavint (ag) THTeeTST G41 (q) a wa Fens cefery afeer armrerrrasat (am) fafedafiret af naa fits ogearered fat (madgeq) | seeur Seat a arent Teoh UfeeeTe 11981 ordisee farrrer ar faqertise: SE FU aS nate reateamrinavi afar: erat: FTE: (Tet) ATRIA: | weer: gash eae af 1941 aamegrtisn: | SRT: aay =| aT Maas =8=—|- RATT Aeeesntereg as orareitt: Foe ee we weer ereegie Lee ae inten at ar a: @ a sa TT Feary NA: | AT aT TT Ry OAT: ST ST so: FST qt sr agar fares as

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erat wiasencary sat warataafe. | area = (far) araferqet (grarat) qe ffir . Saiwenfaare | feast oo mega fafareraarfeaiq Rol! TT: wares wat fer (area) arat faorttare faferarartrat: FAT: UV adartarter: wtadig (fart) fafirq x ay wvewanig = faferfsstrat «<A: RRM ft fad wt vepieay wat aad vero fae: a faery FA: UR wea oo wSaeent =| gant wares Re. RAT fated gst art warfserareg WaT TATU varemfrcre = vatfer «= waaay Grae at CTT SAATATR (A) ATT RAN weer fala ie favrrer Ferg gt afratery (Ant) ferret THT UREU (eat) wast feraterart fre | amass sf vet reset agar TAT FH TAA) Uo fawergt asenftewe: ye adda arar gta qai(:) aq: TRIER TTT URS matintedte earfemeat (aun eae ian ## Page 32 30 VEDANGA JYOTISAM asad owe | Tomer: | TAT LATHATNTAT HUSA AT TT: FAT: ROU rang (&]) ATT afte: (a) feat 1 afer arat: ard: ae: (RY) TT UR aft: osoncfa: att eatsfefea eesti: 1 ater | fret | arta TUR wey Sapa fra wT biel fréfrerat fevitarenty Set faypfadt aes TET tte oT) afeqeaerat get afeadt ar we TNRYN UTA UTA: ATT AAT ATL RU sareqet + frat a fewer santseaqy | wear x war (ware) wher A TAT AT NREL fesfteaia ga array oon ee oe | TET wert se afar ere (&) ager whee (feat) aay aemrenat & Seed eafieeT WaT RSH ‘ was wa ae: Gt gait aire t (want) J Ae: Bsr TH aAT WaT REN (=) ae wat efirmgsarer aaa frat wet feramt oar waft waft GUT J aq free (Aer) Te vo YG eM rg: HET arofrrarear (et) frig arrafirrr ei farang are | aettsaetey 1X z-011 (un-nunibered verse in mss.) ## Page 33

aghast dae ate st waft ea ae Te FT wafer reaeaeTe (wet q) | erernae (weit &) 1 CaTTe (weit 19) | Tateqeet (wat aE) | ar: aearert (FAT 29) | Geter (weit VE) | aTaay (wat 24) 1 1 arent (weit 38) | Gad (xe vq) | ae

argaeitfirey (¥-VJ) : VARIANT READINGS 2 © mena art 3. OF. gat; F. aay 4. ME, wifes for afr; A afer aferrq. 4-0. (c) All mss farqat for 3 gat.; all mss. teafwatar (E F. caf: ae) 5. OE F. qa astfr 8. @ A fariet 9. (0) AEF. ade (c) All mss. $2 fir. (@) B aqet, D agit 0. (@) C. ataarea, D at req (6) B-F aifract (c) BOF. aera ey. (d) A. F. aa 1. ®B C.D. yatgam, all mss. feet, (c) A.B C.D. qe=auatn, F. reaqafer. (d) All mss. 4g (cy); F waem, B.C.D.F. seat 12, (@) All mss. a@4 (c 38a); B. eT Aq (c) B. era, B aq; ABCD. sain, EF sqiur (@BODEF. fafeaatfrat 13. @A fate. (6) A area, BCD aaa, B aaa. (O AF ysour your, (@) EB cai 14 @BCDE wed; CDE F. fara: (6) D. fad; all mss. 52 feat (©) C. aR, E. Fat, F ¥q, all mss amt, BCD.E tig @) AE waa. aftr: 15 @) BF. wit; EF weet, C wat @) All mss. garar; F. aterar’. (d) B. gat ya $, C. faraat 16. (@) A waite, B. aaa (4) C. g7., (©) AE. Sat ang. (a) A. wana, C. cae; BS saz 17. (@) A.B.C.D stat. (6) A. qq; BCD.F. wey (c) B.C. art wareag. (@) All mss. frmtiteat (A. favitten) 18. (a) A. Stat; F. att; BCDE ara, C dam. (b) B.CD.E. faq, F Pay; B.C.D E. g; AF a; BCDEF. art (0) A. taat, B Up, C. Bprs, F. sar ware; all mss oT @ D. eit 19. @ C. war (6) A.B.C. gar 7 (c) All mss. fe waft (2) AEF tqqararnd, BCD aq aqararnt ©. (*q aft) 20. QB geanta 21. ® F. waqr, F. fafa: © All mss. searerreat 22. (6) All mss. # fat. @) B.D. Fret 23. (6) B.D. ait. (@) B. fafa; A. aay ## Page 34 32 24. 25. 26, 27, 29. 30. 31. 32. 33. 34, 35. 36. 37. 38. 39. 40. 41. 42. = 42-0. 43.

© A. qarft, D. geht @ A. wag. (© A. ard.) All mss WaT, @D. gra; B. amma; A. aafa. © A fadtfrafer:. (© AF. fafrfar, B. ferfaqrat, CDE. fafagar; E. qfa:, F. wat. @ All mss. a7 (A Ahm); A. carga; A TAX @ A. far, B.C DF, facia, F. fait; A. watt; A art: (6) A. emreaters. (0) B. afge; C. Toe @ABD «aa, C. daa. @ All mss. wer, @ ABD E. fawergi. ©) E. td (ed) A eR (for Fag. (@) A. GaT:, DF. aay @ A. array: (6) All mss e4 for 4, A. aH, B TATA. (c) A. Efeafereta. @) All mss. Sart (A. 4a) (@) B.C. qafar=ed. () EF vatat, AB. aga. @) BD afaar: eer: @ AE. ferrari, F. oq. @ A. afte: $1, BCD.F dar, E. dat (©) ABD.E. fefang, C. fefauq, A. arateren:, BD.F. arated: C. aay aré:, E. araremi. (@) AD. isin, (a) B. sare (©) B.CD. om. 4 (@ A.BD. add in the beg. aq. (6-c) A. oisfadeererta + 1 aor Hare Gat (c-d) AEF. qarficeatt @ EF. 2aat vat @® BCDEF. sam. (c) All mss. arf: @ All mss. aya. (6) A. Fata; BF Wam:, (c) A Fargy, F Har gT. (a) C. HetATt (a B.CD. afau, F. afm. (6) AEF. enfg, B. emg fe, C.D. aa fe , F. qgteg. (0) A. qfanrg, BF. fafa. @ C. wait, EB vera; A. aftr, B aafat, C. cafes, D. afi. AEF. vaag. (6) A qatarft. (c) All mss, garaft for wararft; AE for g (a) F. acter er. (6) F ¢ aq for aan. (c) All mss aaa, A. faq, F. fare. @ B.C_D. aatfer. @) A. ert, B-F. ara; B wafer (@) AEF. aft, A. TaTere, B.CE.F. wary area, D. varered, (@) B-F. fara, B-E. ufirary @C. ia. @BCD aren; All mss. wt. (@ A. att:; all mss. feerafed. (c) All mss. ferafed. d) A afera, B.C.D. wate ## Page 35 PART B RE-ARRANGED TEXT, TRANSLATION AND NOTES SEcTiON I. BENEDICTION AND VALEDICTION

Section III. FUNDAMENTAL AND DerivepD YUGA CONSTANTS Section IV. Trru, NAKSATRA ETC. OF CERTAIN SPECIAL Days

## Page 37 RE-ARRANGED TEXT OF VEDANGA JYOTISA SECTION I BENEDICTION AND VALEDICTION 1, INTRODUCTION Text 1 paficasamvatsaramayam yugadhyaksam prajapatim| dmartvayanamdasangam pranamya sirasaé Sucih||R-VJ 1; Y-VI1 Jyotisam ayanam punyam pravaksyamyanupirvasah| sammatam brahmanendranam yajfakalarthasiddhaye||R-VJ 3; Y-VJ 2 pranamya Sirasa kalam abhwwadya sarasvatim| kalajfianam pravaksydmi Lagadhasya mahatmanah|/R-VJ 2 Purifying myself and saluting with bent head Prajapati, the embodiment and presider over the five-year-yuga and who has for his limbs time-segments like the day, month, seasons and courses of the Sun (ayana), I shall write syste- matically about the effect on time of the movement of the luminaries, meri- torious by itself and accepted by learned brahmanas, for the purpose of deter- mining the proper time for the different sacrifices. (R-VJ 1, 3; Y-VJ 1-2) Arca-Jyotisa or Rgveda-Vedanga-Jyotisa (R-VJ) has a different second verse, which completes the first, thus: And, having saluted Time with bent head, as also Goddess Sarasvati, I shall write on the lore of Time, as enunciated by sage Lagadha. (R-VJ 2) 2. IMPORTANCE OF ASTRONOMY Text 2 veda hi yajfiartham abhipravrttah kdldnupiirvyd vihitas ca yajhah| tasmad idam kdalavidhanasdstram yo jyotisam veda sa veda yajhan||Y-VJ 3 The vedas have indeed been revealed for the sake of the performance of the sacrifices. But these sacrifices are dependent on the (various segments of) time. Therefore, only he who knows the lore of time, viz. Jyotisa, understands the performance of the sacrifices (fully). (Y-VJ 3) ## Page 38 36 VEDANGA JYOTISA yatha Sikha mayirdndm naganam manayo yatha] tadvad vedangasastranam jyotisan mirdhani sthitam||R-VJ 35; Y-VJ 4 Like the combs of the peacocks and the crest-jewels of the serpents, so does the lore of Jyotisa stand at the head of all the lores forming the auxiliaries of the Vedas. (R-VJ 35; Y-VJ 4) Note I. Ganita, a variant reading for jyotisa means ‘computation’ which is the essence of this science. Note 2. The importance of every kind of lore is stressed by being praised in the manner done here by the writers on that lore.

Text 3 somasiryastrearitam vidvan vedavid aSnute/ somasiiryastrcaritam lokam loke ca santatun|/R-VJ 30; Y-VJ 43 One learned in the Vedas who has also learnt this lore of the movement of the Moon, the Sun and the stars will enjoy, after death, sojourn in the world wherein the Moon, the Sun and the stars have their being, besides having, in this world, an unending line of progeny. (R-VJ 30; Y-VJ 43) Note 1 Different deities or groups of deities have their own worlds, where their devotees go and enjoy happiness after death. 4 VALEDICTION Text 4 ity evam masavarsanam muhiirtodayaparvandm| dinartvayanamdsangam( nam) vyakhydnam Lagadho ‘bravit]/ (¥-VJ, unnumbered verse after 43) Thus did the sage Lagadha speak in detail of the (synodic) months, the year, the muhiirtas, the risings, the syzygies, the days, the (six) seasons and the Courses of the Sun with the (solar) months. (Y-VJ, unnumbered verse after 43) Note I. In Weber’s first and critical edition, this verse appears unnumbered. before the last verse 43 of the Y-VJ. It is not found in the R-VJ. The verse enumerates all items computed in the work, with the name of the source, viz. the work of Lagadha. Perhaps, it is a later addition, to supply this need. Shama Sastry, in his highly un- critical edition of VJ, numbers this as 43, and the last verse as 44, ## Page 39 SECTION II MEASURES OF TIME, ASTERISMS ETC. 1. Time MEASURES Text 5 palani paticadasad apam dhrténi tad Gdhakam dronam atah prameyam| tnbhir vihinam kudavais tu karyam tan nadikdyds tu bhavet pramanam|| Y-VJ 24 A vessel which holds (exactly) 50 palas of water is the measure called ddhaka. From this is derived the droya measure (which is four times the Gdhaka). This lessened by three kudava measures (1.e. three-sixteenths of an Gdhaka) is the volume measured (in the clepsydra) for the length of one nadika of time. (Y-VJ 24) Note 1. According to the dictum that ultimately some terms will have to be left undefined, and taken from usage, the weight and relation between the weight and volume measures alone are mentioned, just as we say 1 gram of pure water at 4°C is 1 cc. The clepsydra also is not described here. There are several types of this, des- cribed in astronomical works. Note 2. R-VJ 17 gives a substitute for this verse: Text 6 nadike dve muhirtas tu paficdsat palamdsakam (? Gdhakam) | mdasa(? Gdha)kat kumbhako dronah kutapair vardhate tribhih||R-VJ 17 Two nadikds are one muhiirta. The adhaka is fifty palas. From the adhaka, kumbhaka or drona increases by three kutapas, (R-VJ 17) Note 1. Kufapa seems to be the same as kudava as current in some parts of India. None of the things mentioned are related to one another or the nadika. Indeed, funda- mentally the lacuna is to be supplied from usage. But here 1s lacuna with a vengeance. Text 7 kala dasa savimsa sydd dve muhirtasya nadike] dvi(? dyu)strimSat tat haldnan tu satechati tryadhika bhavet||R-VJ 16; Y-VJ 38 The nagika (mentioned 1n the previous verse) is ten plus a twentieth kalds of time. Two nadikds make one muhiirta. Thirty times the muhirta is a day which is equal to 603 kalds. (R-VJ 16; Y-VJ 38) ## Page 40 38 VEDANGA JYOTISA Text 8 . -padas trimsat tu saikika](Y-VJ 12b) .. .kasthandm caiva tah kalah|(Y-VJ 30d) 31 kasthds make one pada. (Y-VS 12b). (Four pddas) (equal to 124) kasthas make one kala. (Y-VJ 30d) Note 1. The word tah here refers to the four pddas given in the third foot of the verse as catuspadi. being a compound of caturndm padandm samaharah. The word pada itself means the number 31 by the statement, padas trimSat tu saikika (Y-VJ 12b). The word pada in this verse also signifies 31. Note 2. The reason for adopting the above-said significance is that the day is divided into 124 bhagas or parts. Since a quarter (pada) of this 1s 31, the word pdda 1s used to sigmfy the number 31. Similarly, the asterismal segment also 1s divided into 124 parts called amsas or bhamsas. Text 9 kastha paficaksara bhavet] Y-VJ 39d One kastha is equal to five aksaras (letters of double matras). (Y-VJ 39d) Note I. The aksara mentioned here 1s the length of time called gurvaksara, equal to two matras of time. Text 10 ardhapaficamabhas tvrtuh|(R-VJ 9d; ¥Y-VJ 10d) Four and a half asterismal segments is one rtu. (R-VJ 9d; Y-VJ 10d) Note 1. The period of the Sun or Moon moving through 44 segments is a rtu related to it, ie. the Sun’s rtu or the Moon’s rtu But the popular rtu or seasons is only the Sun’s. (Cf. the Vedic statement. Madhus ca Madhavas ca Vasantikay rtii] Sukras ca Suci§ ca Graignay rtii/Nabhas ca Nabhasyas ca Varsikdv rtulIsas ca iirjas ca Saraday rti|Saha§ ca Sakasya§ ca Haimantav rti|Tapa§ ca Tapasyas ca Saisirav rtii{(Vaj. Sam. 1325; Tait Sam. 4.4.11,1). Text 11 trigatyakndm sasastir abdah sat cartavo ‘yane/ nasa dvadasa sitryah syuh ctat paticagumam yugdm|] Y-VJ 28 ## Page 41 Il. MEASURES OF TIME BTC. 39 Three hundred and sixty-six days form the solar year. In the year there are six rtus and two ayanas (Sun’s courses). In the year there are twelve solar months. Five years make a yuga. (Y-VJ 28)

5 gurvaksaras or 10 matrés = 1 kdstha 124 kdsthas = Lkala 10 1/20 kalas = 1 ndgdika 2 nadikds = 1 muhirta 30 muhirtas = I day (ie the civil day) 366 days = 12 solar months or 6 rtus or 2 ayanas or 1 solar year 5 solar years = 1 yuga Note 2. The nadika 1s thus connected m two ways, first with the speech or musical measure of mdtrd, and second with the flow of water in the clepsydra of 50 palas of pure water, measuring an ddhaka. Note 3. Yuga means ‘joming or coming together’, technically the coming together of two or more of the Sun, the Moon, the star-planets, their nodes and the apogees, at the same place in the zodiacal circle marked by the asterisms. The five-year yuga mentioned here is the period when the Sun and the Moon meet in the same asterismal position in the zodiac, discovered in the Vedic period itself, and which is roughly correct. The Vedas have a name for each of the years of this yuga: Samvatsarah, Parivatsarah, Ida(da)vatsarah, Anuvatsarah, Id( Ud)vatsarah (Vaj. Sam. 27.25), with some variants in certain places.

Text 12 agnih prajdpatih somo rudro “ditir brhaspatih] sarpa§ ca pitaras caiva bhagas caivdryamapi cal] savita tvastétha vayus cendrdgni mitra eva cal indro nirrtir dpo vai viSvedevas' tathaiva cal] visnur vasavo varuno ‘jaekapat tathaiva cal ahirbudhnyas tathé piisd aSvirlo yama eva cal] naksatradevata hy eta etabhir yajflakarmant yajamanasya sastrajfiaih nda naksatrajan smrtim|| (R-VJ 25-28; Y-VJ 32-35) The presiding deities of the asterisms (beginning from Kjttikah) are, respec- tively: Agni, Prajdpati, Soma, Rudra, Aditi, Brhaspati, Serpents, Pitrs (Manes), Bhaga, Aryaman, Savitd, Tvasta, Vayu, Indragni, Mitra, Indra, Niryti, Waters, ## Page 42 40 VEDANGA JYOTISA Visvedevas, Visnu, Vasus, Varuna, Ajaekapad, Ahirbudhnya, Pisan, Asvins and Yama The people learned in the religious lores say that these deity-names are to be substituted for their own names in the (sankalpa of) the yaga (of the person on whose behalf the sacrifice 1s performed, viz.) the yajamdna. (R-VJ 25-28; Y-VJ 32-35) Note 1. While naming a child, it was the custom in ancient times to choose a name the first letter of which is appropriate to the asterism under which the child was born. A set of letters is associated with the asterisms. Even now, conversely, when a@ person’s naksatra is not known, he is given a maksatra appropriate to the first letter of his name, for religious rites or horary predictions In ordinary religious rites, 1t 1s declared in the introductory resolution (savkalpa). ‘I, bearing this name and born under this asterism, am going to perform this rite.’ But when he happens to be the yajamana in a ydga, in the place of his own name and asterism, the deity of the asterism is to be substituted, the idea being that he is now one with the deity and the deity itself is performing the yaga, as, say, ‘Ajaekapad yajate’, meaning, ‘Ajaekapad per- forms this yaga.’ Text 13 ugrany ardra ca citra ca visakha Sravano ‘§vayuk] krirdani tu maghd svati jyestha miilam yamasya yat]| Y-VJ 36 The asterisms Ardrd, Citra, Visakhd, Sravana and AsSvini are fierce. Maghd, Svati, Jyestha, Milam and Bharani are cruel asterisms. (Y-VJ 36) Note 1. These are mentioned here as an exception to the previous verse, and the names cf the deities of these should not be used for the purpose mentioned, Further, these should be avoided in choosing the time for the performance of auspicious rites like marniage. Note 2. The R-VJ does not have this verse. 3. RULE oF THREE Text 14 ity updyasamuddesah bhityo ‘py aknah prakalpayet) Jfeyardsigatabhyasta (? tam) vibhajet jfianarasina]|R-VJ 24; Y-VJ 42 The following is ‘the rule of three’ (for obtaining the desired result). This rule of three is to be applied again and again to the day, (using the fundamental and derived constants given in the work, in order to get the various computa- tional rules and results given in the work). The rule is: The known result is to be multiplied by the quantity for Which the result is wanted, and divided by the quantity for which the known result is given. (R-VJ 24; Y-VJ 42) ## Page 43

Note 1. The instruction is concise and looks like an aphorism. There are four items in a proportion, three known and one unknown, which is obtained from the three knowns. Hence the rule to get this 1s called the ‘Rule of three’. The four items are: (a) If for so much quantity, (6) so much result is got, (c) for this much quantity given now, (d) how much is the result that will be got? The first two are called jfiata- rasis and the next two are called jfieya-rdsis. The application of the rule is: Take the known result, i.e. (6), multiply 1t by the quantity (c) for which the result is to be known, and divide by the quantity (a) for which the result is given; thus the result to be known, i.e. (d), is got. Though the verbal description of the rule is long, it is simple and known to every school boy. SECTION II FUNDAMENTAL AND DERIVED YUGA CONSTANTS 1. YUGA AND ITS ELEMENTS Text 15 udaya vasavasya syuh dinarasih sapaficakah| rser dvisastihinam sydd vimSatyad saikaya strnam|]Y-VJ 29 paficatrumsam Ssatam pausnam ekonam ayandany rseh| parvanam syad catuspado... [|/¥-VJ 30 a-c sdvanendus trmdsanam sastih saikadvisaptkal dyutrimSat sdvanasyardhah siiryah strnam sa paryayah|/¥-VJ 31 sasaptakam bhayuk somah siiryo dyin trayodasal navamani tu paficahnah....//R-VJ 18a-c; Y-VJ 39a-c Note 1. The present section continues from verse Y-VJ 28, given in the previous Section II, Text 11, and its meaning should be understood here, viz. the 366 days form the year and that in the year, there are 6 rtus, 2 id and 12 solar months. Five years make the yuga. ' ‘ The number of risings ‘of the asterism Sravistha i in the yuga is the number of days, plus five (i.¢:,1830-+-5==1835). The'number, of risings of the Moon is the days minus 62 (ie., 1830-621 768). The total of. each of the Moon’s 27 asterisms coming round 67 times in the yuga is the number of the days minus 21 (ie. 1830—21=1809). (¥-VJ 29) In the same way, the total of the asterisms of the Sun (which comes round 5 times) 1s 135. There are one less (i.e. 134) ayanas of the Moon (ie. its north- ward and southward courses). There are 4 pddas (i.e. 4x S124) pe parvas (or paksas, or their ends, i.e. bright and dark fortnights) in the yuga.... (Y-VJ 30 a-c) ## Page 44 2 VEDANGA JYOTISA There are 60+1, 2, 7 (i.e. 61, 62 and 67) sdvana months, lunar (synodic) months, and Moon’s sidereal months (cycles), respectively, in the yuga. Again, the savana month contains 30 days. This plus half (i.e. 303) days make the solar month. The number mentioned here (viz. 30) is the number of solar sidereal cycles in the yuga. (Y¥-VJ 31) The Moon comes into contact with each asterism 60-+7 (i.e. 67) times during the yuga. The Sun stays in each asterism 13 days plus 5/9 days. (R-VJ 18 a-c; Y-VJ 39 a-c). Note 2. Any three elements of the yuga, pertaining to the Sun and Moon, not totally dependent on one another, if given, will enable us to calculate every other thing mentioned here, which latter might be called derived constants with reference to the three fundamentals. For instance, three are in the yuga, (i) 5 years, (it) 1830 days and (iii) 62 synodic lunar months. With a little knowledge of astronomy and knowing the definitions, we can compute the others thus: (a) Sidereal risings (i.e. sidereal days)=solar risings (i.e. ordinary days) plus solar cycles (1.e. solar years)=1830-+-5=1835 (given in the text as risings of Sravisthd). (6) Lunar cycles=Synodic months plus solar years=62-+5=67 (as given in the text). (c) Moon’s risings=Risings of Sravistha (or any other star) minus Moon’s cycles=1835—67=1768, as given in the text. The other given numbers can be obtained from these by division or multiplication. Note 3. Though the Moon’s ayanas are not commonly spoken of, it must also have northward and southward courses, during each sidereal cycle, since 1ts orbit also, roughly following the ecliptic, must cross the celestial equator northward and southward. Note 4. Since there are 2 paksas (parvas) in each synodic month, there are 62x2- =124 paksas in the yuga. It is this that has necessitated the division of the day into 124 parts, in order to give whole number results as far as possible. Note 5. The reading navamdni of R-VJ 18 has been adopted in the place of uttamani of Y-VJ 39, the latter being not suitable to the context. 2. LAGNAS IN THE YUGA Text 16 Stavisthabhyo gu(%ga)udbhyastat pragvilagnan vinirdiset] sii( ?sta)ryan masan salabhyastan vidyat candramasan rtin||R-VJ 19 ## Page 45

Using the risings of Sravisthd in the yuga (viz. 1835), which are also the number of its Orient Ecliptic points (prdg-lagna), and multiplying it by the number in the group (here, of asterisms, viz. 27), we get the total number of Jagnas in the yuga (viz. 1835 x27=49,545). Multiplying the sidereal revolutions of the Moon in 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 translate it also as: Using the distance of Sravistha from the rising point (.e. its hour angle), and multiplying it by 27, we get the Jagna, in asterisms and parts)]. (R-VI 19) Note 1. In the yuga, the Sun makes five rounds forwards in the zodiac, which itself is rotating rapidly backwards round the earth. Since the time of the motion of the Sun relative to the earth 1s the civil day, and there are 1830 civil days in the yuga, the zodiac itself rotates round the earth 1835 (1830-+5) times in the yuga, the time of one rotation being called a sidereal day. Note 2. A single or a group of asterisms of asterismal segments, being fixed in the zodiac, makes the same number of rotations. Lagna, as usually used, is the point of the ecliptic rising on the eastern horizon Sometimes the word prag-lagna is used to distin- guish it from the Occident (West) Ecliptic point and Meridian Ecliptic point (dasama- lagna). Now-a-days lagna is mentioned only in connection with the ragis. In those days there was no division into rasis, but there was the division of the zodiac into naksatra segments. We do not know whether the Jagva, in those days, was of the asterisms themselves or the asterismal segments. The exact time of the rising of any point can be calculated from its distance from the diurnal circle, the whole mandala representing 603 Kalas or 124 parts of time. (See also Section V. 4, below.) Note 3. In the text the syllable gu has been emended into ga, making guna into gana by me. Dikshit has taken guna to mean 3, according to the bhiitasankhya notation, but this notation does not seem to have been in vogue at such an early period. In the whole of the work we do not find 1t used anywhere else. But Barhaspatya commits a worse mistake by interpreting guna as 8 in the bhiitasatkhya, which transgresses all conventions. This kind of transgression will result in ambiguity, while the requirement is that the numbers are precise, Note 4. The Sun or Moon's ayanasis spoken of as beginning from their situation at the first point of the SravisthA segment or midpoint of the Aslesd segment, repsec- tively (See Y-VJ7 in Section IV. 2, below). The ayanas have 3 rtus each. The sidereal period containing 2 ayanas have 6 rtus. In the yuga, having 67 sidereal periods of the Moon, the rtus are 67X6=402. It is noted that while the names of the rtus Sisira, Vasanta etc. beginning with the Sum at Sravistha are significant as referring to real seasons, in the case’ of the Moon, they are simply nominal. » Note'5. lave emendéd siintto sta, making it staryan which means ‘pertaining to the'staxs (str)’, niguchilike:the Vedic word narya, since the word starya is an uncommon ## Page 46 44 VEDANGA JYOTISA word, it is easily mistaken to be siirya in the copying of manuscripts. But the lunar ytus cannot be related to the solar months, as it transgresses the statement ardhapai- camabhas tv rtuh, which justifies the emendation. Rgvedins pronounce even classical da as Ja as in the Veda itself. 3. Day-TIME Text 17 gharmavrddhir apam prasthah ksapahrasa udaggatau| daksine tau viparydsah sanmuhiirtyayanena tu]/R-VJ 7; Y-VJ 8 During the northward course of the Sun, the increase of day-time per day is the same equivalent of one prastha (of water used in the clepsydra) The night decreases at the same rate and vice versa during the southward course. During the whole course (ayana) the increase or decrease amounts of 6 muhiirtas (=12 nddikas). (R-VJ 7; Y-VJ 8) Note I. The time when the courses begin and end is given in the next Section. From the given data the duration of the course can be calculated to be 183 days, and the increase per day, which is given as one prastha, can be calculated from the data in the previous Section to be 4/61 nadika. For the whole course of 183 days, the crease is 183X4/61=12 nadikds or 6 muhiirtas. Note 2. The rate of increase given here is the average per day. It is very crude. Actually, for the first and sixth months of the course it is approximately a sixth of the total, for the second and fifth it is a third, and for the third and fourth it is half. Note 3. The total increase is not the same in all latitudes. It is proportionate to tan declination X tan latitude. The latitude corresponding to the total given here 1s 350, in the extreme north of India. The Vasistha Siddhanta of the Paficasiddhantika of Varahamihira gives the same total mcrease, not to speak of the crude Paitdmaha Siddhanta. SECTION IV TITHI, NAKSATRA ETC. OF CERTAIN SPECIAL DAYS THE Five-YEAR YUGA Text'18 maghasuklaprapannasya pausakrsnasaméapinah| yugasya pafcavarsasya kdlajidnam prackasate||R-VJ 32; Y-VJ 5 Men (like the respected Lagadha) give the details about the times of. various items in the five-year yuga which begins with the bright fortnight of the month, ## Page 47

of Magha and ends with the dark fortnight of the month of Pausa. (R-VJ 32; ¥-VJ5). Note I. This gives the epoch, necessary for calculating any item, using the rule of three given in Section II.3. Note 2. The plural verb needs the understanding of a plural subject. 2, COMMENCEMENT OF THE YUGA Text 19 svar Gkramete somarkau yada sakam savasavau| syat tadadi yugam maghah tapah suklo ‘yanam hy udak]| prapadyete Sravisthadau siiryacandramasay udak| sarpardhe daksinarkas tu maghaSravanayoh sada|| (R-VJ 5-6; Y-VJ 6-7) When the Sun and the Moon occupy the same region of the zodiac togethe1 with the asterism Sravisthd, at that time begins the yuga, and the (synodic) month of Magha, the (solar seasonal) month called Tapas, the bright fortmght (of the synodic month, here Magha), and their northward course (uttaram ayartam). (R-VJ 5; Y-VJ 6). When situated at the beginning of the Sravisthd segment, the Sun and the Moon begin to move north. When they reach the midpoint of the Aslesd segment, they begin moving south. In the case of the Sun, this happens always in the month of Magha and Sravana, respectively. (R-VJ 6; Y-VJ 7) Note 1. The VJ system has simplified the various periods as the 5 sidereal revolu- tions of the Sun in the yuga of 1830 days, 67 sidereal revolutions of the Moon in the same period, etc. This is done for civil calendrical purposes, which demand such simplification, just as, 1n modern times, the year is taken by us now to have 365 days, ordinarily, with one day more once in four years, calling it leap year, with its own further exceptions. This serves only as a framework for a religious clalendar. So, the yuga cannot begin exactly at the first point of Sravisthd segment generally, unless cdtrected. Further, the given cycle-days are mean, while the actual courses depend upon the true Sun and Moon, affected by the equations of the centre. So, only the region marked by the asterism Sravisthd can be specified. The exact points of the segments where the courses begin were determined by simple calculations based on inspection of the sky. Por details see Introduction. The words ddau and ardhe in Y-VJ7 signify that the exact point of the segments are meant, of course, for the civil calendar. Note 2. Prapadyete here means ‘move’, not simply ‘reach’ and ayanam means ‘movement’, primarily. The secondary meaning is ‘the period of moyement’. Only the Spin’s aygnane, is popularly sed, ## Page 48 46 VEDANGA JYOTISA Note 3. The beginning of the northward movement of the Sun at Sravisthd and the mention of the day-time to be least here (see Sn. I11.3, Y-VJ 8) shows that this is the time of the winter solstice. From this, the time when the original work of Lagadha was written can be determined. (See Introduction). Note 4. There is a corrupt reading dinam tyajah for ayanam hyudak. This is made much of by some. (See Introduction). 3. NAKSATRAS AT THE BEGINNING OF THE AYANAS Text 20 prathamam saptamam cahur ayanddyam trayodasam| caturtham dagamam caiva (2a dvih) yugmddyam bahule ‘py rtau||(R-VJ 8; Y-VI9) vasus tvasta bhavo ‘jaf ca mitras sarpo ‘Svinau jalam| dhata@ kas cayanadyads syuh (R-VJ 9a-c; Y-VJ 10 a-c) The first, seventh, and thirteenth tithis of the bright fortnight and the fourth and tenth of the dark fortnight are at the beginnings of the first five ayanas. These occur twice, (i.e. these five are to be repeated for the next five ayanas). (R-VI 8; ¥-VJ9) The naksatras at the beginning of the ayanas are Sravistha, Citra, Ardrd, Pirvaprosthapada, Anuradha, ASslesa, ASvini, Pirvasddhd, Uttaraphalguni and Rohini. (R-VJ 8a-c; Y-VJ 9a-c) Note 1. What is actually given is ‘the beginnings in the even tithis, 4th and 10th, are in the dark fortnight’. In the ayana there are 6 synodic months and 6 fithis more because the yuga=62 synodic months=10 ayanas, already giver. So, every seventh comes as the beginning. R‘u means ‘a repeating period’, here, the fortnight. Note 2. Since in the ayana there are six sidereal revolutions of the Moon and 189 more naksatras, every nineteenth beginning from Sravistha occurs aS an ayana- naksatra, Dhata is used as a synonym for Aryaman. Note 3. I have emended caiva into ca dvih, omitting the useless word eva, which is better than Barhaspatya’s explanation that the last foot with nine syllables is an Grsa-prayoga. 4. Tue Visuva Text 2] visuvam tadgunam dvabhyam riipahinam.tu sadgunam| ; yallabdham téni parvani tathordhvam (tathardhawn) Sa tishiv bhovet|R-VI 31. ## Page 49 IV. TITHI, NAKSATRA ETC. a7 visuvantam dvir abhyastam riiponam sadgunikrtan| paksa yadardham paksanatn tithis sa visuvan smytah]} ¥-VJ 23 trtiyam navamin caiva paurnamasin trayodasim (2 masim athasite)| sasthim ca visuvan proktah dvadasyam (%dasim) ca samam bhavet||R-VI 33 Double the ordinal number of the visuva (or equinoctial point) and subtract one. Multiply this by 6. The parvas gone are got. Halve this number. The tithi at the end of which the visuva occurs is got. (R-VJ 31) Take the ordinal number of the visuva and multiply by 2 Subtract one. Multiply by 6. What has been obtained are the number of parvas gone. Half of this 1s the tithi at the end of which the visuva occurs. (Y-VJ 23) The visuva is declared to occur in the bright fortnight, at the end of the tithis Trtiya, Navami, Full Moon, and in the dark fortnight, at Sasthi and Dvadasi. This is repeated once again. (R-VJ 33) Note 1. The visuvas, being equinoxes, occur at the middle of each of the ten ayanas. The interval between the visuvas 1s 124/10 parvas=12 parvas and 6 tithis. So, the time gone at the mth visuva=(n—4) (12? 6)=(2n—1) (6° 3*)=(2n—1)X6 parvas and half that of tthis. Note 2. There is no verse in either R-VJ or Y-VJ giving the naksatra of these points. Note 3. R-VJ means the same as Y-VJ 23. Also R-VJ is only an enumeration of the result of R-VJ 31. Note 4. trayodaga, meaning the 13th tithi, in R-VJ 33 is wrong, and seems to have found a place here by correspondence to the word trayodasam in R-VJ 8. In that verse it 1s proper since the beginning tithis are given for the ayana points. But here the ends of the tithis are given and there is dvddasim, which 1s correct. dvadasyam in the latter half of the verse is to be emended to dvddasim, to fall in line with the other adverbial accusatives. 5. RTUS IN A YUGA Text 22 ekantare ‘hni, mase ca pirvgam kytva” dir(?m) uttarah| ardhayoh paficavarsanam mrdu (2rdu) paticadasastame||Y-VI 11: In each of the two halves of the five-year-yuga, in the alternating periods of one synodic month and tithi, the next riu occurs after the previous one, (i9 sother words, the consecutive rts occur at intervals of two syrodic months and ## Page 50 48 VEDANGA JYOTISA two tithis because 30 rtus make up 62 synodic months). Regarding the eighth rtu, the 15th tithi comes as the beginning tithi. (Y-VJ 11) Note I. The first rtu of the yuga is Sisira, as can be seen from the statement that the first tz month is Tapas (vide R-VJ7; Y-VJ 6), Tapas and Tapasya being the months of Sisira (cf. Tapas ca Tapasyas ca Saihwav rtit, Vaj. Sam. 13.25; Taitt. Sam. 4.4.1.1). The next rtu Vasanta begins two synodic months and two tithis later, 1.e. on Caitra- Sukla Trtiyd, Sifira having begun in the Magha-Sukla Prathama. This continues for the rest. Note 2. The 15th tithi mentioned as the beginning of the 8th rtu is Parnimd. I have emended mrdu as rdu and have taken it to mean a contraction for rtu-dyu. 6. PART O£ THE DAY AT WHICH PARVA ENDS Text 23 du (?dyu) heyam parva cet pade ... bhagatmand *pavrjyamsan mrdiged adhiko yadi/]Y-VJ 12 a,c-d If the end of the syzygy occurs within the first pdda (ie. 31 parts of the day), that tithi 1s to be omitted from the reckoning. If the parts are more than 31, the parva whose tithi 1s to be omitted is to be found by subtracting the number of parts that has to be lessened for the elapsing of one parva each. (¥-VJ 12 a, c-d) Note I. 31 parts is a quarter of the day which is divided into 124 parts. So, less than 31 parts means ‘before mid-day’. Note 2. Even today, the syzygy falling before or after mid-day 1s crucial im decid- ing the day for the performance of iti, though the tithi 1s taken now as true fifi. Note 3. The parts of the day, at which the end of each successive parva occurs, is 30 parts less and less each parva, since the duration of each parva=days in the yuga divided by 124=15 days minus 30 parts. This mens 2 parts less for each tithi. Note 4. The verse, however, takes for granted that the parts of the day at which the parva ends is known, for then alone can we know in which pada of the day the parva-end falls. This can be learnt only by implication from the second half of this verse, since nowhere else in the work Has it been given: Wevean'prodeed taking the successive 15-day periods in the yuga, subtracting 30 parts for each, to get the end of the successive parvas. This 1s given in the’ verse. But this is the same.as' taking the parva number and subtracting 31 parts, or one pada, for each ‘parva. Since we want only the parts, and can neglect whole days accumulated, and,. since 4 padas wake a full ## Page 51

day, we can cast our fours, take the remainder and subtract one, two or three padas for the remainders 1, 2 or 3. Or, which is the same, we can add 3 pddas or 94 parts, add 2 padas or 62 parts, or add one pada or 31 parts to the number of the parvas for the remainders 1, 2, 3 respectively, interpreting bhdgdtmand to mean pada-bhagatmana. Thus we get the simple rule implied by the second half of the verse: Take the ordinal number of the 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, take the number alone. We get the parts at which the parva ends. Example. Find the parts of the day ending: (i) 37, (i) 43, (iii) 54 and (iv) 68 parvas. () Casting out fours from 37, 1 remains. So, 93-+-37--124=130/124=6 (module 124). So, 61s the number of parts of the day at which the 37th parva ends. Verification: 37x 1830-+124=546 6/124 days and the 37th parva ends. (i) Casting out fours from 43, remainder is 3. So, 43-+-31=74 is the number of parts ending 43 parvas. Verification: 43 x 1830-+-124=634 74/124, which gives 74 parts, neglecting full days. (ii) Casting out fours from 54, 2 remains. So, 62-+54=116 parts at the end of 54 parvas. Verification: 54x 1830+-124=796 116/124 days, which gives 116 parts, neglecting full days. (iv) Casting out fours from 68, zero remains. So, 68 itself is the number of parts of the day at the end of the 68th parva. Verification: 68 X 1830+124=1003 68/124, which gives 68 parts at the end of 68 parvas, neglecting full days. Note 5. For the sake of convenience, the civil calendar requires the reckoning of days from 1 to 15, consecutively, taking the synodic month to contain 29 or 30 full days. By taking or omitting the day for isti according to this rule, the isfi day can be made to be always on the first day of the fortnight, and the jump at any day of the fortnight owing to tithi-ksaya or avama can be avoided. The subsequent fortnight when this tithi-ksaya will fall, can also be determined. Note 6. The Revedic recension does not have this verse, ‘but the number of parts at parva-ending is required for R-VJ 20 and 13. «Note 7. Tilak correctly notes that if the civil calendar is to keep sufficiently near the religious calendar, a day has to be omitted for each yuga, without being counted in it. He thinks that this verse actually gives this by the words dyu heyam. But, where is the day to omit? Like the intercalary month, the day must be mentioned first as an extra day of the yuga, and then it should be said that it be omitted for reckoning the naksatra, tithi etc. and their characteristics. Otherwise dyu heyam cannot meat what he says. For his explanation ‘that the 93rd parva day was so omitted, he says ## Page 52 50 VEDANGA JYOTISA that the Moon’s naksatra parts at the parva is 31. This is wrong. On the other hand, itis 93. Hence the meaning of the verse must be quite different. (See my mterpretation here and the explanation in note 5 above.) Mistakes have also been made by ‘Barhaspatya’ and Sudhakara Dvivedi in their interpretations. D 7. CURRENT YEAR OF THE YUGA Text 24 ye brhaspatina bhuktah minat prabhrti ragayah| trivrtah (?te hrtah) paficabhir r (? bhii) ta yas Sesas sa parigrahah (Y-VJ, un-numbered verse after 4) Count the rasi (30° sign division of the zodiac) in which Jupiter 1s situated from the rasi called Mina (Pisces). Divide the number by five and take the remainder, This is to be taken as the number of the year current in the five- year yuga. (Y-VJ, un-numbered verse after 4). Note 1. The five years are named, respectively, as stated earlier, Samvatsara, Parivatsara, Idavatsara, Anuvatsara and Id (Ud)vatsara. As any day of the Veddnga calendar 1s specified as this day, of this fortnight, of this month, of this year, the ordinal number of the year 1s also required to specify the day. R-VJ 4; Y-VJ 13 under Sn. V. 1, below, will illustrate its use. Note 2. This verse is patently an interpolation. Firstly it 1s un-numbered and found only in the Yajusa recension. Secondly, the word ras itself, meaning the division of the zodiac of 30° each, named Mesa (Ayties), Rsabha (Taurus) to Mina (Pisces), is of foreign origin and came into India only during the first centuries a.p. along with Greek astrology. Up to and including the time of the early astronomical samhitas of the last centuries B.c., the only zodiacal divisions known in India were the naksatra divisions. Rasi as used in the VJ means only ‘group’, for example ‘parva-rasi’, meaning the ‘group of fortnights’ and ‘bha-rasi’, meaning the ‘group of nakgatra segments’. Note 3. This verse serves a useful purpose and that is why it has been interpolated. The calendric system of the VJ is purposely made approximate, in order to serve as a good civil calendar and serve simply as a framework for the religious calendar. In course of time, the erzor from the correct synodic cycle or solar sidereal year will accu- mulate and the calendar, on account of wandering further and further away from the truth, will not serve as a framework for the religious calendar. This happens so rapidly that even within a few yugas it would become useless, if it is not linked to actual ob- servation by periodic corrections, in the same way as the purely lunar calendar of the Mushums is corrected by the observation of the first appearance of the crescent Moon. But unless connected with the solar year, the Muslim months will recur earlier and earlier so that there 1s an excess of three years in a century. The Hindu lunar calendar ## Page 53

is linked with the solar year by intercalary months (adhundsas) so that 1t does wander away. Now, the omission of an adhimdsa at intervals indicated by observation in the sky, will link the erroneous civil VJ calendar with the actual calendar. But, in course of time, less dependance on observation and more on calculation cams inte practice. Here it 1s linked with the correct Jovian year. As discussed in the Introduction, Vara- hamihira, linked the rough Paitamaha Siddhanta of the Paficasiddhantika with the Saka year.

SECTION V

DAILY TITHI, NAKSATRA ETC.

In Section IV calendric details like tithi and naksatra of certain specific days, for example, the beginning of the ayana, were given as already calculated, because they are small in number. Even for the rtus, which are thirty in number, these details were given by a rule for calculation, though very simple. But there are 124 parvas and 1860 tithis. Details like their ending moments cannot be given readymade, because they are so numerous. This calculation has to be done in each case and involves large numbers. To accomplish this mentally, ingenious rules are given in this Section. Scholars who tried to interpret the VJ did not even guess that this is what is done here, and so failed, some to a greater degree and some to a smaller degree, baffled by the obscurity of the terms used, for, as the saying goes, vakyarthajfidne tatparyajfidnam api karanam 2. COMPUTATION OF PARVA-RASI Text 25 mrekam dyadasabhyastam dvigunam gatasamyutam| Sastya sastyd yutam dvabhyam parvanam rdasir ucyate||R-VJ 4; Y-VJ 13 Take the ordinal number of the year in the yuga. Lessen this by 1, multiply by 12, again multiply by 2, add the parvas gone in the year, for every 60 of the total parvas add 2, and the number obtained 1s the parva-ragi (1.e. the total number of parvas gone at the time for which calculations are to be made) (By repeating the word, we can also interpret it as Multiply the years gone by 12, add the months gone, double what.1s obtained, add the parvas gone, if any, etc ) (R-VJ 4; Y-VJ 13) ‘ Example: Find the parya-raSi before the point of time indicated by Anuvatsara, Karttika Bahula Navami, ## Page 54 52 VEDANGA JYOTISA Anuvatsara is the fourth year of the yuga. So, 3 years, 9 months and one parva (Sukla) are gone. From this:

Note 1, In each year there are 12 synodic months, each month having 2 parvas. After 30 months, an extra (adhika) or intercalary month is added to complete the half yuga. This is why the two parvas are added. Thus, we get the total, there being 62 synodic months or 124 parvas in the yuga. 3. ASTERISMAL PARTS Text 26 syuk pado ’rdham tripadya ya tridvyeke "hnah krte( ?ta) sthitim| sdmyenendoh str(2stvr)no "rye tu parvakah paficasammitah||Y-VJ 14 On account of the civil days of the yuga being divided into quarters, halves and three quarters corresponding to the divisibility of the Moon’s asterisms in the yuga, the Moon’s asterismal parts also are a quarter (i.e. 31 parts), two quarters (i.e. 62 parts), three quarters (i.e. 93 parts) and without residue. But the other parts of the asterisms have to be measured in units of fifth divisions of the parts. (¥Y-VJ 14) Note 1. This is what is said in this verse: The number of civil days in the yuga, containing 124 parvas, being 1830, at a quarter (i.e. 31) of the parvas the days gone are 457 and 62 parts. The Moon’s asterisms gone are 1809-4 452 and 31 parts. At half (1c. 62) of the parvas, the days gone are 915 and the asterisms yone are 904 and 62 parts. At three quarters (i.e. 93) of the parvas, the days gone are 1372 and 62 parts and the asterisms gone are 1356 and 93 parts. In these cases, where the day- parts are full quarters, the asterismal parts are also full quarters. But at all other parvas, the day-parts being naturally full, (Since the division of the day into 124 parts are expressed for this purpose), the asterismal parts cannot be full. So another division of the day called Kalas, into 603 parts, is required to express the times of the beginnings of the asterisms. In this unit, the asterism takes exactly 610 to pass. It is five times the number of parts taken by the tithi to pass and we have 122x5=610. This simple statement of fact has made the verse difficult to understand, because it is worded in obscure terms. The difficulty in understanding has naturally led to corruptions in the readings, adding to the difficulty. It is also to be noted that mandates giving the purpose are comparatively easier to understand than Statements, because knowing the purpose it is easy to guess the method given to achieve the purpose from the given data. ## Page 55

Note 2. On account of the difficulty, ‘Barhaspatya’ makes all sorts of emenda- tions. He arbitrarily divides the pratipad ito 8 parts, not known to the ydjfikas, adding some to the new moon fithi and some to the pratipad, for which he has been criti- cized by Tak. Sudhakara Dvivedi has done worse, in his usual manner, making drastic emendations. Tilak himself relates the verse to the intercalary day mooted by him. (cf. Introduction.) 4, BuamSas OR NAKSATRA-PARTS Text 27 bhamsah syur astakah karyah paksadvadasakodgatah| ekadaSagunas conah Sukle ’rdham caindavaé yadi]/R-V¥ 10; Y-VJ 15 Eight naksatra-parts (bhamsas) are to be put down for every unit in the quotient of the number of parvas divided by 12. The remainder is to be multiplied by 11 and added. If the parva in question 1s full moon, 62 parts more are to be added if the parts refer to the Moon’s naksatra (and not the Sun’s). (R-VJ 10; Y-VJ 15) Note 1. The naksatra-parts mentioned here are 124th parts. The parts are intended to be used in verses R-VJ 14-15; Y-VJ 17-18, to find the nakgatra of which these are the parts. This is the point of the maksatra of the Sun and Moon at the end of the new moon, and of the Sun at the full moon parva, without the 62 added, and of the Moon with the 62 added. ' Example. Find the naksatra-part of the Sun and the Moon at the end of the 93rd parya. . ‘Working as per instructions in the verse: 93--12=7 quotient, 9 remainder 7x8+9R 11=155=31, casting out 124. This gives the Sun’s naksatra-part. Since the parva ends a bright fortnight, that is, it is a full moon, the Moon’s naksatra-parts are got by adding 62, 1.e they are 93. At the end of the previous, ie. 92nd parva, which is new moon, the naksatra- parts of both the Sun and the Moon are’ 7x8+8x11=144=20, casting out 124. Note 2. The proof of the rule is as follows: In the yuga; containing 124 parvas, the Sun traverses 5X27=135 naksatra segments. During each parva, it traverses 135+ 124=1+-11/124 naksatra segments. Taking the parts alone, this is 11 of the 124th parts. At the end of 12 parvas, it1s12 (1+-11/124)=13+8/124 Taking the parts alone, this gives 8: So, for every 12 parvas, it accumulates by 8. For the remainder, the pats ## Page 56 54 VEDANGA JYOTISA are 11 for each, and. so the remainder is multiplied by 11 and added. At new moon, the Moon is with the Sun and the parts are the same. But at full moon, the Moon 18 opposite the Sun, that is, 13} segments or 13 naksatras and 62 parts away. So we add 62 parts for the Moon. Note 3. ardham here means ‘half (of 124 parts)’, ic. 62 parts, that being the number of parts in half day. Again, pada being 31 parts or the first quarter of the day, ardham can mean the first half of the day also. Note 4. ‘Barhaspatya’ has not understood the second half of the verse. He writes: “Should the twelve half-months be co-terminous with a complete lunar month, the Moon is half naksatra and 11 amSas behind the full moon, syzygy’’. How can the group of 12 half-months or 6 complete lunar months be at full moon, syzygy? He has missed the meaning of the word nah and thereby the meaning and purpose of the whole verse. Sudhakara Dvivedi has, as usual, done drastic emendations, and missed the meaning of part of the verse. Tilak well understands the meaning and purpose of the verse.

Text 28 navakair udgato ’mSah sydd iinah saptaguno bhavet/ avapas tv ayuje *rdham syat paulastye ’stam gate ’param|/Y-VJ 16 paksat paficadasac cordhvam tad bhuktam iti nirdi§et] navabhis tiidgato ’mSas syad inamsadvyadhikena tu]|R-VJ 13 Dividing the number of parvas by 9, take one part for each quotient. Each of the remainder should be multiplied by 7 and added. If the quotient is odd, add half, (that is 62 parts). If the Moon is setting when the Sun rises f..e. if full moon parva), add another half (1.c. 62 parts). (Y-VWJ 16). Note 1. Paulastya (or Paurastya) is an old name for the Moon. "the sum of the hour angle-parts of the Sun and those of Sravisthd at the end of the parva 1s given here. Since the hour angle of the Sun is already known, we can know the hour angle of Sravistha by subtracting the Sun’s parts from this. As the hour angle-parts of Sravistha gives the rising point of the zodiac, the asterism’s rising point can be got by multiplying it by 27 and dividing by 124 This 1s the Lagna (Onent ecliptic point) in terms of the naksaira and its parts and envisaged in R-VJ 19 in Sn. III. 2 above. There the number of stellar lagnas was only apparently given. Here we get the method to find it. Example. What is the hour angle of Sravistha and the fooee at the end of the 93rd parva 2? ## Page 57

The Sun’s hour angle, already found, is 62, the parts of the day gone being the hour angle (cf. Y-VJ 14, Note lin Sn. V. 3 above). The sum to be got by this verse is found thus: On dividing 93 by 9, the quotient is 10 and the remainder 3. 1x10+-3x7-+62 (for full moon)=93. This is the sum. Subtracting the Sun’s hour angle, 93-62=31, is the hour angle of Sravisthd. 31 x27=124=68 asterisms counted from Sravisthd, i.e. 93 parts of Bharani, is the rising point, /agna. After the 15th tithi of any parva, (1.e. at the end of any parva), the total of the bhaSesa (mentioned in the previous verse, R-VJ 12) is to be got in the following manner: For every quotient of division of the number of parvas by 9, one diurnal part is to be taken. For each remainder, two parts less than 9 (i.e. 7) parts are to be taken. (R-VJ 13) Note 2. It may be seen that R-VJ 13 is parallel to Y-VJ 16 and that its meaning is the same as that of the first half of the latter. Note 3. Since after every 3 tithis, the diurnal parts are 6 less, and the part of the rise of Sravisthd itself 1s one part more, the hour angle of Sravistha after the end of every 3 tithis is 5 parts less, and so at the end of a parva it is 25 diurnal parts less. From this, the diurnal parts of Sravisthd can be got directly for the end of parvas and added. For ease of computation, we can make it 1 part less for every 5 parvas, since 5X(—25)= —125=1 (mod. 124). Note 4. Without using this verse, the hour angle of Sravisthd can be got by adding the zodiacal position of the Sun and the diurnal part (hour angle of the Sun) at parva. In this verse, the result of adding the diurnal parts to the hour angle of Sravistha is given. So, if 7 is the number of the parvas, the result got in the verse=5n-}-2 diurnal parts. nj124x5x 124=5n, being the zodiacal position of the Sun 5n+2x94n=5n-+64n (mod. 124) =5nt-+2n+62n=7n (if n is even) or 7n-+62n (if n is odd, i.e. full moon, when the Moon is opposite the Sun). Now, 7#=nx 63/9=63 (q-+r/9), where q is the quotient and r the remainder of n/9. =63q-+Tr=(62-+1) q+7r=624g+q+7r ' =:q-+7r (if q is even) and 62+9¢+7r (if q is odd) Thus we have the total result given by the verse, 7+7r, (+62 if q is odd, 62 more if 7 is odd or full moon). ## Page 58 56 VEDANGA JYOTISA Note 5. ‘Barhaspatya’ has not translated the third quarter of Y-VJ 16, not understanding what it means. This has landed him in difficulties and he gets out by assuming that the hour angles are not counted from the eastern horizon, as is natural, but are counted separately for each part of the diurnal circle, viz. the eastern horizon, the meridian, the western horizon and the nadir meridian. Tilak has condemned this as baseless. 6. NAKSATRA AT ANY PARVA Text 29 javadyamSsaih samam vidyat pirvardhe parvasiittarah| bhadanam syac caturdasyam dvi(%dyu)bhagebhyo "dhiko yadil| R-VJ 15; Y-VI17 jau dra& gah khe Sve *hi ro sa cin mit san yah si ma dha nah/ re mr ghd sva ‘po ‘jah kr syo ha jye stha ityrksa hngaih|| R-VJ 14; Y-VJ 18 Take the naksatras represented symbolically by jau etc. in the given series, in the order one, two, three etc. of the parts of the maksatras (found in verse R- VJ 10, Y-VJ 15; Sn. V. 4), each to each. So many parts of that naksatra has gone at the end of that parva for which that bhamSa has been found. If the parva falls within the first half of the parva-naksatra, (.e. 1f the naksatra-part 1s 62 or less at parva), the beginning of the naksatra to be found (bhddanam) will fall in the parva-tithi, i.e., the 15th tithi itself. If the maksatra-parts is greater than the parts of the day at which the parva falls, the beginning of the naksatra falls in the Caturdasi tithi day. (R-VJ 15, 14; Y-VJ 17, 18)

No. Symbol Naksatra No. Symbol Naksatra 1 Jau Asvayujau 14. Ma ttarapha 4 Khe Vigathe oP 17 Re Read 5 Sve Vidvedenth, 1) He es Mrgasirsam asa hah Mi a eee ee I Sar H Ea Repiot othe 22 Jah » AY Seat aoe ll Sa Satabhigak 35 Boh Hane 12 Nyah Bi yah 26 = Sye Jyestha 13° Sa 27‘ §than Sravigthah ## Page 59

Note 1. In the Javadi arrangement of naksatras enumerated here, they have been arranged from Asvini, each being the sixth from the previous and represented by means of indicatory symbols formed by syllables taken from their names or their deities. Example. At the end of the 93rd parva, what is the naksatra of the Sun and of the Moon, and also show how many parts of each have gone by. From the previous example, the Sun’s parts at the end of 93 parvas are 31 and the Moon’s 93. So the Sun’s naksatra is 31 (mod. 27), i.e. the 4th naksatra in the Javadi series, viz. Visadkbha at parts 31. The Moon’s naksatra 1s 93 (mod. 27)=12 giving Bharani at parts 93. Note that the Sun and Moon are 13} naksatras from each other. The answers can be verified directly thus: For the 124 parvas of the yuga, the Sun traverses 135 naksatra segments. For 93 parvas it traverses 93 x 135+124=101 and 31/124 which (mod. 27) is 20 and 31/124, i.e. 31 parts in the twentyfirst naksatra, ie. Visakhd, reckoned from the first, viz. Sravistha. Note 2. The R-VJ recension has the reading uttare in the place of uttara, which gives better grammatical agreement. The last quarter of this recension, the corrupt kasthandm devind kalan, has strayed here from elsewhere. The words dyubhdgebhyo ‘dhiko yadi is essential to complete the expression bhddanam sydc caturdasyam. Example. The number of the Moon's naksatra-parts is 93 at the end of the 93rd parva, falling at 62 parts of the day. Does the beginning of the naksatra fall in the 15th or 14th tithi? The Moon’s naksatra-parts being greater than 62, the beginning of the maksatra falls in the CaturdaSi tithi. This is got by contrast from the given rule. Positively, the Moon’s naksatra-parts, 93 being greater than the day-parts, 62, the beginning falls in the Caturdasi day, that is, the previous day. Explanation. Since the naksatra takes 7 kalds longer than the day to pass, the naksatra-part takes longer than a day-part to pass. So, if the maksatra at parva is greater than the day-parts, more time than the day-parts would have been taken by the naksatra-parts to pass. Therefore, the naksatra must have began earlier than the civil day. How much earlier is given by the verse R-VJ 11; Y-VJ 19, below. (Sn. V. 7) As for the first rule, referring to the tithi proper, half the naksatra-parts, i.e. 62, takes certainly less time than one tithi, which takes 122 parts to pass. So the naksatra must have begun right within the parva-tithi, that is, the 15th tithi itself, either on that civil day itself, or on the previous civil day. ## Page 60 58 VEDANGA JYOTISA Note 3. From the explanation given above, it will be seen that the two rules are not redundant: one refers to the tith: proper and the other to the civil day marked by the tithi. For example, if at parva end the naksatra-parts are 44 and the day-parts are 4, the beginning falls in the 15th tithi itself but on the previous day. If the naksatra- parts are 22 and day-parts 64, the beginning falls mn the 15th tithi on the same civil day. 7. KALAS FOR Moon’s NAKSATRA Text 30 karya bhamsastakasthane kala ekdnnavimSatih] iinasthane dvi(?tri)saptatim udvaped iinasambhave]/R-VJ 11; Y-VJ 19 R-VJ has a better reading for the last quarter: saptatir udvaped iinasammitah. For every 8 naksatra-parts, 19 kalas are to be set down for work For the less (i.e the remainder), when the remainder occurs, take away 73 kalds for each of the number remaining. (This meaning is clearer in the R-VJ reading.) (We get the time of the day, in kalds, at the beginning of the parva-naksatra, that is, the Moon’s naksatra at the new or full moon.) (R-VJ 11; YaVJ 19) Note I. These Kalas are called Bha’ dana-kalah, to be understood in the context, from the reference to it in Y-VJ 17 and the work done in Y-VJ 21. (See Sn. V. 6, 9) Example. Find the kalas at which the Moon’s naksatra at the 93rd parva begins. From the previous example, the naksatra-parts at parva is 93=11x8, plus 5, remainder. The Kalas required=11x 19~73.% 5=209—365, which, counted from the beginning of the previous day is (209-+-603)36 —5=447 of the previous day. The above result can be verified thus: The time of the day when the 93rd. parva ends is 62 parts (as found in Note 1 to verse Y-VJ 14, Sn. V. 3) which 1s 62 X 603-+124=3014 kalds of time. The Moon’s maksatra-parts gone is 93. Since each naksatra takes 610 kalas to pass, to pass 93 it takes 93x 610-+-124—457} kalds. So the naksatra begins at 457} kalds earlier than the 3014 Kalas of the day, which is 3014-+603—4574=447 kalas of the previous day. To chnch the matter, in addition to this verification, a proof might also be given. After each period of 17 parvas, the Moon’s naksatras increase by 17% 67X27-+-124 = 248+-1/124, which gives rise to one part. 248 naksatras take 248 x 610--603=250 days +530 kaldés=251 days 73 halas. This corresponds to one part. For 8: parts, it is 8x(—73)= —584=19, neglecting whole days. : ## Page 61

Note 2. This verification itself shows that the emendation of dvi into tri is necessary and correct. Tilak has mistaken the meaning of the word udvapet as ‘putt- ing in or adding’, and made mistakes in his interpretation. Avdpa means ‘sowing or putting in’, not udvdpa which mean ‘taking out’, dvdpodvdpa meaning ‘putting in and taking out’. His interpretation will give an error of a few kalds, even after his unnecessary supplementation of this verse with verses R-VJ 12 (Y-VJ 27), R-VJ 13 and Y-VJ 16, (with several pages of explanation for this simple thing). This involved explanation ttself must have told him that there 1s something wrong with his meaning, for he was transgressing his own dictum in his Introduction. His taking the 8 parts mentioned not as 1t is, but as 12 parvas (the origin of the 8 parts), has added. to his difficulties. ‘Rarhaspatya’ has understood the meaning of udvapet correctly, but has made the same mistake in understanding dima as he has done in Y-VJ 15 (Sn V. 4). He translates the second half as: “Introduce minus 72 kalds in place of the subtrakend”, which does not yield any meaning. In his proof, he has done the first part correctly, but to prove the second part, he has arbitrarily taken ‘6 circuits of the Moon’, just to get —72 kalds given in the text. So he has not been able to realise that it must be —73, not —72. 8. TirHi-NAKSATRA IN THE JAVADI SERIES Text 31 uthin ekddasabhyastam parvabhamsasamanvitam| vibhayya bhasamithena tithinaksatram Gdiset|] Y-VJI 20 Multuply the tithis gone after a parva by 11, and adding it to the parts of the naksatra current at the end of the parva, and dividing out by the total number of naksatras, (viz. 27). Taking the remainder, and using 1t in the Javadi series, the naksatra current at the tithi must be found. ( ¥-VJ 20) Example. Find the naksatra of the 8th tithi after the 93rd parva. 8xX11+93 parts (got for 93 parvas)=181 (mod. 27) Applying the Javad: series, the 19th, Maghd, is the naksatra of the 8th tithi. Rough verification: Normally the Moon’s naksatra increases one per day, as also the fithi. So the 8th after Bharani, Maghi is the naksatra required here. Explanation: The rule given here is just to get the tithi-naksaira by a reference to the Javadi series. In this series, the consecutive numbers are the same as the parts “nod. 27) of the nakgatra givelx, The next naksatra occurs 11 places away. The nakgatra ## Page 62 60 VEDANGA JYOTISA next to a given maksatra will occur 11 places off, because 115 1/124=55 11 /124=1 11/124 (mod. 27). Now, roughly, successive tithis have successive naksatras (the difference being 17 naksatra-parts less for every 5 tithis). So, if the tithis are multiplied by 11 and added to the parva-naksatra-parts, we get the naksatra equal to the number of tithis after the parva-naksatra as the naksatra for that tithi. But, as mentioned above, the loss of 17 parts for every 5 tithis have to be subtracted from the parts of the parva-naksatra to get the actual parts of the tithi-naksatra and this may make the tithi-naksatra one less than what we get by this rule if the parva-parts are less than the correction. Example. Find the naksatra of the end of 10 tithis after 36 Parvas. By ¥-VJ 15, the naksatra-parts are 24 at parva. By this tule, 24411 10=134— 26 (mod. 27). The 26th in the Javadi is Jyesthd. But the correct naksatra is Anuradha 114 parts at the end of 10 sithis. It is got thus: The required naksatra and parts at parva=the naksatra and parts at parva (that is, Pusya 24 parts)-+11 naksatras—17X 10-5 (=34 parts)=Aniradha 114 parts. Note I. We can see that this rule has been given simply by a desire to use the Javadi for this purpose. Otherwise, the precise rule, which is easy, could have been given. Tilak has got the idea correctly. But ‘Barhaspatya’, missing the meaning, has given an involved formula, needing a more involved explanation. Sudhakara Dvivedi, thinking that the formula must give the naksatra-parts also correctly (the parts are not given in this rule) has made drastic emendations in his usual way, with bhiita- sankhyd, which could never have been used by the author. 9. BHADANAKALA Text 32 yah parvabhadanakalas tdsu saptagunam titkim| uktah (2yuktya) tdsdm vijaniyat tithibhadanikah kalah]/R-VJ 21; Y-VJ 21 R-VJ reads the second half as: praksipet kala (%pettat) samithas tu vidyad adanakih (Whaddnikdh) kalah| Adding Kalas equal to seven times the tithis elapsed after the parva, to the bhaddnakala of the parva we get, the bhadapakalas pertaining to the tithis Ge. the times of the beginning of the naksatras current at the end of the tithis). (R-VI 21; Y-VI21) Note I. The tithi here is loosely taken, as equal to the day, though Correctly it is 2 parts (about 10 kalds) less. Since the duration of the naksatra is 610 kalas, ## Page 63

that 1s, 7 kalas more than a day, the naksatra begins 7 kalds later each day or loosely each tthi. Hence the rule of adding 7 times the sithis. Example. Find the beginning of the naksatra current at the end of the 8th tithi after the 93rd parva, The beginning of the naksatra in question is 7x 8=56 kalés later than the parva- bhddanakalds got in the example in Y-VJ 19 (Sn. V. 7), viz. 447-+56= 503 kalds of the day previous to the 8th sithi. 10. Time OF THE Day : Posirion oF THE SUN Text 33 atitaparvabhdgebhyah Sodhayed dvigundam. tithim| tesu mandalabhagesu tithinisthamgato ravih||R-VI 20; Y-VJ 22 Subtract twice the number of fithis after a parva from the parts of the day ending the parva. We get the parts of the day when the tithi ends, (which is the same as the position of the Sun in the diurnal circle (technically) called nddimandala) (divided into 124 parts). (R-VJ 20; Y-VJ 22) Note 1. Y-VJ 25 and 26 which follow, (Sn. V. 11, 12), deal purely with the Sun. The present verse faces both ways, on one side giving the time of the day when the tithi ends and, on the other side, the position of the Sun in the sky, that 1s, in the diurnal circle at that time. Example. What is the time of the day when the 8th tithi after the 93rd parva ends? Where is the Sun in the diurnal circle at that moment? The time of the day=The time of the 93rd parva minus 8X2=62—16=46 parts of the day. a Dividing the diurnal circle into 124 parts, the Sun will be at the end of 46 parts counted from the east. Note .2. ‘Barhaspatya’, in his' explanation, asks us to take for example, the Sun’s diurnal position at parva to be 31. It can never be an odd number of parts. If he takes, as he does in his interpretation of Y-VJ 16 (Sn. V. 5), that the parts are reckoned for'each quarter-day separately, how are we to know in which quarter-day the partslie?7 °° ## Page 64 62 VEDANGA JYOTISA 11. Sun’s NAKsATRA AT ANY TIME Text 34 ekadasabhir abhyasya parvani navabhis tithim| yugalabdham saparva syat vartamanadrkabham kramat|] Y-VJ 25 Multiplying (the number of) parvas elapsed by 11 and the tithis elapsed after that by 9, (adding the two) and dividing (the total by the number of parvas in) the yuga (viz. 124), and taking the quotients and parts, and adding the number of the parvas to the quotient, we get the total number and parts of the Sun’s naksatra which have elapsed, (counted from Sravistha) in the regular order. (Y-VJ 25) Example. Find the Sun’s naksatra and parts at the end of the 8th tithi after the 93rd parva. According to the rule, (93 11+8x9)=8 full maksatras and 103 parts. Adding 93 to the 8 full naksatras elapsed since and counting from Sravisthd, we have 101 naksatras and 103 parts in the next, 1.e. the Sun is at the 103rd part of the 21st naksatra, Visakhd, since 102=21 (mod. 27). Note I. The R-VJ does not have this verse, perhaps feeling no need for the Sun’s naksatra. Even in Y-VJ 15 (Sn. V. 4) the purpose is, perhaps, only to get the Moon’s naksatra and parts, the Sun’s naksatra and parts only coming by the way. We can get the Sun’s naksatras and parts envisaged in this verse by simply multiply- ing the tithis elapsed by 9 parts and adding it to the Sun’s naksatra already found. For instance, adding 8x 9=72 parts to Visakha 31 parts found in the example under ¥-VJ 17-18 (Sn. V. 6), we get Visakha@ 103 parts, found in the example here. Note 2. ‘Barhaspaty’s’ translation is defective, because saparva has been omitted. He says that the Sun’s naksatra 1s got by this verse. Without adding the number of parvas as given by the expression saparva, the naksatras cannot be found because the whole aksatra per parva would be omitted taking only the parts. Also, hus inter- pretation that two rules are given here, one for the parva and the other for the tithi, 1s also unnecessary, since the parva-naksatra can be found simply by taking the tithi elapsed after that as zero. Tilak remarks that yugalabdham does not mean dividing by 124 parts, but simply adding the two results of the first half. He is wrong, because Saparva, meaning to add whole naksatras elapsed, requires that the parts be converted into naksatras. In another context, he himself wants the division. Further, we are not told that the two results are parts, and so the instruction to divide by 124 is necessary. ## Page 65 V. DAILY TITHI, NAKSATRA ETC. 63 12. Day’s PARTS AT THE BEGINNING OF A NAKSATRA Text 35 siiryarksabhaggn navabhir vibhajya Sesam dvirabhyasya dinopabhuktih| tithi(?the)r yuta bhuktidinesu kalo yogam (?yogo) dinaikddasakena tadvat|/¥-VJ 26 Divide the parts of the Sun’s naksatra by 9. Multiply the remainder by 2. This is termed the partial complement for the day’s parts. Add to this the comple- ment for tithis, got as quotient, to obtain the total complement to be added to the day’s parts. Add the total complement to the maksatra-parts and divide by 11. The result is the day before the completed day’s parts when the naksatra began. (Y¥-VJ 26) Example, The parts of the Sun’s naksatra at the ertd of the 8th tithi after the 93rd parva is 103 of Visakha. The parts of the day when ths tithi ends is 46 Find the day and parts when Visakha began. Since 103/9=11 and 4/9, the partial complement is 8/9. The quotient being 11, the complement due to the fithis is 11X2=22. The total complement, i.e. 22 8/9, added to the parts of the day, viz. 46, is 46+22 8/9=68 8/9, and this 1s the completed parts of the day. Days for the 103 parts to pass=(103+22+8/9)+J1=I11 4/9. So, Visakhad began 11 4/9 days before the 68 8/9 parts of the day of the 8th tithi, i.e. 13 7/9 parts of the day of the 12th tithi. Note 1. The translation given by me here, follows that suggested by Tilak, after examining the translations of Sudhakara and ‘Barhaspatya’. All agree in the final result. But Tilak’s is a circumlocution because he wishes to use all the words in the verse. As itis, neglecting the last part, the rule can be given simply as: “Divide the Sun’s naksatra-parts by 9. Double the ‘result’. Add this to the parts of the day for which the naksarra-parts are given. The day and parts, when the naksatra began is the ‘result’ taken as days before the added parts of the given tithi-day.” In the example, 103 are the parts of the maksatra at 46 parts of the day of the 8th tithi. 103/9=11 4/9 is the ‘result’. This doubled is 22 8/9. 46422 8/9=68 8/9 are the increased parts of the day. The ‘result’ taken as days, i.e. 11 4/9 days, before 68 8/9 parts of the given (8th) tithi-day is 13 7/9 parts of the 12th tithi-day, as already found. , Note 2. The explanation of the rule 1s as follows: The nakgatra-parts divided by 9 gives the tithi periods for the parts to go. But the number of sithis can be taken as the number, of days if twice the number of tithis, taken as parts of a day, is sub- ## Page 66 64 VEDANGA JYOTISA tracted from it, because each tithi is two parts less than a day. But these days have to be subtracted from the given day and parts. So, twice the number of tithis, taken as parts, are added to the parts of the day and the number of tithis, taken as days, are subtracted from the point of the added parts of the day. Note 3. It may be that some other rule is lurking in the last part where the division by 11 appears, not visible to us because of some corruption in this part.

Text 36 tryamso bhaseso divasamsabhagas caturda$as cdpyapaniya bhinnam| bhdardhe *dhike cdpi gate paro ’mSo dvav uttame tan navakair avedyah (2tya)|/R-VJ 12; Y-VJ27 The excess in rising of the zodiac over the diurnal circle in terms of its 124th parts 1s a third of the number of days elapsed in the year, rounding off the fraction upto fourteen days in any parva. When (nearly) half a zodiac has been got as rise, add one more part, and, as the second half 1s (nearly) completed, add another one. This result can be obtained by extending the navaka rule (already given for the ending moments of the parvas in Y-VJ 16: Sn. V. 5). (R-VI 12; Y-VI27) Note I. There are 367 risings of Sravistha (or revolutions of the zodiac or sidereal days) in the year, while the civil days are 366. The defect in the sidereal day adds up to one sidereal day in the year, in which 124 parts of the zodiac rises. At the rate of one-third part daily, for 366 civil days there will be 122 parts rising, the two parts remaining being due to neglecting the fraction, viz. 2/366 each day. This neglect is taken into account by adding one.part every half year, during which one- half of the zodiac, or one-half of the total naksatras in the zodiac, would have risen. Note 2. The navaka rule already seen follows this verse according to the R-VJ recension. It occurs next to verse 15 of the Y-VJ version, as verse 16, because the manner of computation in both is the same. There the tithi or parva unit is used to find the time-angle of Sravistha im daily parts and no neglected fraction is involved, but here the day-unit (so much part of the day) in used, and the fraction occurs. This will not matter, because, in actual practice, everything we got is only approximate or mean. In a note here, its extension to the fithi has been shown. Example: Find the time-angle of Sravistha after 122 days in the year. ## Page 67

One-third of 122 is 40%. For neglecting the fraction we may add 2/3, since we are asked to add one per half year, and make it 414 to be exact, though the rule here envisages only whole parts. Thus we have 41 parts. 14. CoRRECTION FOR THE YUGA Text 37 dvyii( 2dyii)nam dvisastibhdgena heyam saurydt saparvanam| yatkrtav upajdyete madhy ’nte cddhimasakau|/Y-VJ 37 The lunar day is less than the civil day by its 62nd part. The civil day is sub- tractable from the solar day (i.e. less than the latter). This defect, combined with the defect in the lunar day causes one extra month at the end of the half- yuga and another extra month at the end of the yuga. (Y-VJ 37) Note I. In the half-yuga there are 900 solar days, 915 civil days and 930 lunar days. So, in the one to one correspondence between the solar and the lunar months, one extra month has to be added at the end of each half-yuga to fit the lunar year reckoning with the solar year reckoning just as one more day is given to the civil year of 365 days to fit in with the correct year, once in four years, though even this 1s @ little rough. 15. RTUSEsA (TITHIS YET TO ELAPSE IN A RTU) Text 38 yadartham dinabhdganam saga parvani parvanil rtusesam tu tad vidyat sankhydya saha parvanam|/R-VJ 23; Y-VJ 41 Adding all the half-tithis occuring after each parva of all the parvas, (that pass normally at the rate of 4 per parva), we get what is called tusesa (that 1s, the tithis which remain in the last rtu and have to be passed to complete it). (R-VJ 23; Y-VJ 41) Note I. While the last verse is required to know the number of parvas, the present verse gives the rtusesa. : Example. (i) Find the rtuSesa and (ii), how much is required after 93 parvas to complete the rtu @) At 4 parvas per rtu, 23 rtus must have elasped at the end of 92 parvas, 92x 4=46 tithis, have to pass to complete the rtu: 7 (i) At the end of 93 parvus, one parva of this rtusesa has.gone and 31 tithis (2 parvas and. 11 titht) remain to’ pass in the'23rd rtu, that is, in Sarad of the fourth year. ## Page 68 66 VEDANGA JYOTISA Verification: 23 rtus require actually 23x 124—-30=95 parvas and 1 tithi. Since 93 parvas have elapsed, 2 parvas and 1 tithi remain to complete the rtu. 16. DAY-TIME AT ANY PARVA Text 39 yad uttarsydyanato gatam sya- che(%cche)sam tatha daksinato ‘yanasyal tadek( ?ka)sastyd dvigunam vibhaktam sadvadasam sydd divasapramadnam|/R-YV 22; Y-VJ 40 The number of days which have elapsed in the northward course of the Sun (uttarayana) or the remaining days in the southward course (daksindyana) doubled and divided by 61, plus 12, is the day-time (1n muhirtas) of the day taken. (R-VJ 22; Y-VJ 40) Example: Find the day-time at the end of (i) the 93rd parva and (it) the 54th parva. (i) Since there are 10 ayanas for the 124 parvas in the yuga, each ayana takes 12 parvas and 6 tithis. In 93 parvas, 7 full ayanas have elapsed and 6 parvas and 3 tithis have passed in the 8th ayana, which 1s a daksipdyana. 6X15+3=93 tithis, remain in this ayana. Since 1 tithi 1s day minus 2 parts, 93 tithis are 914 days. There- fore, the day-time by the given rule is: (914x2+61)+12=15 muhiirtas. In fact, this is the autumnal equinox. (a) In 54 parvas, 4 ayanas have elapsed and in the 5th aygna, an uttardyana, 4 parvas and 6 tithis have also passed. Now, 4 15+€=66 tithis=64 days. So the day-time 1s (64X2-+-61)+12=14,8 muhiirtas=28 nddis and 12 vinddis. 17. UPAVASATHA AND INTERCALARY Days Text 40 caturdasim upavasathas tatha bhavet yathodito dinam upaiti candramah| maghasuklahniko yuikte Sravisthayam ca varsikim]|R-VJ 34 That Caturdasi tithi on which the Moon rises just after the Sun has risen is the day of the Upavasatha. Any characteristic of the first day of the bright fortnight of the month of Magha links the naksatra of the last day of the pre- vious year (viz. Sravana) with Sravigtha, (that is, it is common to both). (R-VI 34). ## Page 69 V DAILY TITHI, NAKSATRA ETC. 67 Note 1. This verse 1s not found in the Y-W/. Note 2. Upavasatha day 1s the day of which the previous day 1s the ddhana or diksd day, that day itself 1s the pmdapitryajia day and the next day is the ist: day. Note 3. The Moon rising just after sunrise indicates that the time 1s near new moon. By contrast, 1f the Moon rises before sunrise, and becomes what is technically called Ud-dysta all excepting the Vajasaneyins and Baudhdyanas have to perform an expiatory rite to nullify the evil that will acrue and perform punaradhdna if the Gdhana had been done on the previous day. The next day will be the upavasatha and the next the isf: day. This shows how careful the priests would have been to avoid such a thing happemmng and, naturally, they must have had rules, formed from long observation, to fix the religious calendar tolerably well, using the system of the Vedanga Jyotisa as framework, Note 4. The second half of the verse suggests how the conditions of the first half can arise. On account of the lunar year bemg shorter by 11 days, and this accumulating to almost one month before intercalation is made, the naksatra of the first day of Magha can be Sravana or even Uttarasidha. Even at the end of the yuga, the new yuga can begin with part of Sravana, because actually the 62 Iunar months of the yuga take 1830.8965 days, not 1830 days, as the latter has been adopted just for civil convenience. Therefore, all the characteristics like naksatra and its endings will apply better to the first day of the next yuga. This will vitiate the characteristics of all the days of the next yuga and also accumulate yuga after yuga. Thus, the civil calendar will wander farther and farther away from the religious calendar. This can be avoided if the day next to the 1830 days of the yuga is not reckoned and the next day to that is taken as the first day of the new yuga, In fact, this day will be an inter- calary day made at the end of each yuge. It is this that is suggested by the second half of the verse. ## Page 70 BIBLIOGRAPHY i. TEXT EDITIONS AND TRANSLATIONS Lagadha Jyousha, ed by Captain H Jervis at the end of his Indian Metrology, 1834 (Arca-Jyotisa, R-VJ only). Uber den Vedakalender, namens Jyotisham von A Weber, Abh der Komg. Akademie der Wiss zu Berlin, 1862, pp. 1-130 (Text n Roman of Yajusa-Jyotisa with Somakara’s com , German Tr. and Notes). Arca-Jyotisam, ed. with a Marathi Tr , by J. B Modak, Thana, 1885 (Six Veddngas, cluding ‘Lagadha’s Jyotisam’), Ms form, Bombay Tattvavivechaka Press, 1892 Yéyusajyautisa, with the Bhasyas of Somakara Sesa and Sudhakara Divevedin and Arca-Jyautisa with the Bhasya of Sudhakara Dvivedin and Prof Muralidhar Jha’s explanatory notes, ed by Sudhakara Dvivedin, serially in the Pandit (Banaras), 29 (1907) 1.-xu; Rep., Bombay, 1908. The obscure text of the Jyotisha Vedanga, bemg a reprint of papers published in the Hindustan Review and contaimmg.. ‘text with varie lectionnes .. translation with a full com by Barhaspatya (Lala Chote Lal), Allahabad, 1907. —, Text alone issued separately. ——, Repninted: Jyotisha, a system of astronomy connected with the schools of the Rgveda and Yayurveda. A revised text prepared by Lala Chote Lal (Barhaspatya Kavi), with verbal analysis and notes, pub by A. Weber with a Preface by Jagannatha Tripathi of Jhansi, Allahabad, 1960. Vedangajyautisha, ed. with his own Enghsh Tr and Skt com by R Shamasastiy, Mysore, 1936 Vedangajyautisam (ed. with Bengali Tr and Notes) by Sitisacandra Bhattacharya, Sanskrit College, Calcutta 1974 (Caleutta Skt Col. Series, No. 89). (cludes both R-VJ and Y-VJ) Atharvana Jyotisam or the Vedénga of the Atharva Veda, ed, by Bhagavad Datta, Lahore, 1924. (Panjab Skt. Series, No. 6) 1i, STUDIES Burgess, E., ‘On the origin of the lunar division of the zodiac, represented by the Naksatra system of the Hindus, J. Am ‘Or Soc , § (1886), 309-34 Dikshit, S. B., Sections on ‘Revedic Jyotisa and Yajurvedic Jyotisa’ in his Bharatiya Jyotisa Sastra (in Marathi) 2nd edn., Poona, 1931, pp. 70-98; English Translation by R V Vaidya, Pt I, Delhi, 1969, pp 66-97 Chakravarty, Apurba Kumar, ‘The working principle of the Vedanga Jyotisha calendar’, Indian Studies Past and Present, (Calcutta), 10.1 (Oct.-Dec , 1968), 31-42. Kulkarni, B R., ‘The Lagna system of the Vedanga Jyotisa’, Dhulia, 1934 Prasad, Gorakh, ‘The astronomy of the Vedahga Jyotisa’, J Ganganatha Jha Res Inst. 4 (1946-47), Sastry, T S. Kuppanna, ‘Calendar in Hindu tradition’, Bulletin of the Inst, of Traditional Cultures, Univ of Madras, 1968, Pt. 1, 41-114 (Report of Seminar). Shamasastry, R, ‘Light on the Vedatga Jyotisa’, Prof. S Kuppuswanu Sastri Com Vol, Madras, Shamasastry, R., ‘The Parva-rasi or full and new moon of the Veddnga Jyottsa’, Proc. of the All- Dr Cal Gees a aa inga Jyottsa’, Proc. of the All-India Thibaut, G , ‘Contributions to the explanation of the Jyotisa Veditiga’, J A: Calcutta, 47 (1887), Pt 1, 411-37 vous gO) eat ae seni sono eat ‘Note eee interpretation of eed siera Jyotisha (Critisism and tons)’, included in a collection of his writings entitled Vedic ch Jyotisha, Poona City, 1925, pp. 43-104. es ens eee aa Me ‘Uber das Aufzahlung der vier Zeitmaasse bei Gaiga’, Indische Studien, 9 (1889), ## Page 71

[Note The entries are arranged in the Sanskrit alphabetical order. Both the Rk and Yajus recensions, with variants, of the work are mcluded m the Index and are indicated, respectively, by R and Y. The references are to verse numbers and pddas, a, b,c, d, of the Critical texts edited in Pt A The occurrence of the verses in Pt. B is indicated by the Section numbers (1 to v) and Topic numbers therein Citations in the Introduction have been mdexed with the prefix ‘Intro.’ and from the footnotes with the prefix ‘intro fn.’.] saafag Intro. fn. 4 afta somafr R 25a, Y 32a; 11. 2 aa waa R 27a, Y 34b; 11. 2 adtart R 20a, Y 22a; v. 10 gaat Intro fn 4 wararag Intro fn 6 aa qa Intro fn 2 mee We Y 28b; 0 1 afafaet weet Intro. fn. 2 aftare R 2b; i. 1 waar R 8b, Y 9b; 1v 3 waaear R 9d, Y 10d, is. 1 mea. gt Y 11c; 1. 5 ofiaet aH R274, Y 34d; i 2 R 27c, ¥ 34c; 1 2 R1%, in 1 ath Het Intro. fn. 2 att tadt Intro fn. 2 gravresa Y 16c;v 5 wert R 24a, ¥ 42a; 11 3 wead ara Y (after 42) a;i 4 ware fra R 26b, Y 33b; 1 2 wait frat R 26c, Y 3c; 11. 2 waarearat R 21a, Y 21c; v.9 sararat Y 36a; ii 2. saur araaer Y 29a; iii. 1 weaq R 11d, Y 19d; v 7 oar at Y 16b; v 5 great R 1c, ¥ 19¢; v. 7 gate R 13d; v. 5 waaay & Intro. fn 5 aig R 23c, Y 41c;v 15 Y 11d, w. 5 sata ¥ 290; i 1 my R 10c, Y 15c, v. 4 Y 25a; v. 11 wart Y 11a; 1. 5 warrrrarg Y 30b; ui. 1 Y¥ 28d; 1i 1 get (sfaat) g Intro, § 2 warfires R 28b, Y 35b; ii, 2 ear wera R 11c, ¥ 19b; v 7 aet ar R 16a, Y 38a, 1 arat ara R lla, ¥ 19a; v 7 areata R 2c, 32d, ¥ 5d; 1. 1, 1v. 1 wrarg Y 3b; 1.2 arsarat aa Y 30d;1i 1 arset qeararat Y 39d, ti 1 q. R 17d; u. 1 Set. sem Tntro §2 aft J Y 36c, ii. 2 R 7b, Y 8b; m. 3 afr R 35a, ¥ 4d; i 2 f qi Intro. fn 4 EA OR 70, ¥ 8a; m 3 i TAT R 8c, Y 9c; 1v 3 R J2b, Y 27b; v. 13 ages R 34a; v 17 . R14b, Y 18b; v 6 wrarest R 15a, Y 17a; v. 6 sfava_-R 14a, Y 18a, v. 6 serafit R 24c, Y 42c, ii 3 savor yer ¥ 36d; u. 2 aitfrs wits R 35d, Y 4451.2 satfrsrqad R 3a, Y 2a;1 1 aad R 31d, iv 4 aad R 31d; 1v 4 aaron Y 24b, u 1 aeayseut R 22c, ¥ 40c; v 16 agyrt R 13b;v 5 wag Fang R 35c, ¥ 4c; i2 Y¥ 24d, 1 rie R 5d, Y 6d; iv. 2 Y 3c,1.2 arg wa R 21a, Y 21b, v. 9 fafa: a fa Y 23d; 1. 4 fafareta Y 20d; v. 8 fafufrser R 20d, ¥ 22d; v. 10 fafirarat Y 21d fafatreram Y 20a, v 8 Y 26c;v 12 fertfat Y 26c; v. 12 ## Page 72 70 VEDANGA JYOTISA qtr wart R 33a; iv. 4 Ruse R 20c, Y 22c; v. 10 & gat ¥ (after 4) c; iv. 7 faatase Y 14b; v.3 i Y 24c; ii. 1 faa Y (after 4) c; iv. 7 t Y 28a; ii. 1 Bint waret Y 27a; v. 13 afartt at R 7c, Y 8c; ii. 3 feerarfir: ¥ 29b; in 1 faacdart R 1c, ¥ 1c; ¥ (after 42) c; i. 1, 4 2rqaat Intro. fa. 8 aa Y 12a; iv. 6 dat fg ¥ 3a; i. 2 arat. Y 31c; sii. 1 qatar R 15d, ¥ 17d; v6 afedwg R 16c, Y 38¢; ii. 1 afedacarad Y 3ic, sii. 1 @ aa ¥ 12a; wv. 6 aa fasfte Y 37a; v 14 grams: Intro. fn. 1 areeat (?xft) R 33d; iv. 4 argay R 12d, Y 27d; v. 13 fai a R 4b, ¥ 13b; v.2 fenraeit R 15d, ¥ 174; v. 6 fafeaag R 16c, Y 38c;1i 1 2 agier R 16, Y¥ 38b; 1. 2 aaa fe Y 37a; v 14 erat wet R 9c, Y 10c; iv. 3 waaeaat R 28a, ¥ 35a; i. 2 awaheadt Y 16a; v. 5 aafieg R 13c; v. 5 want g R 18c, Y 39c; ni. 1 ariat R 35b, Y 4b; i. 2 arfe® & R 17a; ii. 1 arrraa R 28d, ¥ 35d; ii. 2 fata at R 4a, ¥ 13a; v. 2 fafaate Y 12d; wv. 6 qataramt R 10b, Y 15b; v. 4 qq R 13a; v 5 wurunt ¥ Zora. 4 qeafast Y 30a; iii. 1 qeqdacat R la, Y la; i. 1 qeareretet R 17b; 1. 1 qaat TT Y 14d; v. 3 aur aft R 4d, ¥ 13d; v. 2 qtr earg Y 30c; iit. 1 gaara Y 20b; v8 qaifir waft Y 25b; v. 11 qarfr war ¥ 24a; i. 1 Y¥ 12b; ti. 1 get xf Intro. fn 2 Grag Tat Intro. fn. 2 gear Y 11b; iv 5 qa@ R 15b, Y 17b, v 6 ghrarat R 33b; iv. 4 dered Y 16d; v 5 qiyeer R 32b, Y 5b; iv. 1 sfarte wat R 21c; v. 9 sfatq aa R 210; v. 9 sarart Intro. § 2 wmeq R 1d, 2a, Y 1d; i. 1 wat ard R 8a, Y 9a, iv. 4 mrad R 6a, Y 7a; iv. 2 saearfy R 3b, Y 2b; i 1 siftacrr R 19b; iii 2 ameia R 25d, Y 32d; it. 2 raven Intro. fn 4 amt By R 10a, Y 15a; v. 4 armenat Y 12c; iv. 6 arate cag R 15c, Y 17e; v 6 amasfirs R 12c, Y 27c; v. 13 R 24b, Y 42b; ii. 3 wart Intro §1; i. 1 aease aifiz ¥ 37d; v 14 aragaat 17 R 32a, Y 5a; iv. 1 R 34c; v 17 araaratt R 6d, Y 7d, iv. 2 arvatg R 17; 11. 1 arat area Y 28c; 0 1 far. ad? R 9b, Y 10b; iv. 3 Y (after 4) b; iv. 7 Y (after 42) b; i. 4 Wg ga Y 11d; iv. 5 7 & qi Intro. fn. 4 a. We: 7 Y (after 4) d; iv. 7 waar R 28c, Y 35c; i. 2 usta R 3d, Y 2431.1 Y¥ 37, v. 14 ear q@ Intro. fn. 4 phat shes fn. 6 aa frat R350, ¥ 4a; 1.2 qutfadt R 34b, v. 17 wad fer R 23a, Y 41a; v. 15 wet are R 5b, Y 6b; iv. 2 R 22a, Y 40a; v. 16 aeasd aft R 31c; iv. 4 ar. gaat R 21a, ¥ 21a; v. 9 aree wera Intro. § 2 arat Y 21c; v. 9 arse Y 25¢; v. i1 qrer wa R 32c, Y Se; iv. 1 arreaet R 1b, ¥ 1b;1.1 R 8d, Y 9d, 1v. 3 3 ageafart ¥ (after 4) a; sv. 7 ar fat: Y 26d; v. 12 ## Page 73 anit fet Y 26d; v 12 at wit Y 3d;1 2 we frag Intro fn 2 eaisfafa R 25b, Y 32b; u. 2 wadtt R 31b; wv. 4 Sarr VE Y 23b; iv. 4 R 14c, Y 18c; v. 6 ll ate al R 30d, Y 43d,1 3 adararest Y 25d; v 11 R 9a, Y 10a; 1v. 3 fameat Garat Y 29d; iu 1 frarararfrat R 21d; v 9 fagra Aafaq R 30b, Y 43b; i. 3 fanstq art R 24d, ¥ 42d, in 3 fawsr st Y 20c;v 8 frarar saat Y 36b, u 2 fawddat R 26d, ¥ 33d; in. 2 faga R 3la; iv 4 faqart Y 23a; 1v 4 fasmtaat R 27a, Y 34a; u2 aat fe ¥ 3a;i 2 aareata array Y (after 42) d, 1. 4 st R 10d, Y 15a, v 4 ate gat R 22b, Y 40b, v 16 ity fireeren Y 26b; v. 12 wreta fa R 20b, Y 22b; v. 10 afasredt R 19a; ii 2 afasrar & R 34d; v. 17 yewet R 16d, ¥ 38d; ii. 1 yuqgat R 7d, ¥ 8d; tit, 3

wise ae Y 31b; tit. 1 wea gra R 4c, Y 13c, v. 2 wat aR 33c, wv 4 Sarre R 19d; 1m 2 ware oft u. 1 aaertisfs Intro fn. 7 wera ag R 23d, Y 41d; v 15 wat Tafir R 23b, Y 41b; v 15 water R 22d, Y 40d; v. 16 werd R 3c, Y 2c; 1.1 water fire R 25c, Y 32c; in. 2 afeat eset R 26a, ¥ 33a; ii 2 wacrae R 18a, Y 39a; in 1 area rat Y J4c; v. 3 arid R 6c, Y 7c; iy. 2 ara = Y 31a; ii. 1 aera Intro. fn. 2 Beet ¥ 31d; in. 1 qatar Y 26a; v 12 R 6b, Y 7b; 1v 2 at aft R 18b, Y 39b; m1. 1 R 19¢;3 11. 2 i R 30a, c, Y 43a, c, 1.3 R 19¢; m. 2 earearfa R 5c, ¥ 6c; 1v. 2 ey: oetsd Y 14a; v. 3 eararana R 5a, Y 6a; iv. 2 eratiter Intro. fn, 4 Braver R 14d, Y 18d; v 6 Pol watz Y 37b; v. 14 ## Page 75

[Note The references are to Section numbers and not to pages. Those from the Introduction are prefixed by ‘Intro ’ and those from Part B—Translation and Notes by the Sections (1 to v) and the Topics therein.]

Adhaka, ii. 1

Adhana (Diksd) day, v. 17

Agrahdyana, Intro. § 1

Amhaspati, Intro. § 1

Anuvatsara, Intro 81; 1;1v 7;v 1

Arthasastra, Intro §7

Astronomy, in the Veda, Intro 1ff See also Vedanga Jyotisa

Atharva Veda, Intro § 1

Atharvana Jyautisa, Intro. § 3

Atri family of Vedic astronomers, Intro. § 1

Barhaspatya alias Chote Lal,—work on VJ, Intro § 8; m1. 2; 1v. 3, 6, v. 3, 4, 5, 7, 8, 10, Bhadanakala, v 7, —at any tithi, v. 9 BhamSa, i. 1. See also Naksatra—parts

Bharatiya-Jyotisa-Sastra, Intro. § 8

Bhitasankhya, Intro. § 8; ui 2, v 8

ira Calendar, correction by observation, Intro. § 4, 5; iv. 7. See also Yuga, correction

intro

Chote Lal ahas Barhaspatya See Barhaspatya

Colebrooke, H. T, on VJ, Intro § 8

Darsapiirnamasa, Intro. § 1, 8

Dasgamalagna, iii. 2

Day, sidereal, correction of, v. 13

Day-time, iii 3; —at any parva, v. 16

Dikshit, S. B., work on VJ, Intro. § 8; iu. 2

Diksa day, v. 17

Drk almanac of Kumbhakonam Mutt, Intro 5

Drona, measure, it. 1

Epoch of VJ, iv. 1,2

Founders of Sciences mn Ancient India, Intro, § 8

Gargasamhita, Intro § 3

Godbole, H. K., work of VJ, Intro. § 8

Hour-angle, v. 5

Idavatsara, Intro. § 1; ii. 1; 1. 7

Idavatsara, Intro. § 1; ii. 1; 1v 7

Intercalary day, v 3, 17

Istt,iv6

Jones, Sur William, on VJ, Intro. § 8

Javadi series, v. 6, 8

lyotisakaranda, Intro, Kala, measure of tume, ii. 1; v. 3, 7. See also Bhadanakala

Kastha, measure of time, ii. 1

KaSyapa, Intro. § 3

Kudava (Kutapa), ii. 1

Lagadha, Intro § 3, 8; i. 1,4; —date of, Intro. 5

Lagna, v. 5, in a yuga, 1, 2

Mautrdyaniya-Brahmana-Upanigad, datable passages in, Intro § 2

Masaka, 1. 1

Modern calendar, corrections to, 1v 7

Month, solar, in a yuga, m. 1

Moon, tisings in a yuga, ui 1; —rtu of,i 1

Muharta, measure, 11 1

Muharta astrology, Intro § 3

Mulsum calendar, Intro. § 7; iv 7

Naksatra, Intro 2; at any parva, v. 6; at any tithi, v. 8, 9, at the beginning of the ayanas, 1. 3; deities of, ti 2; fierce and cruel, ii 2; for naming 1i 2; Javadi table, v 6, 8

Naksatra-parts, v 3ff

Naksatra-vidya, Intro § 2

Naming a child, 1. 2

Paitamaha Siddhanta, Intro. 3, 6, 7; ui. 3, 7

Paksas, 0 a yuga, 11 1

Pala, measure, 11 1

Pancasiddhantika, Intro § 3, 4; ti. 3, 7

Parva, in a yuga, 11 1; —ending time, iv. 6

Pilla, L. D. Swamikannu: _Swamikannou Pilla

Pindapitryaytia day, v. 17

Prag-lagna, ii. 2

Punarddhana, v.17

Ras (sign), of foreign orig, iv 7

Rtus (seasons), Intro 1;ii.1, iv 5; —nsings in a yuga, iu 1

Rtusesa, v. 15

Saka era, iv. 7

Samsarpa, Intro 1

Sarhvatsara, Intro 1; 131.1; v 7

Satapatha Brahmana, Tatro. 2

Seasons, Vedic, Intro. § 1 See also Rtu _ Shamasastry, work on VJ, Intro. § 8; i. 4

Siddhdnta Siromani, Intro. § 5

Sudhakara Dvivedi, work on VJ, Intro. § 8; iv. 6; v 3, 4,8 . Sun, —naksatra of, at any time, v. 11, 12; —position at any time, v. 10; —rtu of, i. 1

1 datable passages, ## Page 76 14 VEDANGA JYOTISA

Siryaprajnapti, Intro. § 6, 7

Swamikannu Pillai, L. D., on date of W, Intro. § 5, 8

Syzygy: Parva

Taittiriya Aranyaka, Intro. § 1

Taittirtya Bra Intro. § 2

-panchanga, Intro.

Thibaut, G., work on VJ, Intro. § 8

Tilak, B. G., work on WJ, Intro. 8; iv 6; v 3, 4, 5, 7, 11, 12

v-1 Tithi(s), —at viguva, iv. 4; —Bhddanakala of, v. 9; —naksatra at any time, v 8; —omitted, iv. 6; —to elapse in a rtu, v.15 Tithi-ksaya, iv. 6 Tithi-naksatra, v.8 Udvdapa, interpretation of, Intro. § 8; v. 7 Upavasatha day, v. 17 Uttardyana, Intro. § 1 Varthancthina Pats & 103) 43. 3; w 7 tro. § 1, 3, 4; iff. 3; 1v Vasisthasiddhanta, iti. 3 Veda, —astronomy of, Intro. § 1; —datable passages in, Intro. § 2; —place of astronomy in, i. 1; —reference to astronomers, Intro 2 Vedanga Jyotisa (VJ), accuracy of, Intro § 7; —authorship of, Intro. 3; —benefit of the study of, 1. 2; —contents of, Intro. § 6; —date of, 4, 5; —division of time, Intro §6; —epoch of, iv. 1, 2; —modern studies in, Intro. § 8; —nature of calculations, Intro. § 6; i-v; —nature of contents, Intro. § 3; —related to North India, ili. 3; —scope of error in, Intro § 7; v. 17

Yajurveda, —astronomy m, Intro § 1; —datable passages mn, Intro § 2

Yamanaksatras, Intro § 2

Year, divisions of, i. 1

Yuga of five years, ii. 1; —commencement, iv. 1, 2;—conversion of elements, in. 1; —corre- ction for, Intro. § 8; v.13, 14;—current year, iv 7; —days, ayanas, rtus, months etc. in, iii_ 1; —divisions of, it, 1; —elements of, iii, 1; —the five years of, 1i. 1; —Jagnasin, 1.2; —risings of stars im, iii. 1; —rtus in, 1. 5; —Vedic, Intro. 1, 6 Weber, A, work on VJ, Intro. § 8, i. 4 Whitney, D W., work on WJ, Intro. § 8 ## Page 78

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