´ÉänùɺiÉÉ´ÉiÉ ªÉYÉEò¨ÉÇ|É´ÉÞkÉÉ&
ªÉYÉÉ& |ÉÉäHòÉ& iÉä iÉÖ EòÉ™ôɸɪÉähÉ *
¶ÉÉÛÉÉnùº¨ÉÉiÉ EòÉ™ô¤ÉÉävÉÉä ªÉiÉ& ºªÉÉiÉÂ
´ÉänùɃói´ÉÆ VªÉÉäÊiɹɺªÉÉäHò¨Éº¨ÉÉiÉ **
[Sayana] in his Preface to the [Rgvedabhasya] strikes a note on the use of Jyotisha by citing the [Paniniya-siksa](41-42):
Uôxnù& {ÉÉnùÉè iÉÖ ´ÉänùºªÉ ½þ®úiÉÉè Eò±{ÉÉä%ªÉ {É`ö¬iÉä *
VªÉÉäÊiɹÉɨɪÉxÉÆ SÉIÉÖÌxɯûHÆò ¸ÉÉäjɨÉÖSªÉiÉä **
Metre represents the feet of the [Veda-purusha], Kalpa the hands, the science of Jyotisha its eyes, and Etymology its ears.
The use of the morphemic sequence ªÉYÉEòÉ™ôÉlÉÇʺÉrùªÉä occurring in the [Vedangajyotisha] (3) justifies the view that astronomy arose to establish the times and seasons for conduting sacrifices. [Sayana] further refers to several passages of the [Taittirya] School in support of the above view. The text, [samivatsaram]... indicates the periods of years. The text, [vasante]... refers to the seasons. the text [masi masi]... refers to months. the text [Yam Kama-yeta]... refers to half months . the text [ekastakayam]... days. The text [Krttikasu]refers to naksatras. Hence is the need for [Jyotisha] for determing the times and seasons proper for performing sacrifices.
Occasional referces are made in the Vedas to new moon and the full moon, the number of days in a year, the two halves of the year indicated by the terms, [Devayana] and [Pitryana], the additional or intercalary month(adhikamasa) and the deletory month (Ksayamasa). The text-"These
Krttikas (constellation of pleiades) do not deflect from the East"-suggests that the pleiades were observed to rise always at the east point. This is possible only when the first point of Aries was in the constellation of pleiades, since these are situated in the ecliptic. The point has, of course, shifted backwards now. From this observation, it emerges out that the stars of the zodiac were enumerated, commencing from the Krttikas (ArkaSomayaji, A CriticalStudy of Ancient Hindu Astronomy, p.1,1971).
The [Taittiriya Sam. (==TS) at 4,4, 10 lists the [Naksatras] starting from krttikas to
[Bharani]. This section in TS contains mantras for the naksatra bricks which are arranged in a circle round the naturally perforated brick, beginning on the south-east with krttikas and ending with [Visakha], then continuing on the north-west with [Anuradha] and ending with [Bharani]. The full moon brick is placed at the east point and the new moon at the west point (keith's notes to TS 4,4,10). Vedic [Astronomy cum mathematics shows the determination to count large numerical notations. The TS at 4,4, 11, ii-iii (==Vajasaneyi)[Madhyandina Samhita] XVII -ii) enumerates such numerical terms as [eka], [dasa], [sata], [sahasra], [ayuta]-(10,000), [niyuta]-(100,000), [Prayuta]-(1,000,000), [arbuda]-(10,000,000), [nyarbuda]-(100,000,000), [samudra]-(1,000,000,000), and [Parardha]-(1,000,000,000,000). [Mahidhara's] commentary at [Vaj].[Madh]. [Sam]. XVII -ii is worth quoting here:
+jÉèEòÉÊnù {É®úÉPÉÇ{ɪÉÇxiÉè& ¶É¤nèù°ükÉ®úÉäkÉ®Æú
nù¶ÉMÉÖÊhÉiÉÉ ºÉÆJªÉÉäSªÉiÉä **
Apart from division of the sphere into 27 or 28 [naksatras], Vedic astronomy has contributed to out understanding of the conception of great yugas-of course, carrying out a radical change of the heavenly bodies -- and that of the [Tithi].
In the area of geometry, the [Sulba]- [sutras] (c.200 B.C.) which are concerned with the measurements of sacrificial altars, discuss the construction of squares and rectangles, the relation of the diagonal to the
sides, the equivalence of rectangles and squares and the constrtuction of equivalent squares and circles.
The [Vedanga]-[Jyotisha] is a post-vedic development. The fourth verse of this texts treats Mathematics as standing at the head of all [Vedangas]; and it reads:
ªÉlÉÉ Ê¶ÉJÉÉ ¨ÉªÉÚ®úÉhÉÉÆ xÉÉMÉÉxÉÉÆ ¨ÉhɪÉÉä ªÉlÉÉ *
iÉuùuäùnùiÉÉRÂóMɶÉɺjÉÉhÉÉÆ MÉÊhÉiÉÆ ¨ÉÚvÉÇÊxÉ ÎºlÉiɨÉ **
Thus Mathematics and astronomy are twin disciplinces, the one complementing the other. [Ganitam] includes astronomy, and geometry (Ksetraganitam) belongs to the science of [Kalpasutras]. Geometry included the scope of ganitam. Ganitam also includes fundamental opertaions (Parikrama-), determinations (Vyavahara) and so on. Subsequently arose the [Siddhanta]-literature.
A [Siddhanta] text is an astronomical treatise, dealing with various measures of time, ranging from a [Trti] upto the duration of a [Kalpa] (which culminates in a deluge), planetrary theory, arithmetical computations as well as algebraical processes, problems relating to intricate ideas and their solutions, location of the earth, the stars and the planets and description and usage of instruments (SS vs.6). Of the eighteen [Siddhanta] works that are moticed, mention could down to us: [Suryasiddhanta],[Paitamaha], [siddhanta], [Romaka]-[Siddhanta], [Paulisa-siddhanta], [Vasisthasiddhanta], [Brahmasiddhanta] and
[Vrddhavasisthasiddhanta]. [Varahamihira] wrote the [Pancasiddhantika] and [Paitamahasiddhanta].
Of these the [Suryasiddhanta] and the [Brahmasiddhanta] deserve special mention here, since both these have received correction from time to time. At the same time the former work has shown " the process of adaptation of the new science to Indian ideas in its most pronounced state" (Keith, Hist. of Skt. Lit., 518). It reveals in the theory of kalpas, restores the pre-eminence of mount [Meru] at the north pole and deals with such astronomical concepts as [Naksakras] and others in the Indian context.
The astronomer who wrote the [Aryabhatiyam] (499 A.D.) is [Aryabhata] (born in 478 A.D.) who introduced new ideas into Indian
astronomy. He is the Sanskiritist to write a distinct chapter on mathematics in relation to astronomy. It may not be an exaggeration to say that he was the only Hindu astronomer to propound the doctrine of diurnal rotation of the earth, as stated by [Arka] [Somayaji]in ACritical Study of the Ancient Hindu Astronomy (p.2). The astronomers who followed him were Lalla (500 A.D.), [Varahamihira] (505 A.D.), [Brahmagupta], [Mahavira] (628 A.D.), [Sridhara] (750 A.D.), [Munjala] (932 A.D.),[Sripati] (1039 A.D.), [Bhaskara] II, the author of SS (1150 A.D.), [Makaranda] (1478 A.D.) and [Ganesa] (1520 A.D.). The names of others such as [Garga], [Vrddhagarga] and [Narada], who existed before [Varahamihira], may be added to this list.
The authorities on Ancient Sanskrit astronomy and mathematics are of the opinion that the last scientific work in [Jyotisha] is SS. A temple inscription quoted by O.E.SMITH, (History of Mathematics) runs as under:
[Triumphant] is the illustrious [Bhaskaracharya]
whose feet are revered by the wise, eminently learned.
[Bhaskara] II worked at the [Astronomical observatory in [Ujjain] where [Brahmagupta] is said to have conducted certain experiment several centuries ago.
Actually there were two [Bhaskaracharyas]. the first was a contemporary of the well-known astronomer, [Brahmagupta]. He wrote the [Mahabhaskariya], [Laghu bhaskariya], and the [Aryabhatiya] which are commentaries on the famous work of [Aryabhata]. The second [Bhaskara](1114-1185 A.D.), as has been stated in SS (vs 3.) composed the crest-jewel of astronomical treatises, i,e, SS, after having mastered the science under his talented father, [Mahesvara], a pioneer in astronomy, who championed the cause of [Jyotisha] in the eleventh century A.D.
The chief contribution made by [Bhaskara] II to mathematics [cum] astronomy consisted in realishing the true nature of division by Zero, anticipating the modern theory on convention of signs, representing unknown quantities by phonemes, presenting solutions for quadriatic equations reduced to a single type taking into consideration only positive roots as genuine, solving a few cubic and bi-quadriatic equations and indeterminate
BIBLIOGRAPHY OF
Prof. T.S.K.SASTRY'S WRITINGS
BOOKS
1. [Mahabhaskariya] of Bhaskara I, ed. with the Commentary of [Govindasvamin] and the Super-commentary of [Paramesvara], with detailed Introduction and Indices.Govt. Oriental Mss. Library, Madras, 1957.
2. [Vakyakarana], with the commentary of Sundararaja, with detailed Introduction, Notes and Appendices. K.S. Research Institute, Madras, 1962.
3. [Vedanga Jyotisha], Critically edited with [Translation] and [Notes]. Indian National Science Academy, New Delhi, 1985.
4. Collected Papers on Astronomy and Mathematics. Kendriya Sanskrit Vidyapeetha, Tirupati (1989).
5. [Panchasiddhantika] of [Varahamihira], Critically edited and Translated with Notes. (To be issued by the INSA, New Delhi)
6. [Vakyakarana] with Translation and Notes. ( In Ms. form)
7. Manual on Eclipses (In Ms.form)
8. Moon Tables (In Ms.form)
PAPERS
1. 'The Vasistha Sun and Moon in [Varahamihira,s] [Panchasiddhantika'] Journal of Oriental Research 25 (1955-56) 19-41; Collected papers, pp. 1-28.
2. 'Calendar in Hindu Tradition', Bulletin of the Inst. of Traditional Cultures, Univ. of Madras, 1958, pt.i,Rep. of Seminars, 41-114.
3. 'The [Bijopanaya]: Is it a work of [Bhaskaracharya]?' Jl. of the Oriental Institute (Baroda), 8 (1958-59), 399-409; Collectede Papers, pp. 29-45.
4. 'The Saka era of [Varahamihira] (Salivahana Saka)', Jl. of Indian History 36 (1958) 343-67; Collected Papers, pp. 255-67.
5. 'The untenability of the postulated Saka of 580 B.C.', Jl. of Indian History, 37 (1959) 201-24; Collected Papers, pp. 288-317.
6. 'A historical development of certain Hindu astronomical processes' Indian Jl. of Hist. of Science, 4 (1969) 107-25; Collected Papers pp. 46-75.
7. 'The system of [Vatesvara Siddhanta]', Indian Jl. of Hist. of science, 4(1949) 135-43; Collected Papers, pp. 76-88.
8. 'The school of [Aryabhata] and the peculiarities thereof', Indian Jl. of Hist. of Science, 4 (1969) 126-34; Collected Papers, pp. 89-101.
9. 'Some mis-interpretations and omissions in [Thibaut] and [Sudhakara Dvivedi] in the [Panchasiddhantika] of [Varahamihira]', Vishveshvaranand Indological Journal, 11(1973) 107-18; Collected Papers,pp. 102-17.
10. 'Determination of the date of the [Mahabharata]: The possibility therof ', Vishv. Ind.Jl.14(1976) 48-56; Collected Papers, pp. 318 -28.
11. 'The eposh of the Romaka [Siddhanta] in the [Panchasiddhantika] and the epoch longitudes of the Sun and Moon in the [Vasishtha-Paulisa]' Goverment Arts College, Kumbhakonam and in the Madras Presidency College from where he retired in 1955. Then he taught at the Madras Sanskrit College for about five years as Professor of comparative Philology and History of Sanskrit Literature. Even after retirement he served the college as Honorary Professor of Sanskirit.
Professor SASTRY critically edited six astronomical texts. He brought out a critical edition of the [Mahabhaskariya] with the commentaries of [Govindasvamin] and [parameshvara] with annotation and indices in 1957. Again he edited the [Vakyakarana], the basis of the [Vakya] almanacs of South India, with the commentary of [Sundararaja in 1962. He also critically edited the [Vedangajyotisha]with translation and notes. Subsequently he critically edited the [Pancasiddhantika] with translation and notes.
Dr. K.V. Sarma (now Professor at the Adyar Library Research Centre) who informally collaborated with Professor SASTRY in editing the first two works mentioned above, writes (in the Bio-data of Professor T.S.Kuppanna Sastry) as under:
His )Prof.Sastry's) deep understanding o Indian astronomy...helped him in preparing a rational edition with detailed exposition in English of the [Vedanga Jyotisha] and the [Pancasiddhantika], both of which are master -pieces illustrative of forensic skill in presenting distended facts to prove his point. He prepared also a book on the computation of eclispses incorporating modern corrections, but couched in such a form that it could be used by Indian almanao makers.
His collected papers issued by the Vidyapeetha, is a collection of valuable and original papers-publised in several learned Journals-numbering about twenty. The author has made a systematic, thorough-going and comparative study of the Hindu and Western systems of astronomy. The book deals with such interesting and illuminating topics as the [Vasistha] Sun and Moon, calender in Hindu Tradition, [Varahamihira's Saka Era], Hindu astronomical processes, [Vatesvara] [Siddhanta], [Aryabhata] School of Astronomy, Hindu Astronomy in the age corresponding to pre-copernican European Astronomy, Tamil Astronomy, determining the date of [AdiSankaracharya] (on astronomical grounds), the law of gravitation, the structure of atom and the theory of Relativity and others. Needless to say, among the astromers who have attempted a methodological and cirtical study of Jyotisha, Professor T.S.Kuppannna Sastry, the eminent scholar of ancient and modern astronomy, stands out as preeminent. I state in all hunility that the development of astronomy, marshalled in its historical perspective in the collected papers, will furnish some definite criteria governing the relecvancy and applicability of ancient Indian observations as enshrined in Jyotisha to modern astronomy.
It is now left for us to thank DR.K.V.Sarma sincerely for his hearty cooperation and assistance in printing this book. He read through the proofs, compiled the Bibliography of Prof.SASTRY's writings and sent us the author's Bio-data. Special acknowledgement should
be made to the Rathanam Press, Madras for setting the appropriate types for the book.
Lastly I pay homage to my guru, Professor T.S.Kuppanna Sastry for his excellent contribution to mathematics cum astronomy.
Kendriya Sanskrit
Vidyapeetha M.D. BALASUBRAHMANYAM
TIRUPATI. Principal (1975-85) 20-3-1989.
equations of the first and second degree, computing elaborate tables of sines, studing regularpolygons upto 384 sides, giving the value of as 754/240 and anticipating kepler's method of determining the surface and volume of a sphere (N.N.Sachitanand's] article in the Hindu, Madras dated
1-7-1979 and M.D.Balasubrahmanyam's Foreward to the Annotation of SS by Arka Somayaji, Kendriya Sanskrit Vidyapeetha, Tirupati series No.29,1980). Furthermore, [Bhaskara] II gave a scientific exposition of the sidereal revolution of planets, circumfrence of the earth, lunar eclipses, measurement technique of celestial bodies, longitude of the stars and other astromical facts. Needless to say, the third and fourth parts of SS, --under the heading, [Ganitadhyaya] (or Grahaganita) and (Goladhyaya)--are exclusively devoted to astronomy.
After [Bhaskara] II, very little original work appeared in India in this field. Later scholars were content with the writing of some commentaries on the earlier standard treatises of stalwarts, simply to whet their appetite. But for the scholarly compositions of eminent Sanskritists like [Nilakanta] and the rest, belonging to the productive Kerala School of astronomy, Jyotisha Pandits concentrated their attention more on astrology than on studies and research in mathematical astronomy.
However, in recent times scholars have been attempting to exdamine astronomical theories in the light of western through.*
Realising that specialisation in mathematical astronomy and other sciences has witnessed a decline, the Tirupati Vidyapeetha started a project entitled,'Coordination of Sanskrit and Ancient India', so that unpublised and rare works on Sanskrit mathematics, astronomy, and other disciplines might be critically edited with translation and annotation, besides monographs on historical and descriptive studies on Jyotisha might be brought out. Under this scheme, the Vidyapeetha has already brought out Dr.Arka Somayaji's Exposition in English and Annotation of [Bhaskaracarya's]SS.-(1980). Under the same project, the Vidyapeetha has now come forward to issue Professor T.S.KUPPANNA SASTRY'S Collected papers on Hindu astronomy, mathematics and other related discilines. I record here that it is rather unfortunate for SASTRY and us that he could not live to see his outstanding publication-the last challenging magnum opus of SASTRY. That Professor SASTRY, an eminent scholar in almost all the branches of Sanskrit literature (including mathematics and Astronomy) was specially qualified to write the collected papers, will
become evident, if we look at his curriculum vitae and publications .
Professor SASTRY (1900-1982) alias Srinivasan, was born in
Tirumanilayoor (near Karur, Tiruchirapalli district of Tamilnadu) to Subrahmanya Iyer and Bhagirathi Ammal. A scion of [Nilakantha Diksita, the celebrated Sanskrit polymath of the sixteenth century, Professor SASTRY devoted all his time to a critical study and appreciation of almost all the Sanskrit [Shastras] including [Ganita], [Jyotisha], and modern astronomy. In boyhood he underwent training in the traditional recitation of [Samavedic hymnology]. Having completed his schooling in Karur, he paased the B.A. examination as a student of the famous St.Joseph's College, Tiruchirapalli. He worked as Headmaster of the High School at Tirumayam (erstwhile Pudukkottah State), and then joined the Maharaja's High School, Pudukkottah (later known as Brihadambal High School). Subsequently he worked as lecturer, Assistant Professor in Sanskrit at Maharaja's College, Pudukkottah, Indian Jl. of Hist. of Science 13 (1978) 151-58; Collected papers,pp. 188-200.
12. The Vasishtha -Paulisa Venus in the [Panchasiddhantika] of [Varahamihira]', Indian Jl. of Hist. of Science 14 (1979); Collected Papers, 141-48.
13. 'The main characteristics of Hindu astronomy in the period corresponding to pre-Copernious European astronomy', Collected Papers, pp.118-40.
14. 'Vasishtha-Paulisa Jupiter and Saturn in the [Panchasiddhantika]', Collected Papers,pp.148-68.
15. 'The [Vasishtha -Paulisa] Mars in the [Panchasiddhantika] of Varahamihira]', Collected Papers, pp.169-87.
16. 'The epoch constants of the Vasishtha-Paulisa Star Planets ', Collected Papers, pp.201-05.
17. ['Saurasiddhanta] of [Panchasiddhantika]: Planetary constants and computation ', Collected Papers, pp, 206-40.
18. '[Panchasiddhantika] XVIII. 64-81: An Interpolation', Collected Papers, pp. 241-54.
19. ' A Brief History of Tamil Astronomy', Madras Univ. Jl., Section C, 41.ii; 120-33; Collected Papers, pp. 329-44.
20. 'The Age of Sankara: I', Collected Papers, pp.344-61.
21. 'The Age of Sankara: II', Collected Papers, pp.362 ff.
Complied by
K.V.SARMA
Library Research Centre,
Adyar (Madras).
TABLE OF CONTENTS
Foreword Pages
Bibliography of Prof. SASTRY'S writings xiv
1. The [Vasistha Sun and Moon in
[Varahamihira's [Pancasiddhantika] ... 1- 28
2. The [Bijopanaya: Is it a work of
[Bhaskaracarya]? ... 29-45
3. A Historical Development of certain
Hindu Astronomical Processes ... 46-75
4. The System of the Vatesvara [Siddhanta] ... 76-88
5. The School of [Aryabhata] and the
peculiarities thereof ... 89-101
6. Some Mis-Interpretations and Omissions
by Thibaut and Sudhakara Dvivedi in the
[Pancasiddhantika] of [Varahamihira] ... 102-117
7. The main characteristics of Hindu
Astronomy in the period corresponding
to Pre-Copernican European Astronomy ... 118-140
8. The [Vasistha-Paulisa] Venus in the
[Pancasiddhantika] of [Varahamihira] ... 141-147
9. [Vaistha-Paulisa] Jupiter and Saturn in
the [Pancasiddhantika] ... 148-168
10. The [Vasistha-Paulisa] Mars in the
[Pancasiddhantika] of [Varahamihira] ... 169-187
11. The Epoch of the Romaka Siddhanta in
the [Pancasiddhantika], and the Epoch
Longitudes of the Sun and Moon in the
[Vasistha-Paulisa] ... 188-200
12. The Epoch Constants of the [Vasistha-
Paulisa] Star Planets ... 201-205
13. [Saurasiddhanta] of [Pancasiddhantika]:
Planetary Constants and computation
(PS XVI,XVII, XVIII) ... 206-240
14. [Pancasiddhantika] XVIII 64-81: AN
Interpolation ... 241-254
15. The [Saka Era] of [Varahamihira]
(Salivahana Saka) ... 255-287
16. The Untenability of the Postulated Saka
of 550 B.C. ... 288-317
17. Determination of the Date of the
[Mahabharata]: The Possibility Thereof ... 318-328
18. A Brief History of Tamil Astronomy ... 329-344
19. The Age of Sankara: I ... 345-361
20. The Age of Sankara: II ... 362-370
21. Astronomy ... 371-378
22. The Stars ... 379-384
23. The Structure of the Atom ... 385-390
24. Newton and the Law of Gravitation ... 391-398
25. The Evolution of the Universe
According to Sir James Jeans ... 399-403
26. The Duration of Eclipses ... 404-408
27. The Lunar Eclipse in Hindu Astronomy ... 409-414
28. The Theory of Relativity ... 415-436
29. Computation of the Solar Eclipse in
Hindu Astronomy ... 437-450
30. Hindu Astronomy Through the Ages --
A Short Sketch ... 451-459
THE [VASISTHA]SUN AND MOON IN
[VARAHAMIHIRA'S] [PANCASIDDHATIKA]
(Reprinted from J.O.R, K.S.R.I., Madras, 1955-56)
The [Vasistha] Sun and Moon are contained in Ch.II and in Ch. III. 4 of the [Pancasiddhatika]. II. 1 gives the true sun, II. 2-6 give the cimputation of the true moon, III.4 gives a rule for the daily motion of the moon, II.7 gives rules for the sun or moon's Naksatra and the [Tithi], and II.8-1 deal with topics related with the sun, like the duration of day-light, the length of the noon-shadow when the sun is known and [vice versa], and lastly finding the Orient Ecliptic Point (Lagna) when the shadow is known and [vice versa].
Obviously, the most important parts are II. 1, II.2-6, and III.4, which form the basis for the rest of the work. Also these parts are very interesting from a historical from the more ancient astronomy represented by the [Paitamaha Siddhanta] condensed by [Varaha], giving only mean sun and moon, to the later epicyclic astrronomy represented by the Saura [Siddhanta] condensed by him. Of these, about II.1,Dr.Thibaut(T) makes the remark, "a stanza of obscure import," and leaves it at that, without attempting to translate it, and Sudhakara Dvidevi (5) remarks: "+xÉäxÉ ¶±ÉÉäEäòxÉ ËEò ºÉÉvÉ.ªÉiÉÒÊiÉ xÉ YÉɪÉiÉä, +iªÉ¶ÉÖrùi´É iÉÖ". So much for the sun. About II.2-6, T says (and S echoes him): "Of the above stanzas we have succeded in making out the sense in part only. They manifestly teach how to find the mean and perhaps also the true postitions of the moon by means of a process more compendious than the one usually employed in Indian Astronomy.
" What Preliminary operation is presented in stanza 1, we are altogether unable to say....... It is not apparent why stanza 5 directs us to add for that half-gati six Signs plus four minutes to the moon's mean place, for the moon's meanmotion in one half-gati amounts to considerably more, Viz. six Signs plus about 92 minutes. Nor are we at present able to throw light upon the meaning of the processes prescribed in stanza 6. They possible refer to the operation of finding the moon's true place, although we are more inclined to think that this latter part is treated in stanzas 4-9 of the next (i.e., III) chapter. And S says: "MÉiªÉPÉæ Eò±ÉÉSÉiÉÖ¹]õªÉºÉƺEòÉ®úºªÉ iÉlÉÉ ¶±ÉÉäEòºªÉ <nù xÉÓ{ɪÉÇxiÉÆ xÉ ¤ÉÖrùÉ ={É{ÉÊkÉ." Thus T and S are both unaware that stanza 6 indeed gives the operation of finding the true moon. Further, their
interpretation of II.3-5 is wrong in several places, and by this they have shut out important necessary data. About III. 4. (including th next five stanzas as well), T remarks without being able to give any translation, "Six stanzas referring to the moon. The details, however, are obscure." About the same S says, "+xªÉä¹ÉÆ (i.e. 4-9) ´ªÉÉ®ú´ªÉÉÆ +OÉä ´ÉIªÉä," and he has left it there without coming back to it. In spite of this self-confessed ignorance, T remarks on p.li of his Introduction,"......the methods are so crude and so completely omit to distinguish between mean and true astronomical quantities that the [Vasistha Siddhanta] can hardly be included within scientific HIndu Astronomy".
The [Prancasiddhantika] was first printed in 1889 and during these nearly 70 years nobody, to my knowledge, has thrown light on the true nature of the [Vasistha Siddhanta]. In dealing with the topic in question, it is my desire also to discuss the readings of the text. We have only two manuscripts to go by, one badly vitiated and the other worse, both printed in the edition, one against the emended text and the other as footnotes. Frequent quotations, from the [Pancasiddhantika] are found in [Bhattotpala's] commentary of the [Brhatsamhita], but the range of our topic is limited, the whole thing taking only 14 [aryas], and these are not found quoted anywhere, as far as I know. But the subject matter being scientific, it is possibleto fix the correct text fairly well in most places of doubt, taking for our guidance the [arya] metre and the relics of the slaughtered words, provided we are certain of the intention of the author. I now proceed to the elucidation of the text. The under standing of the text every where comes first, as that is the basis for the correction of the text.
The Sun
II. 1.
EÞòiÉMÉÖhɪɹɨÉÞiÉÖªÉÖiɨÉèEòiÉÖǨÉ- EÞòiÉMÉÖhɨÉÞiÉÖªÉÖiɨÉäEò-
xÉÖ¾þiÉÆ ¹Éb÷¬¨ÉäxnÖùʦÉ̴ɦÉVÉäiÉÂ* iÉÖǨÉxÉÖ¾þiÉÆ ¹Éb÷¬¨ÉäxnÖùʦÉ̴ɦÉVÉäiÉ *
¶ÉʶÉJÉJÉJɪɨɺ´É®úGòiÉ- ¶ÉʶÉJÉJÉJɪɨÉEÞòiɺ´É®ú-
xÉ´ÉxɴɴɺÉÖ¹É]ÂõEòʴɹɪÉÉäxÉè& ** xÉ´ÉxɴɴɺÉÖ¹É]ÂõEòʴɹɪÉÉäxÉè& **
II.1. The days from epoch (Ahargana) are to be multiplied by 4, and 6 added to the product. This is to be divided by 1461 (and the remainder taken). From the reminder should be deducted successively 126 minus 1,0,0,0,2,4,7,9,9,8,6,5,(i.e., the twelve quantities 125, 126, 126,126,
124,122,119,117,117,118,120,121, are to be
deducted successively ). (The sun's [Rasis], Mesa etc., are successively got).
It is to be noted that Ahargana is not mentioned, that we should take the remainder for the operation is not mentioned, and what we get by this rule is not given. We have to presume all these. The word Ahargana can be easily understoood, because that is the starting point of of computation. The rule give, as also the numebrs, point to the necessity of taking the remainder, and to the true sun in [Rasis], as the obect of the operation.
The rule is explained as follows: The days from the epoch by being multiplied by 4 are converted into quater-days. 6 quater days are added to this because the beginning of the year, (in this case the true year), is 11/2 days before the epoch, and by the addition of the 6 quarter -days we get the total quarter-days from the beginning of the true year. According to this [Siddhanta] the year contains 365 1/4 days or 1461 and taking the remiander we get the quater days by 1461 and taking the remainder we get the quater days from the beginning of the current year. During the first 125 quater days (i.e., 31 1/4 days) of the year the sun traverses the first [Rasi], i.e., Mesa. During the next 126 quarter days (i.e.,31 1/2 days) he crosses the second, i.e., [Rsabha Rasi] and so on. It is to be noted that there are 12 quantities for the 12 [Rasis], and that these add up to 1461. The sun's position within a [Rasi] is expected to be found by proportion.
Thus if the days from epoch is 942, says, the quarter days from the beginning of the year just before the epoch is, 942X4+6==3774. Dividing out by 1461, we get 2 full solar years elapsed (which are not wnated), and 852 quarter days are left over in the thrid year. We can take from this 125, 126,126,126,124 and 122,and 103 quarter days are left over, i.e. the sun has passed six full [Rasis], and in the seventh he has gone 103/119 parts or 26o.
At epoch, the sun is 6/125X30o==1o26/ in Mesa, at sunrise at Ujjain on Sunday, (near the end of `saka 427). What is the epoch, and how we
are to find the days from epoch, these two things are not mentioned here. But ch.I.8-13 gives to find the days from epoch and we can adopt it, though given for Romaka and Pauli`sa, for the interval between two points of time is invariant. Only we must take into account the timeof day of epoch. [Vasistha] epoch mist probably is sunrise at Ujjain, Sunday, at the end of `saka 427. This matter will be discussed subsequently.
Now we are in a position to discuss the adopted readings, T and S, because they have not understood the stanza, have simply corected the obvious scriptory errors, and so far as they go, they are correct. The text -reading ªÉ¹É¨ÉÞiÉÖ has been
corrected into ¹É½Âþ@ñiÉÖÇ, following the variant reading¹ÉnÚùGòiÉÖ: ªÉÖiɨÉèEòiÉè is corrected into ªÉÖxɨÉäEòiÉÖÇ. º¤É®úHò is corrected as º´É®úCEò. I have made the following further corrections: (1) ¹ÉbÂ÷ has been deleted and only @ñiÉÖ retained, because the first foot clearly ends with ¨ÉäEò®Âú and there are two [matras] extra. It is better ¹ÉbÂ÷ is omitted because one Ms. has it, the other haivng a corruption, ªÉ¹É. But both Mss. have@ñiÉÖ. (2) In the third foot, I have interchanged º´É®úEÞòiÉ and made it EÞòiɺ´É®ú, because order requires it. There must be a gradual and continuous fall from 126 to 117. The valused indeed must have been obtained empirically, but it is too much to assume that the [Siddhanta] was aware of the gradual nature of the fall and rise, and gave what it saw as º´É®úEÞòiÉ. the error of observation also would be too great if it is º´É®úEÞòiÉ.
The Moon
II.2-6
®úºÉMÉÖhÉxÉ´ÉäxnÖùªÉÖHò 2 ®úºÉMÉÖhÉxÉ´ÉäxnÖùªÉÖHäò
¶ÉʶÉMÉÖhÉJÉMÉÖhÉÉänÂùvÉÞiÉätiÉÉtÖMÉhÉä * ¶ÉʶÉMÉÖhÉJÉMÉÖhÉÉänÂùvÉÞiÉä PÉxÉÉ tÖMÉhÉä *
¶Éä¹Éä xÉ´ÉʦÉMÉÖÇÊhÉiÉä ¶Éä¹Éä xÉ´ÉʦÉMÉÖÇÊhÉiÉä
MÉiɪÉÉä%¹]õÊVÉxÉè& {ÉnÆù ¶Éä¹É ** MÉiɪÉÉä%¹]õÊVÉxÉè& {ÉnÆù ¶Éä¹É¨É **
txÉ (¹ÉÉäb÷¶É) ¾þiÉÆ ¶Éä¹ÉÆ 3 PÉxÉ (¹ÉÉäb÷¶É) ¾þiɶÉä¹ÉÆ
|ÉÉäVVªÉÉtκjÉMÉÖÊhÉiÉÆ SÉiÉÖ¦ÉÇHÆò * |ÉÉäVYªÉÉvÉκjÉMÉÖÊhÉiÉÆ SÉiÉÖ¦ÉÇHò¨É *
¦ÉÉÊnùEò±ÉÉÊuùMÉÖhÉtÉxÉÉ ¦ÉÉÊnù Eò±ÉÉÊuùMÉÖhÉPÉxÉÉ
¶ÉʶɨÉÖÊxÉ xɴɪɨÉÉ·É®úɶÉÉtÉ ** ¶ÉʶɨÉÖÊxÉ xɴɪɨÉÉ·É ®úɶªÉÉt& *
ʴɹªÉvÉÞiɪÉÉä MÉÊiÉPxÉÉ 4. ʴɹɪÉvÉÞiɪÉÉä MÉÊiÉPxÉÉ
MÉiÉÊiɹɹ]õÉƶÉÉäÊxÉiÉÉ Eò±ÉÉ& |ÉÉäHòÉ& * MÉÊiÉEòÉ,#Â]õÉƶÉÉäÊxÉiÉÉ& Eò±ÉÉ& |ÉÉäHòÉ&
´ÉänùÉEòÉÇ& {ÉÉnùºÉÆJªÉÉ ´ÉänùÉEòÉÇ& {ÉnùºÉÆJªÉÉ
MÉiªÉÆPÉÇ vÉxɨÉÞhÉÆ {É®úiÉ& ** MÉiªÉvÉæ vÉxɨÉÞhÉÆ {É®úiÉ& **
MÉiªÉvÉæ ¦ÉMÉhÉÉÆvÉÇ 5. MÉiªÉvÉæ ¦ÉMÉhÉÉÆvÉÇ
näùªÉÆ Ê±É{iÉɶSÉiÉÖ¹EòºÉƪÉÖHÆò * näùªÉÆ Ê±É{iÉÉ SÉiÉÖ¹EòºÉƪÉÖHò¨É *
¶Éä¹É{ÉnùºÉ¨ÉÉ·ÉÉƶÉÉ- ¶Éä¹É{ÉnùºÉ¨ÉɶSÉƶÉÉ-
ºiÉ·É vÉxÉhÉÉÇiÉ ¡ò±ÉÆ nùxiªÉÆ ** ºiÉè·É vÉxÉhÉÉÇi¡ò±ÉÆ näùªÉ¨É **
¤ªÉäEò{ÉnùʨÉÎxpùªÉPxÉÆ 6. ´ªÉäEò{ÉnùʨÉÎxpùªÉPxÉÆ
EÞòiÉxÉ´Énù¶ÉºÉƪÉÖiÉÆ Ê´ÉªÉÖHÆò SÉ * EÞòiÉxÉ´Énù¶ÉºÉƪÉÖiÉÆ Ê´ÉªÉÖHÆò SÉ *
¨ÉxÉÖ´ÉänùªÉ¨Éä¦{É& {Énù- ¨ÉxÉÖ´ÉänùªÉ¨Éä¦{É& {Énù-
MÉÖhÉä Êjɹɹ]õ¬Éä vÉÞiÉä ʱÉ{iÉÉ ** MÉÖhÉä Êjɤɹ]õ¬ÉänÂùvÉÞiÉä ʱÉ{iÉ& **
III. 4
xÉMÉÉi{ÉnùÉqù¶ÉPxÉÉiÉ (Ê´É) xÉ´ÉÉi{ÉnùÉqù¶ÉPxÉÉiÉÂ
ºÉ{iÉÉƶÉ& ºÉÊ·É ºÉÉÆ´É®úÉä¦ÉÖÊHò& * ºÉ{iÉÉƶɺºÉÉÊ·ÉJɺ´É®úÉä ¦ÉÖÊHò& *
MÉiªÉvÉÉÇxiÉÉ UôÉävªÉÉä MÉiªÉvÉÉÇxiÉÉSUôÉävªÉÉä
ʱÉ{iÉɦªÉÉä ´ÉºÉÖ¨ÉÖÊxÉxɴɦªÉ& ** ʱÉ{iÉɦªÉÉä xɴɨÉÖÊxɴɺÉÖ¦ªÉ& **
II.2. 1936 is added to the days from epoch, and the total divided by 3031. The quotient are called Ghanas. The remainder is to be multiplied by 9 and divided by 248. The quotient are called Gatis. The remainder are called Padas.
II.3. The Ghanas are to be divided by 16 and the remainder taken. This should be multiplied by 3 and divided by 4. This is [Rasi] etc. It should be deducated from 12 [Rasis] (and the remainder written down). Minutes of are equal to twice total Ghanas (are to be added). One [Rasi], 7 degrees and 29 minutes are (also to be added).
II. 4. 185 multiplied by the Gatis minus a tenth of the Gatis are minutes (which are also to be added). The (first) 124 Padas are designated a half-gati. (If the Padas are less than 124) they are called plus-padas. If more then 124, 124 is taken from it to form a half-gati, and the remainder are called minus-padas.
II. 5. If there is a half-gati, (for the sake of that half-gati) 6 [Rasis] and
4 minutes are to be added. Also degrees equal in number to the plus-padas or minuspadas (are to be added). With these plus or minus padas respectively, the minutes got by the plus operation or minus operation respectively (in II.6) are to be added.
II. 6. Deduct one from the plus-pada or minuspada, and multiply this by 5. (If plus-pada) add the product to 1094, multiplied the sum by the plus pada and divide by 63. The resulting minutes (are to be added). If minus-pada, the product is to be substracted from 2414, the remainder multiplied by the minus-pada, and divided by 63. The resulting minutes (are to be added). (Thus the true moon is got).
III. 4. Deduct 9 from the number of plus or minus padas, multiply this by 10 and divided by 7. Add this to 702 if plus-padas. Deduct this from 879 if minuspadas. The resulting minutes are the daily motion (for the day ending with the padas).
The following is the explanation of the process. The true moon at a given time t. is, (i) the mean moon at t plus (ii) the equation of the centre for t. (i) is given here in five parts. We shall call them a, b,c,d,e which are to be added up to get the total mean moon. a (usually called the [Mula-dhruva) is the position of the mean moon at a point of time 1936 days before the epoch, when the moon's apogee and the mean moon exactly coincided, according to this [Siddhanta]. This is given as ¶ÉʶɨÉÖÊxÉxɴɪɨÉɸ´É ®úɶªÉÉtÉ:, i.e. 1 [Rasi], 7 degrees, 29 minutes. b is the mean motion during a whole numbers of cycles of 3031 days, each cycle equal to 110 anomalistic revolutions of the moon, from that point of time. This b is found by multiplying the mean motion per cycle,(110 revolutions; 11 [Rasis], 7 degrees, 32 minutes), by the number of cycles, called Ghanas, obtained as quotient by dividing the Ahargana plus 1936 days, by 3031. As full revolutions may be neglected, it is enough if we multiply the Ghanas X2' is given by ÊuùMÉÖhÉPÉxÉÉ: Eò±ÉÉ: (ªÉÉäVªÉÉ:). Because 16 Ghanas X 11 7o30/equal 15 full revolutions, it is enough if we divide out the Ghanas by 16 and take the remainder alone for multiplication, which we are asked to do by PɴɹÉÉb÷¶É½þiɶÉä¹É¨ÉÂ. As 11' 7o30/ is 3/4 [Rasi less than a full revolution, we can
multiply the remaining Ghanas by 3/4 [Rasi] and take this as substractive, which we are instructed to do by |ÉÉäVZÉÚªÉÉ PɺjÉÖËhÉiÉ SÉiÉÖ¦ÉèCEÆò ¦ÉÉÊnù. Thus b is disposed of, c is the mean motion during the subsequent full anomalistic
revolutions called Gatis, which form the quotient got by dividing the remaining days by the anomalistic period, 248/9days; (multiplying the days by 9 and dividing by 248 is only dividing by 248/9). For each Gati the mean motion is 1 revolution and 184 9/10 minutes. Hence the rule to multiply the Gatis by 185'and deduct minutes equal to 1/10 of the Gatis. This is given by ʴɹɪÉvÉÞiɪÉÉä MÉÊiÉ´PÉÉ MÉÊiÉEòÉ´¹ÉÉƶÉÉäÊxÉiÉÉ:Eò±ÉÉ: (ªÉÉäVªÉÉ:). What are now left over are 9ths of days called Padas (and these obviously would be less than 248). The mean motion perpada to complete the mean motion till t. Of this the [Siddhanta] asks us to add 1oper Pada first which is given by ¶Éä¹É{ÉnùºÉ¨Éɸ´ÉÉƶÉÉ: (ªÉÉäVªÉÉ:) This forms d. The residue 27'.843 per Pada forming e is combined with the equation of the centre (ii) and given by the two equations of II.6. If the Pada contain a half-gati, the value of d+e+(ii) for the half-gati part are combined together and given as 180o4'. This180o4'is got as follows: The half -gati is equal to 124 padas. So d==124o. e+(ii) given by the equation is {(1094+5X(124-1)}X124/63==3364'==56o4'; 124o+56o4'==180o4'. Thus it is that we get 180o4' for a half-gati, given by MÉiªÉPÉè ¦ÉMÉhÉÉPÉè näùªÉÆ Ê±Éi{ÉÉSÉiÉÖ¹EòºÉƪÉÖ¨ÉÚ, which instruction has so much puzzled T and S. But of course this is incorrect, and the defect lies in the equation of the centre part of the formulae in II, 6, which give the zero value for the equation of the centre not at 124 Padas, but at 133 Padas,as I shall show presently.
I shall first explain II, 6, and show how the formulae here combine the residual mean motion, viz. Padas X27'. 843(==e), with what is identifiable with the equation of the centre (==ii). If p==plus or minus Padas, the formula for plus-padas can be written down as {1094+5(P--1)}P/63, and the formula for minus-padas, as {2414-5(P-1)}P/63. Let us first take the plus take the plus-pada formula. As we have said e+(ii)=={1094+5(P-1}p/63, and e==27'.843 P.
Therefore (ii)=={1094+5(P-1)} P/63-27'.843P
==(1089+5P)P/63X27'.843P/63.
==(1089-1754+5P) P/63.
==(5 P-665)P/63.
Taking the minus -pada formula,
(ii)=={2414-5(P-1)}P/63-27'.843P
==(2419-5P)P/63-63X27'.843P/63
==(2419-1754-5P)P/63
==(665-5)P/63
Now, the plus -pada representing the original Padas lying within 0 to 124 Padas, correspond to teh anomaly lying between 0 and 180o and 360o. So for the plus-pada the equation of the centre must be negative. We see, (5P-665) P/63 is
indeed negative for all values of plus-pada, and (665-5p) p/63 is positive for all values of minus-pada. It is to be noted that the one is the negative of the other. Again, the former starts from the value 0 for P==0, gradually goes to a minimum for p=661/2 and again gradually, increases reaching 0 for p==133, (but P stops with 124), while the latter starting from 0 value for p=0, goes to a maximum for p=661/2 and falls gradually to 0 in a similar manner. Thus the equations roughly behave like the term of the equation of the centre of modern astronomy, -k sin0, and therefore identiable with the equation of the centre. This is noteworthy, as forming a transition from a stage of no equation of the centre to the stage of epicyclic astronomy giving the equation of the centre in the form, -ksin0. Substituting 661/2 for p we get the maximum or minimum equation of the centre =351.
I now proceed to the explanation of III.4, giving the formulae for the daily motion. They can be written down thus:
For plus -padas, 702'+10'(p-9)/7. For minus -padas, 879'-10'(P-9)/7. We see, the being linear equations, that the increase or decrease in the daily motion is uniform, from 702' to 879' and and back again from 879'to 702'. 702' is the minimum and 879' is the maximum, the former being 88'.5less and the latter 88'.5more than the mean motion790'.6. Though mathematically we can get values less than 702' and more than 879' for P less than 9, this is not envisaged by the [Siddhanta]. I shall now derive these rules from those of II.6 and thus show that these belong to the [Vasistha], to whatever other [Siddhanta] also they belong.
The daily motion for the day ending P padas is clearly, the ture moon for P minus thr true moon for (p-9). So for plus-padas the daily motion is,
[(a+b+c+Po+{1094=5(p-1)p}p/63)]
--[(a+b+c+(P-9)o+ {1094+5(P-1-9)}
(P-9)/63)]in minutes
==540+1089p/63+5P2/63-1089 (p-9)/63-5(p-9)2/63
==540+1089 (p-9+9)/63+5(P-9+9)2/63-1089 (p-9)/63
-5(p-9)2/63
==540+1089X9/63+5X92/63+90 (p-9)/63
==540+162+10(P-9)/7
== 702+10(p-9)/7.
In the same way for the minus -padas,
[(a+b+c+po+{2414-5(P-1)}P/63)]
--[(a+b+c+(p-9)o+{(2414-5(p-1-9))}(P-9)/63]
( in minutes)
==540+2419P/63-5P2/63-2419 (p-9)/63+5(P-9)2/63
==540+2419 (p-9+9)/63-5(p-9+9)2/63-2419
(p-9)/63+5(P-9)2/63.
==540+2419X9/63-5X92/63-90 (p-9)/63
==540+339-10 (p-9)/7
==879-10(P-9)/7.
It is also possible to establish the connection, by summing the two expressions of III.4, and arriving at the formulae of II.6. For the matter of that, there are reasons to surmise that II.6. was got from III. 4. by summation. The difference from the mean position must have been first noticed. This must have been accounted for by a variation in the motion from a minimum to a maximum and vice versa, postulating the variation to be constant as in III.4. The factor (p-9) must have been introduced because the minimum 702' must be obtained for the first day ending 9 Padas, and so on for the others, (though P-4 1/2 would have done better). Then is why the 0 value of the equation of the centre results for 133 padas instead of 124, and for a half-gati we get 180o 4' instead of the correct 181o32'. Otherwise, it is easy to have given the 0value for 124 padas, and the maximum or minimum for 62 padas, by making the equation of the cntre formulae equal to +(5p-620)Xp/63, and combining these with 27'.843 P. The factor (P-1) in the formulae of II. 6, seems to form a relic of a prior summation, which [Varaha] seems to have retained out of respect for the
original [Siddhanta], for the same result will be got by the more simplified forms, (1089+5P) P/63 and (2419-5P) P/63.
I shall now point out some of the errors committed by T and S. They have seriously gone wrong in their interpretation of the second half of II. 3, and this after making two uncalled for emendations of the Ms. text, (See discussion of the text). In this part, as we have laready seen, we are asked to add minutes equal to twice the Ghanas, and also add the [Mula-Dhruva], (or Ksepa), 1 [Rasi] 7o29'. T and S interpret it as, "Multiply the Ghanas by 2 and divide by 2971. The resulting [Rasis] etc. are to be added". This means, instead of 2' per Ghana we add 1'13'', and we do not add the Ksepa 1[Rasi] 7o29' at all. As for the 1'13'', this is unwarranted when both the Mss. say 2' per Ghana. An emendation is called for only when a quantity given is so far removed from the actual that it is not likely to be the quantity given by the [Siddhanta]. Now the value 2' agrees better with the mean motion (siderial)per Ghana, viz. 110 revolutions 11 [Rasis] 7o32' 15'' for the time of [Varaha]. It agrees almost prefectly with the value of [Siddhanta] [Siromani] of [Bhaskara] II. While it is a matter for wonder and admiration how the ancient [Vasistha] achieved a thing not achieved by most later [Siddhantas], T and S come in and spoil the whole thing by their emendations.
As for the Ksepa which T and S have obliterated, it is essential, as it supplies the [Muladhruva]. This can be seen from the mean moon I give according to different systems for sun-set at [Yavanapura], (Alexandria), i.e., for 37 [nadis], 20[vinadis] after mean sun-rise at [Ujjain], Sunday, close to the end of 'saka 427.
Modern astronomy (this from the Vernal equinox of epoch) 354o48'
[Vasistha] (with the Ksepa), taking Ujjain sunrise for the
[Vasistha epoch) 355o6'
[Vasistha](without the Ksepa, taking Ujjain sunrise
for the [Vasistha] epoch) 317o37'
[Siddhanta Siromani] 355o49'
Romaka 356o12'
Saura (with Ujjain noon for epoch, given) 355o6'
[Vasistha] (with the Ksepa, taking Ujjain
37-20 [nadikas] for epoch for [Vasistha] also) 346o54'
[Vasistha](without the Ksepa, taking Ujjain
37-20 [nadikas] for [Vasistha] epoch also) 309o25'
We see that with the Ksepa in tact [Vasistha] mean moon agrees with the other [Siddhantas] and modern astronomy. With the Ksepa gone, there is a defect of 37o.
Incidentally we must discuss another point here, viz. what time of the day is the [Vasistha] epoch. [Varaha] gives different times of day for different [Siddhantas], and sometimes times even for the same [Siddhanta]. For the Saura sun, moon, moon's apogee and [Rahu], midday at Ujjain (Sunday) is given as the time of epoch, and for the planets, the midnight following. For the [Paitamaha] the time of day of epoch is morning (though the year is different). For the Romaka the epoch time of day is sunset at Yavanapura (Alexandria) which is equal to 37 [nadikas] 20 [vinadikas] from sunrise at Ujjain (Sunday), excepting for the moon's apogee, for which sunset at Ujjain is given as the time. In the case of the Paulisa the time is not mentioned, unless we strain xÉÉ%ÊiÉÊSÉ®äú {ÉÉèʱɶÉÉä%{ªÉä´ÉÆ (I.10.) a bit, and make it mean that the Pauli'sa time of epoch also is sunset at Yavanapura like the Romaka. But we can infer that it is indeed so, from III. 13-15. For the [Vasistha] also the time is not mentioned. Is it sunset at Yavanapura, because it has been given as a general instruction? Or is it sunrise at Ujjain, as in the [Paitamaha]? If it is sunrise at Ujjain, the [Vasistha] moon agrees closely with those of other [Siddhantas] as also modern astronomy. If is sunset at Yavanapura it is defective by about 8o. (If the Ksepa is not taken into account the defect will be about 45o). Now 8o difference is too much, especially when we consider the accuracy of the [Vasistha] moon's mean motion. So the time of day of the epoch for [Vasistha] must be mean sunrise at Ujjain (Sunday). If we emend II.3.into,".....¶ÉʶɨÉxÉÖ xɴɪɨÉMɸ´É®úɶªÉÉtÉ:," then the Ksepa is lr-14o29'. In this case the [Vasistha] moon will be 353o54' at Ujjain 37-20 [Nadikas], which agrees approximately with other [Siddhantas]. So we can take the Ksepa as 1-14o29', and keep sun-set at Yavanapura. But here there is the weight of the emendation.
We shall now continue our main discussion. In their interpretation of II. 4-5 also. T and S have fallen into material errors. In II.4, two terms,
plus-padas and minus-padas are defined, to be used in II.6, which have been missed by them.
In II.5, T's translation wants us to add degrees equal to the number of Padas, only in the case of the Padas left over after deducting 124, i.e., in the case of what amount to the minus-padas only as well. But S's commentary gives the correct interpretation. In the second part of this stanza, T's translation is non-committal. S's interpretation is positively erroneous. He says: "+lÉÇiÉÚ ´ÉänùÉEòɱ{É{Énäù¹ÉÖ @ñhÉÆ, +ÊvÉEäò¹ÉÖ vÉxÉʨÉÊiÉ ¤ÉÖÊrù¨ÉÎnÂù¦É:º´ÉªÉ¨Éä´ÉÉäÁ¨ÉÂ". i.e., if the original padas are less then 124, additive. Evidently he thinks that II.6. gives the equation of the centre, pure and simple, and it must be subtractive for padas less than 124, and additive otherwise. But as I have already explained, there are two rules in II.6, the first requiring the addition of two terms, and the second requiring the addition of two terms, and the second requiring the substraction of one term from another. In the first, Padas less than 124 are to be used. But the result of either rule is to be added to the mean moon so far obtained. There is no question of subtraction here at all.
As for II. 6.T and S have said in so many words they do not understand it, but nevertheless given an interpretation, which naturally is wrong. III. 4, they have not touched.
Now we are in aposition to discuss the readings of II.2-6. and III.4.
In II.2. there are the scriptory errors, ªÉÖHò¶ÉʶÉMÉÖhÉ for ªÉÖHäò¶ÉʶÉMÉÖhÉ, and txÉÉ which T and S have corrected. I have adopted these corrections.
In II.3, the scribal errors txÉ forPÉxÉ, ¿iÉÆ ¶Éä¹ÉÆ for ¿iɶÉä¹ÉÆ, tκjÉMÉÖÊhÉiÉÆ for PÉxÉÉ and ¸´É®úɶÉtÉ for ¸´É ®úɶªÉMÉtÉ:, which T and S have corrected, I have adopted. T and S have corrected ¹ÉÉä½þ¶É, and printed within brackets, and I have adopted this.
Apart from these small errors the Ms. is alright. But T and S have carried out two uncalled for emendations which seriously affect the subject matter, The first is the changing ofEò±ÉÉ into ¡ò±ÉÆ, (when both Mss. give Eò±ÉÉ),simply because if the second emendation is made, Eò±ÉÉ would be troublesome. The second is the conversion of ¶ÉʶɨÉÖÊxÉxɴɪɨÉɸ´É into ¶ÉʶɨÉÖÊxÉxɴɪɨɿiÉɸ´É, when neither Ms. has ¼±ÉiÉ, and the [arya] metre is sinned against by the addition of the two [matras], thrus giving 18 [matras] to teh fourth foot and making it a [Giti], which [Varaha] nowhere uses in his text.
Further they have done this thinking they are improving the text. On the other hand they have spoiled the already correct and better text, and also shut out a necessary data (viz., the [Muladhruva]), as we have shown before.
In II.4, T and S have corrected ÊxÉiÉÉ Eò±ÉÉ: into ÊxÉiÉÉ:Eò±ÉÉ:, which I have also done. Metre requires that {ÉÉnùºÉÆJªÉÉ, must be changed into {ÉnùºÉÆJªÉÉ and {Énù will be a better word also. T and S have failed to notice this, and retained {ÉÉnùºÉÆJªÉÉ. ¹É¹ÉÞƶÉ, (a likely corruption for ¹É¹`öÉƶÉ. T and S have corrected {É®úiÉ:, not understanding the text properly, and {É®úiÉ: