Pramāṇa · Search · About · API

Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c15: Epilogue

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c15

Language
English

Contents

Epilogue

v2.c15.1

We have so far discussed Indian astronomy in elaborate detail. The condition of astronomy in the Vedic and Vedāṅga periods preceding the Siddhāntic period was described in Part I and that in the Siddhāntic period in Part II. Each of the three main branches of Jyotiṣa viz. Gaṇita*, Saṃhitā and Jātaka has been separately treated in Part II. Now the author offers his concluding remarks on this Survey.

v2.c15.2

∗ The author will add here some more information about other mathematical works which were received later (From the Notes on the Hindu Astronomy by J. Burgess, 1893 :-).

v2.c15.3

(1) Europeans first obtained some knowledge worth the name about Indian Astronomy from a copy of an astronomical work procured from Siam. This work has adopted 365d-15i-31p-30v as the length of the year (which is the same as that in the original Sūrya siddhānta and Khaṇḍakhādyaka). Cassini, a French astronomer, says that the epochal positions have been given for Saturday, the new moon day, 21st March, 638 A. D. (According to the original Sūrya Siddhānta, the mean Aries ingress occurred on the 2nd lunar day of the bright half of Vaiśākha, Śaka 560, i.e. Sunday the 22nd March 638, at 12gh. 58p. after (mean) sunrise, and the preceding mean new moon of Caitra occurred on Friday at 49gh-35p i.e. on Saturday, 21st March according to European reckoning) The original epochal positions may have been true for Narasingpur near Pithāpur in Godāvari district or for Vārāṇasi. The sun's apogee given in this work is 80°. The maximum value of the equation of centr of the Sun is 2°-14' and that for the Moon is 4°-56'. This shows that the work may have followed either the original Sūrya Siddhānta or some Karaṇa work now lost, by Āryabhaṭa I who followed the Sūryu Siddhānta.

v2.c15.4

(2) Ullamudayan’s Karaṇa, Śaka 1165.

What Foreign Element Has Entered Indian Astronomy

v2.c15.s1.1

Most of the European scholars are of opinion that the Indian people borrowed astronomy, particularly mathematical astronomy and astrology from the Chaldeans (Babylonians), the Egyptians or from the Greeks of Alexandria. This view has already been considered incidentally in the foregoing pages. The question will now be thrashed out in greater detail here and then other matters will be taken up for consideration in this conclusion.

v2.c15.s1.2

NAKṢATRA SYSTEM NOT BABYLONIAN

v2.c15.s1.3

The question, to whom the nakṣatra system originally belonged or who first originated the Rāśi system is immaterial. The author has already stressed the fact that what is really of supreme importance is the mathematics relating to the mean motions and true motions of planets. He has, however, come across an important article concerning nakṣatras which is summarized below :—

v2.c15.s1.4

This important article on the question whether the nakṣatra system originated with the Babylonians was written by Dr. Thibaut in 1894 in the Bengal Asiatic Society's Journal. Vol. 63 for the year 1894. A number of Babylonian tablets have been recently excavated. Father Epping took great pains to decipher the writings on the clay tablets with the help of Father Strassmaier and published some facts of astronomical interest in his book, Astronomisches and Babylon in 1889 A. D. The tablets which have been found, contain many

v2.c15.s1.5

(3) The Vākyakaraṇa, Kṛṣṇāpur Śaka 1413. The new moon preceding the epoch of the work, i.e., the 30th lunar day of the previous year's Phalguna fell on 10th March. Warren attributes the work to Vararuci.

v2.c15.s1.6

(4) The Pañcāṅga Śiromaṇi, Narsāpur, 1569 (or 1659). The length of the year adopted by these two works is 365d-15g-31p-15v, that is the same as that of the first Ārya Siddhānta. They, however, give 2°-10'-34'' as the equation of centre for the Sun and 5°-2'-26'' as that for the Moon.

v2.c15.s1.7

(5) The Graha Taraṅgiṇī, Śaka (n) 1618.

v2.c15.s1.8

(6) The Siddhānta Mañjarī 1619. From Warren's Kālasaṅkalitā:—

v2.c15.s1.9

(7) Mallikārjuna's Karaṇa-work, Śaka 1100. The abdaps etc. adopted by it are true for the longitude of Rāmeśwara. Mallikārjuna was a Telang. From this it seems that this work may have followed the S. S..

v2.c15.s1.10

(8) Bālāditya Kallū's Karaṇa work, Śaka 1378, true for the longitude of Rāmeśāara. (From the list of books presented by Bentley to Cambridge University).

v2.c15.s1.11

(9) The Brahma-Siddhānta, 26 Chapters, 11 of which are devoted to astronomy and the remaining to muhūrta etc. It begins with the verse :—

v2.c15.s1.12

“Om shryarkaḥ paramo bramhā shryarkaḥ paramaḥ Śivaḥ.”

v2.c15.s1.13

(10) The Viṣṇu Siddhānta containing 11 chapters. The opening verse is the same as the one in the Brahma Siddhānta above.

v2.c15.s1.14

(11) The Siddhānta Laghukhamāṇik, 15th Century A. D. compiled by Keśava, follows S. S. and contains 9 chapters.

v2.c15.s1.15

(12) The Sūrya Siddhānta Rahasya, compiled by Rāghava, Śaka 1513.

v2.c15.s1.16

(13) Mathurānātha's Sūrya siddhānta mañjarī, Śaka 1531. Mathurānātha was an astronomer at the court of a king named Śatrujit.

v2.c15.s1.17

(14) The Jyotissiddhānta Sāra, Śaka 1704 ; this is compiled by Mathurānātha (referred to on page 174 before); contains 8 chapters. Sadānanda, father of Mathurānātha, was originally a resident of Pātnā, but later on shifted to Vārāṇasi. This work appears to have been written with the help of some European work.

v2.c15.s1.18

(15) The Graha Mañjarī. The date of its compilation has been given, but it is not quite intelligible.

v2.c15.s1.19

records of observations. For example, “On the 20th night of the month of Airu (April or May) in the 189th year (124 or 123 B. C.) of the Seleucidan Era, Venus was visible or expected to be visible in the eastern part of the sky. The star in the region of the head of the constellation Aries appeared at a distance of 4 yards above it.* In the same year Mars appeared in the eastern sky on the 26th night of the month of Abu (July or August). At a distance of 8 inches above it was seen the Western star in the mouth of the constellation Gemini, in the same year, Mercury set while in the sign of Taurus, on the 4th day of the month of Airu. In the year 201 of the seleucidan Era, Mars rose in the sign Libra on the 8th night of the month of Tischritu”. Considering all these things, Thibaut came to the conclusion that the Babylonians used to indicate planet’s positions with respect to the signs and that the 27 or 28 divisions of the ecliptic called nakṣatras were never current among them. Thus there is no room left for the contention that the Hindus borrowed the nakṣatra system from the Babylonians. In other words the contention must be dismissed as worthless.**

v2.c15.s1.20

VIEWS OF EUROPEANS

v2.c15.s1.21

Let us now examine the views of Europeans regarding planetary motions and astrology. Some of our people regard the views of European scholars as gospel truth, no matter what the calibre of the scholar concerned is.

v2.c15.s1.22

It is really surprising that even some of our seasoned scholars feel that way. But it is not proper to arrive at any conclusion unless we consider the locus standi of the scholar delivering the judgment on some question or unless we are ourselves fully entitled to form our own judgment. Other people naturally rely upon the views of eminent scholars, and hence, such scholars should declare their views only after due consideration. Now, as for making a pronouncement on the mathematical branch of astronomy in India and Europe, one is entitled to compare the works compiled in the two nations and to declare who borrowed from whom, if only one has a fair knowledge of the practical and theoretical astronomy of both India and Europe, or of one of these two pairs or at least of some part of practical or theoretical astronomy of both. Similarly, for making a pronouncement on astrology, one must have at least an elementary knowledge of astrology in addition to the competence mentioned above. In the same way, one must have sufficient means at one's command for one's competence in this respect varies with such means. Such means as would enable one to pass a correct judgment on Indian astronomy are multiplying every day. The means that we possess at present were not available 10 years ago.

v2.c15.s1.23

∗ It could not be decided whether the information contained in these writings was the record of positions actually seen or of those which were expected to occur in future. The capacity to predict requires knowledge of mathematical astronomy. It has not been definitely known if the Babylonians possessed such knowledge in those times.

v2.c15.s1.24

∗∗ While commenting on this point, Thibaut remarks that history does not support the view that the Chinese nakṣatras were originally 24 in number, and that later on about the year 1100, they became 28. Although Thibaut observes that all the three system viz. the Hindu, the Chinese, and the Arabic have much in common, he has not given any reasons for this similarity. But in his private letter dated 5th September 1896, he writes to the author; “I have not as yet found a satisfactory explanation for the similarity of the Chinese, Arabic, and Hindu nakṣatras”. If any two persons, who have absolutely no relation to each other, begin to select stars lying on the moon’s path, they will naturally select prominent stars of the first magnitude, like Rohiṇī, Punarvasu, Maghā, Citrā and Jyeṣṭhā. The same would be the case with Aśvinī and other stars of the second magnitude. Similarly, clusters of faint stars like those of Kṛttikās will be found in the selecton of both. This principle is acceptable to Thibaut and should be equally acceptable to others. Still in view of the fact that the stars Mṛgaśirṣa, Mūla, Pūrvā and Uttarā Bhādrapadā, and Bharaṇī are common to all the three systems, that Pūrvā and Uttarā Phālgunī are selected by the Hindus and the Arabs, while the Āśleṣā nakṣatra is common to the Hindus and the Chinese. Thibaut is inclined to believe that the three systems must have originated from a common source. But if the moon and the stars are observed for about 10 years, or even for one year, the stars chosen by two or three persons will naturally be found to agree not only this, but also one cannot but be convinced that all the nakṣatras have been suggested to the Indian mind in the natural course. The author is convinced in that respect by observing the moon’s conjunction with stars for more than ten years. It is not that the Chinese nakṣatra system tallies with that of the Hindus completely. There is some difference between the two; and it is quite probable that the Chinese might have established their system independently.

v2.c15.s1.25

Colebrooke, E. Burgess, Whitney, and Dr. Thibaut have expressed their views on the mathematical branch. The author has no first hand knowledge of Greek astronomy, but some facts could be gleaned from the writings of these four scholars. He is, therefore, reproducing here, verbatim, necessary passages from their writings. Even European scholars have no knowledge of Greek astronomy before the times of Ptolemy, because, as Thibaut's remarks would show later, it is not available at all. Colebrooke gave his verdict during the period from 1807 to 1817 A. D. The verdicts of the next two were given about 1860 A. D. while that of Thibaut was given in 1889. Much of the information about Indian astronomy that is given in this book was not available to Colebrooke. A considerable part of it was also not available even in the times of Burgess and Whitney. Most of it is now available to Thibaut, though part of it is still wanting. Apart from the question of the material at their disposal, all of them are competent to judge this question and their judgment, favourable or adverse, must naturally carry weight. Burgess and Whitney had the same material in hand ( see page 43 ) and yet they have expressed divergent views. Bentley has not devoted much thought to the question regarding the origin of astronomy. Dr. Kern in his Preface to the Bṛhat Saṃhitā (1865 A. D.) and James Burgess in an article published in 1893, have made only some passing remarks on the question. Both of them have expressed the view that the Hindus have borrowed both astronomy and astrology from the Greeks. But as they have not written articles specially on this subject, their discussion is not elaborate and is lacking in necessary evidence, and, therefore, the author is not reproducing it here, though he will incidentally deal with their views later. Apart from these authors, he has neither seen nor heard of any English article on this subject written by a competent European scholar. No one from amongst our own people too appears to have written on this subject. The views set forth below may also impart some new information regarding Indian astronomy. Colebrooke's* essay contains his views both on mathematical astronomy and astrology, as also his views on the astronomy of the Arabs. It was once believed by some that the Hindus borrowed astronomy from the Arabs but owing to the additional information that has since become available, there is not even a shadow of doubt today that it was the Arabs who first borrowed astronomy from the Hindus. It has already been mentioned before that the Tājik system was transmitted to our country by the Muslims.

v2.c15.s1.26

¹ 1

v2.c15.s1.27

∗ Henry Thomas Colebrooke was born in 1765 A. D. He came to India in 1782. He became Chief Judge of the Civil Court, Calutta in 1801. He spent a lakh of rupees in buying Sanskrit manuscripts. These are now entrusted to the India Office. His articles were published in the Asiatic Researches, Vol. 9, 1807, in Vol. 12, 1816, and with the translation of Pāṭīgaṇita and Bīja Gaṇita in 1817. All of them were collected and published in 1872 A. D. under the title Miscellaneous Essays by Colebrooke, Vol. II”. The above extracts have been taken from this book. The pages mentioned refer to the book published in 1872.

v2.c15.s1.28

COLEBROOKE

v2.c15.s1.29.1

Colebrooke writes (1807 A D.) (p. 322) “I apprehend that it must have been the Arabs who adopted (with slight variations) a division* of the zodiac familiar to the Hindus.” (p. 344) “The Hindus have likewise adopted the division of the ecliptic and zodiac into twelve signs, agreeing in figure and designation with those of the Greeks and differing merely in the fact that their initial point is carried on a few degrees further west than that of the Greeks. That the Hindus took the hint of this mode of dividing the ecliptic from the Greeks, is not perhaps altogether improbable ; but, if such be the origin of it they have not implicitly received the arrangement suggested to them, but have reconciled and adapted it to their own ancient distribution of the ecliptic into twenty-seven parts.” “In like manner, they may have either received from the Greeks or given them the hint of an armillary sphere as an instrument for astronomical observation; but certainly they have not copied the instrument which was described by Ptolemy, for the construction differs considerably.” “The *Almagest*** was first translated into Arabic in 827 A. D. by Alhazen Ben Yusef. Other versions are also mentioned but none of them are anterior to the ninth century.” (p. 364) “The Hindus, like the Egyptians and Babylonians, divide each sign into three parts (which are called Dreṣkāṇas).” (p.

v2.c15.s1.29.2

527)- “The Dreṣkāṇa system is not implicitly the same among the Hindu astrologers, which it was among the Chaldeans, with whom that of the Egyptians and Persians coincided. Variations have been noticed,” (p. 371). “This astrological notion was confessedly received from foreign nations..” “The doctrine seems to be ascribed by Firmicus to Nekepso, king of Egypt : and Psellus cites a Babylonian author who he calls Teucer and who is also noticed by Porphyrius. The word ‘Dreṣkāṇa’ is supposed to not be originally Sanskrit. For the same reason, it is likely, that the astrological doctrine itself may be exotic in India. The casting of nativities, though its practice is of more ancient date in India, may also have been received from Western astrologers : Egyptians, Chaldeans or even Greeks***. If so, it is likely that the Hindus may have received astronomical hints at the same time. By their own acknowledgment, they have cultivated astronomy for the sake of astrology; and they may have done so with the aid of hints received from the same quarter from which their astrology is derived. The name of Yavanācārya would not be alone decisive. It will be requisite to collect all the passages in which Yavanācārya is cited by Sanskrit authors and to compare the doctrines ascribed to him with those of the Grecian writers on astronomy”. (1816 A. D.) (p. 399).

v2.c15.s1.29.3

“ The planet revolves with an equal but contrary motion in an epicycle, of which the centre is carried with like but direct motion on a concentric orbit. To account for the still greater apparent irregularities of the five minor planets, the Hindu astronomers make them revolve with direct motion on an epicycle borne on an eccentric deferent. (In the case of the two inferior planets, the revolution in the eccentric is performed in the same time with the sun : consequently the planet’s motion in its epicycle is in fact its proper revolution in its orbit. In the instance of the superior planets, on the contrary, the epicycle corresponds in time to a revolution of the sun, and the eccentric deferent answers to the true revolution of the planet in its orbit). So far the Indian system agrees with the Ptolemaic. At the first glance it will remind the reader of the hypothesis of an eccentric orbit devised by Hipparchus : and of that of an epicycle on a deferent, said to have been invented by Apollonius, but applied by Hipparchus. At the same time the omission of an equant (having double the eccentricity of the deferent) imagined by Ptolemy for the five minor planets, as well as the epicycle with a deferent of the centre of the eccentric, contrived by him to account for the evection of the moon; and the circle of anomaly of eccentricity, adapted to the inequality of Mercury's motions, cannot fail to attract notice.

v2.c15.s1.29.4

The Hindus give an oval form to the eccentric or equivalent epicycle, as well as to the planet's proper epicycle. Āryabhaṭa (the First) and the Sūrya Siddhānta make both epicycles of all the planets oval, placing however the short axis of the proper epicycles of Jupiter and Saturn in the line of mean conjunction, termed by Hindu astronomers their ‘quick apogee’ (Śīghrocca). Brahamagupta and Bhāskara, on the contrary, acknowledge only the epicycles of Mars and Venus to be oval and insist that the rest are circular.” (p. 411) “If these circumstances (that is to say, the frequent recurrence of such names as Yavanācārya and Romaka Siddhānta in the compilations of Hindu astronomers), joined to a resemblance hardly to be supposed casual, which the Hindu astronomy, with its apparatus of eccentrics, and epicycles, bears in many respects to that of the Greeks, be thought to authorize a belief, that the Hindus received from the Greeks that knowledge which enabled them to correct and improve their own imperfect astronomy, I shall not be inclined to dissent from the opinion.” In another article Colebrooke observes (p. 449):— “Taking into consideration the analogy, though not identity, of the Ptolemaic system or rather that of Hipparchus, and the Indian one of eccentric deferents and epicycles, no doubt can be entertained that the Hindus received hints from the astronomical schools of the Greeks.”

v2.c15.s1.30

∗ These are the exact words of Colebrooke and it is clear from the context that they refer to the twenty-seven naksatra divisions of the zodiac. In the Marathi translation of this sentence, however, the phrase ‘twelvefold division’ (dvādaśadhā vibhāgāci padḍhati) seems to have crept in through oversight. The same passage has been referred to elwsewhere when it is correctly interpreted in its bearing on the naksatra divisions. (R. V. V.)

v2.c15.s1.31

∗∗ The *Almagest* is the same work as Mijasti mentioned before.

v2.c15.s1.32

∗∗∗ Colebrooke reiterated the view in 1817, that the Hindus borrowed their astrology from the Greeks.

v2.c15.s1.33

WHITNEY

v2.c15.s1.34

Now a resume* of the views of Whitney and Burgess will be presented to you. First the result will be reproduced of the comparative view taken by Whitney in the chapter on true places in the English Translation of the Sūrya-Siddhānta, in respect of the problem of the true positions and motions of planets dealt with in Greek and Hindu astronomy. Whitney observes : ‘It is evident in the first place that in all their grand features the two systems are essentially the same. Both analyze in the same manner with remarkable success the irregularities of the apparent motions of the planets into the two main elements of which they are made up, and both adoptt he same method of representing and calculating those irregularities. Both substitute likewise eccentric circles for the true eliptic orbits of the planets. Both agree in assigning to Mercury and Venus the same mean orbit and motion as to the sun, and in giving them epicycles which in fact correspond to their heliocentric orbits, making the centre of those epicycles, however, not the true, but the mean place of the sun, and also applying to the latter the corrections due to the eccentricity of the orbit. Both transfer the centre of the orbits of the superior planets from the sun to the earth, and then assign to each, as an epicycle, the earth’s orbit ; not, however, in the form of an ellipse, but in that of a true circle ; and here too both make the place of the centre of the epicycle to depend upon the mean instead of the true place of the sun. . . . . . . The differences between the two systems are much less fundamental and important. The moon’s evection, the discovery of Ptolemy, is equally wanting in the Hindu astronomy. And another innovation introduced into Greek system by Ptolemy is unknown to the Hindus. Ptolemy applies first the whole correction for the eccentricity of the orbit and then corrects the place thus obtained, for the parallax of the earth’s position. The Hindus, on the other hand, apply both the corrections twice. The change of dimensions of the epicycles in the odd and even quadrant is also a striking peculiarity of the Hindu system.”

v2.c15.s1.35

∗ Some of Whitney's arguments have been examined in the proper context. Some of those already examined will be again dealt with further.

v2.c15.s1.36.1

In his final verdict Whitney writes : “The application of *bīja* (empirical correction) to the elements of the *Sūrya-Siddhānta* is calculated at least to suggest the suspicion that Muslim science may have had something to do with it. That observation and the improvement of their system by deductions from observation were ever matters of such serious earnestness with the Hindus that they should have been led to make such amendments independently, is yet to be proved* . . . . The Hindu system is not one of nature ; it is a thoroughly artificial structure, full of arbitrary assumptions, of absurdities even which have no foundation in nature, and could be invented by one as well as another. We need only to refer, as instances, to the framework of monstrous chronological periods to the common epoch of the commencement of the Iron Age, with its exact or nearly exact conjunction of all the planets- to the form of statement of the mean motions, yielding recurring conjunctions, at longer or shorter intervals-to the assumption of a starting-point for the planets at or near *Zeta Piscium*-to the revolutions of the apsides and nodes of the planets-to the double system of epicycles-to the determination of planetary orbits etc., etc. These are plain indications that the Hindu science emanated from one centre ;

v2.c15.s1.36.2

that it was the elaboration of a period and of a school, if not of a single master, who had power enough to impose his idiosyncracy upon the whole nation.” “The question, then, of the comparative antiquity of single treatises** is lost in the higher interest of the inquiry-when, where and under what influence originated the system which they all agree in representing? . . . . We regard the Hindu science as an offshoot from the Greek, planted not far from the commencement of the Christian era, and attaining its fully developed form in the course of the fifth and sixth centuries. The grounds of this opinion we will proceed briefly to state. There can be no question that, from what we know in other respects of the character and tendencies of the Hindu mind, we should not at all look to find the Hindus in possession of an astronomical science containing so much of truth. They have been from the beginning distinguished by a remarkable inaptitude and disinclination to observe, to collect facts, to record, to make inductive investigations . . . . The Hindus have ever been weak in positive science; metaphysics and grammar with, perhaps algebra and arithmetic-being the only branches of knowledge in which they have independently won honourable distinction . . . .

v2.c15.s1.36.3

The infrequency of references to the stars in the early Sanskrit literature, the late date of the earliest mention of the planets, prove that there was no special impulse leading the nation to devote itself to the studying the movements of the heavenly bodies. All evidence goes to show that the Hindus, even after they had derived from abroad a systematic division of the ecliptic, limited their attention to the two chief luminaries, the sun and the moon, and contented themselves with establishing a method of maintaining the concordance of the solar year with the order of the lunar months. If, then, at a later period, we find them in possession of a full astronomy of the solar system, our first impulse is to inquire, whence did they obtain it?” “A closer inspection does not tend to inspire us with confidence in it as of Hindu origin. The whole system may be divided into two portions : one containing truth successfully deduced, the other composed of absurd imaginations drawn from Pauranic literature. The question presses itself, then, strangely upon us, whether these two portions can possibly have the same origin : whether the scientific habit of mind which could lead to the discovery of the one is compatible with those traits which would permit its admixture with the other.

v2.c15.s1.36.4

But most especially, could a system founded—as this, if original, must have been—upon protracted observation of the heavenly bodies, so entirely ignore the ground-work upon which it rested, and refuse and deny all possibility of future improvement by like means, as does this Hindu system, in whose text-books appears no record of an observation, and no confessed deduction from observations ; in which the astronomer is remanded to his text-book as the sole and sufficient source of knowledge, nor even taught or counselled to study the heavens except for the purpose of determining his longitude, his latitude and the local time? Surely, we have a right to say that the system, in its form as laid before us, must come from another people or another generation than that which laid its scientific foundation ; that it must be the work of a race which either had never known, or had had time to forget, the observing habits and the inductive methods of those who gave it origin. But the hypothesis that an earlier generation in India itself performed the labours of which the later system-makers reaped the fruit, is well-nigh excluded by the absence, already referred to, of all evidence in the more ancient literature of deep astronomical investigation : the other alternative, of derivation from a foreign source, remains, if not the only possible, at least the only probable one.” The absurdities to which Whitney alludes here consist of the Yuga system etc.

v2.c15.s1.36.5

But in rejecting the Yuga system which had struck a deep root by tradition among our people, one would only incur the stigma of anti-Vedic heresy as is evident from the strictures passed by Brahmagupta against Romaka. Our astronomers, of course, could not take that risk. Although this may be a serious lapse from the European point of view, it is not so from ours. On the contrary we would rather appreciate the ingenuity that they displayed in reconciling the Yuga system with the hard facts of their science.

v2.c15.s1.37

∗ He means to say that the observations of Hindus had not reached that degree of excellence. Though not quite convinced of the truth of this assertion Whitney suggests that the Hindus may have borrowed their *bīja* correction from some Muslim work. This shows the attitude he has taken up.

v2.c15.s1.38

∗∗ This refers to the estimates about the date of the *Sūrya-Siddhānta*.

v2.c15.s1.39

Whitney further observes : “We come, then, next to consider the direct evidences of a Greek origin. The system of epicycles is essentially alike and the same in both systems. Now, notwithstanding the fact that such secondary circles do in fact represent, to a certain degree, true quantities in nature, there is yet too much that is strange and arbitrary in them to leave any probability to the suppositions that the two nations could have devised them independently. But there are sufficient grounds for believing the Greeks to have actually created their own system, bringing it by successive steps of elaboration to the form in which Ptolemy finally presents it. The Greeks tell us what they owed to the Egyptians, what to the Chaldeans : we trace the conceptions which were the source of their scheme of epicycles, the observations on which it was based, the inductive and deductive methods by which it was worked out and established. In the Hindu astronomy on the other hand, we find neither the conceptions, nor the observations, nor the methods : the whole is gravely put forth as a complete and perfect fabric of divine origin and immemorial antiquity. On the agreement of the two sciences in point of numerical data we will not lay any stress, since it might well enough be supposed that two nations, if once set upon the same track toward the discovery of truth, would arrive independently so near an accordance with nature and with one another.”

v2.c15.s1.40

The scheme of epicycles is not independent in each of the two systems It appears probable that the two systems were inter-related in this respect Whitney, however, does not clearly admit the obvious fact that since the numerical data of the two nations do not agree, it follows that their labours were being carried on independently ; nevertheless, his phrase, “two nations once set upon the same track towards the discovery of truth” amounts to a tacit admission that the researches of the Hindus were independent. Surely no one would say that the researches continued for a day or two and then ended up with the production of some scientific work. The reason why we have no records of ancient observations has already been explained before on page 1.

v2.c15.s1.41.1

Whitney then continues : “The division of the circle, into signs, degrees minutes and seconds, is the same in both systems. Now the names of the first sub-divisions, the signs, are the same in Greece and in India. But with the Greeks they belong to certain fixed arcs of the ecliptic, being derived from the constellations occupying those arcs ; with the Hindus they are applied to successive arcs of 30°, counted from any point that may be chosen : this is an unambiguous indication that the latter have borrowed them, and forgotten or neglected their original significance.” The author for one, considers it particularly important that we disregarded the original significance of the names Aries, Taurus etc. and applied the names to equal divisions, for these names have got no importance of their own. And even if it be true that they were borrowed from others, they were borrowed before Hipparchus, probably from the Chaldeans, as has been shown further on. Whitney then adds : “The Hindu term for ‘minute’ is no Sanskrit word but taken directly from Greek, being liptā. The regents of the days of the week also are not of Hindu origin. On tracing the institution of the week to its very foundation, we find there another Greek word, horā. Once more, in the cardinal operation of finding the true place of a planet, we see that one of the most important data, the mean anomaly, is called by another name of Greek origin, namely Kendra.

v2.c15.s1.41.2

These three words, occurring where they do, not upon the outskirts of the Hindu science, but in its very centre and citadel, amount of themselves almost to full proof of its Greek origin ; taken in connection with the other concurrent evidences, they form an argument which can neither be set aside nor refuted. Moreover, the Hindu treatises and commentaries often refer to the yavanas, “Greeks” or “Westerners,” and to “Yavanācāryas,” “the Greek (or Western) teachers” ; and floating traditions* are met with, to the effect that some of the Siddhāntas were revealed to their human promulgators in Romaka-city, that is to say, at Rome. Farther witness to the same truth, deducible from other coincidences of the two systems, we pass unnoticed here". The question relating to the days of the week has been considered before (p. 275). The *horās* and the days of the week have nothing to do with the knowledge of the true places and motions of planets, even though they did not originate with us. *Kendra* and *liptā* will be dealt with later. In conclusion Whitney observes : "The question next arises, when and in what manner the knowledge of astronomy was communicated from Greece to India. In reply to this, only probabilities offer themselves, yet in some points the indications are pretty distinct.

v2.c15.s1.41.3

It is, in our own view, altogether likely that the science came in connection with the lively commerce which, during the first centuries of our era, was carried on by sea between *Alexandria* as the port and mart of Rome, and the western coast of India and that is why *Ujjayin* became the chief site of the Hindu science. Had the Hindus derived their knowledge overland, through the *Syrian*, *Persian* and *Bactrian* kingdoms, the name of Rome would not have stood forth with such prominence and some city other than *Ujjayin* would have been the cradle of the new science. The absence from the Hindu system of any of the improvements introduced by Ptolemy into that of the Greeks and the fact that the numerical elements adopted by the Hindus vary considerably from those of the *Syntaxis* tend strongly to prove that the transmission of the principal ground work of the Hindu science took place before the time of Ptolemy. Whether the information was transmitted through the medium of Hindus who visited the Mediterranean, or of learned Greeks who made the voyage to India, or by the translation of Greek treatises, or by what other methods, we would not at present even offer a conjecture. Whatever may have been the date of the first communication of that information, there is good reason to suppose that its final reduction to its present form did not take place until some time during the fifth and sixth centuries when the initial point of the fixed sphere coincided with the equinox.

v2.c15.s1.41.4

It is evident that the elaboration of the system must have been a work of time, probably of many generations. Among the changes of method introduced the most useful and important was the substitution of sines for chords* ; the general substitution of an arithmetical for a geometrical form also deserves particular notice. That no great amount of geometrical science is implied in any part of the system is very evident ; the equality of the square of the hypotenuse to the sum of the squares of the base and perpendicular—the comparison of similar right-angled triangles—the formation and combination of proportions, the rule of three—are the characteristic features of the early Hindu mathematical knowledge, as displayed in the *Sūrya-Siddhānta*. Of other treatises which give evidence of knowledge more profound in arithmetic and algebra, we cannot at present speak." It is our good fortune, indeed, that a modicum of praise has fallen to our share from Whitney's pen at last. The writer cannot, however, help adducing here an instance of Whitney's biassed attitude. It consists in this that even though it has become clear at several places, as well as on Whitney's own showing, that the Hindus have borrowed nothing from Ptolemy's works, he characterizes as "not an altogether impossible supposition" the view expressed by Biot that the Hindus obtained their sines directly from the chords of Ptolemy or Hipparchus**.

v2.c15.s1.41.5

Another instance of Whitney's line of reasoning has already been cited while discussing the question of apsides and nodes. (p. 71).

v2.c15.s1.42

∗ This refers to p. 37 verse 7.

v2.c15.s1.43

∗ Though not italicized—by Whitney, these words are printed in bold type in the Marathi original.

v2.c15.s1.44

∗∗ Translation of the *Sūrya Siddhānta*, p. 284.

v2.c15.s1.45

Burgess

v2.c15.s1.46

Let us now turn to the verdict of the Rev. E. Burgess. Burgess was living in India for a number of years and he had a fair knowledge of our manners and customs; on the other hand, Whitney, living in America, was utterly ignorant in this respect. Evidently Burgess was more competent than Whitney to deliver judgment on this question. Burgess writes :—"I had prepared a somewhat extended and elaborate essay on the history of astronomy among the Hindus. But owing to the length of this essay it was not thought advisable to insert it here. However, as my opinions on some points differ from those advanced by Prof. Whitney in his very valuable additions to the notes upon the translation, it seems necessary for me to present at least a brief summary of the results at which I arrived in that essay in reference to the points in question. Prof. Whitney seems to hold the opinion that the Hindus derived their astronomy and astrology almost physically from the Greeks—and what they did not borrow from the Greeks, they derived from other people, as the Arabians, Chaldeans and Chinese, I think he does not give the HINDUS the credit due to them and awards to the Greeks more credit than they are justly entitled to. I admit that the Greeks, at a later period, were the more successful cultivators of astronomical science. And yet, I must think the HINDUS original in regard to most of the elementary facts and principles of astronomy and for the most part also in their cultivation of the science and that the Greeks borrowed from them these facts and principles. For the sake of clearness, I should state more specifically a few of the more important facts and principles of this nature. (1) The division of THE ZODIAC into twenty-seven or twenty-eight asterisms is common, with slight modifications, to the Hindu, Arabian and Chinese systems. (2) As for the division of the Zodiac into twelve signs, the names of the signs are, in their import, precisely the same in the Hindu and Greek systems. The theory of the division and the names of the parts having proceeded from one original source is unquestionably the correct one. (3) The theory of epicycles adopted for finding the motions and true places of planets is common to the Hindu and Greek astronomies. The coincidenc of the two systems in this respect is such as would preclude the idea of indepene-dent origin or invention. (4) Coincidences and even a similarity in some parts-between the systems of astrology received among the Hindus, Greeks and Arabians strongly indicate for those systems, in their primitive and essential elements, a common origin. (5) The names of the five planets known to the ancients, and the application of these names to the days of the week.

v2.c15.s1.47

In regard to these specifications I remark in general :—

v2.c15.s1.48

"First, in reference to no one of them do the claims of any people to the honour, of having been the original inventors or discoverers appear to be better founded than those of the Hindus."

v2.c15.s1.49

"Secondly, in reference to most of them, the evidence of originality I regard as clearly in favour of the Hindus; and in regard to some, and those the more important, this evidence appears to me nearly or quite conclusive."

v2.c15.s1.50

"A brief remark, for the sake of clearness, seems called for in reference to each of the above five specifications :

v2.c15.s1.51.1

(1) As regards the twenty-seven or twenty-eight asterisms, the undoubted antiquity of this division, even in its elaborated form, among the HINDUS, in connection with the absence or paucity* of such evidence among any other people incline me decidedly to the opinion that the division is of a purely Hindu origin. This is still my opinion, notwithstanding the views advanced by *M. Biot* and others in favour of another origin. (2) As regards the division of the Zodiac into twelve parts and the names of those parts, the use of this division, and the present names of the signs, can be proved to have existed in India at as early a period as in any other country and there is evidence less clear and satisfactory, it is true, yet of such a character as to create a high degree of probability, that this division was known to the Hindus centuries before any traces can be found in existence among any other people.

v2.c15.s1.51.2

As corroborative of this position, I may be allowed to adduce the opinions of *Idcler* and *Lepsius* as quoted by *Humboldt* : "Idcler is inclined to believe that the Orientals had names, but not constellations, for the Dodecatomeria and Lepsius regards it as a natural assumption that the Greeks should have added to their own the Chaldean constellations from which the twelve divisions were named." Whether Idcler meant by "Orientals" the Chaldeans, or some other eastern people, the application of the term to the Hindus exactly suits the supposition of the Indian origin of the division in question, since in Indian astronomy the names of the signs are merely names of the twelve parts of the ecliptic, and are never applied to constellations. Humboldt's opinion is, that the twelve divisions of the ecliptic with the names of the signs, came to the Greeks from Chaldea. I think the evidence preponderates in favour of a more eastern, if not a Hindu, origin. (3) The theory of epicycles. The difference in the development of this theory in the Greek and Hindu systems precludes the idea that one of these people derived more than a hint respecting it from the other. But so far as this point alone is concerned, we have as much reason to suppose the Greeks to have been the borrowers as the contrary ; but other considerations seem to favour the supposition that the Hindus were the original inventors of this theory.

v2.c15.s1.51.3

(4) As regards astrology, there is not much honour, in any estimation, connected with its invention and culture. The coincidences that exist between the Hindu and Greek systems are too remarkable to admit of the supposition of an independent origin for them. But the honour of original invention, such as it is, lies, I think, between the Hindus and the Chaldeans. The evidence of priority of invention and culture seems, on the whole, to be in favour of the former ; the existence of three or four Arabic and Greek terms in the Hindu system being accounted for on the supposition that they were introduced at a comparatively recent period. In reference to the so-called Greek words found in Hindu astronomical treatises, I would remark that we may refer them with propriety to that numerous class of words common to the Greek and Sanskrit languages which either came to both from a common source or passed from the Sanskrit to the Greek at a period of high antiquity ; for no one maintains that the Greek is the parent of the Sanskrit, to the extent indicated by this numerous class of words, and by the similarity of grammatical inflections in the two languages. (5) *Herodotus* says : "The names of the gods came into Greece from Egypt". The names of the planets are names of gods. Herodotus's opinion indicates the belief of the Greeks in reference to the origin of these names.

v2.c15.s1.51.4

As to the application of the names of the planets to the days of the week, it is impossible to determine definitely where it originated. Respecting this matter, Prof. H. H. Wilson observes : "The origin of this arrangement is not very precisely ascertained as it was unknown to the Greeks, and not adopted by the Romans until a late period. It is commonly ascribed to the Egyptians and Babylonians, but upon no very sufficient authority, and the Hindus appear to have at least as good a title to the invention as any other people."

v2.c15.s1.52

∗ This point did not strike Whitney.

v2.c15.s1.53

∗ Burgess has cited the sources from which all these quotations have been taken ; but there is no need to repeat them here.

v2.c15.s1.54

"One word on the claims of the Arabians to the honour of original invention in astronomical science. And first, they themselves claim no such honour. That the Arabians were thoroughly imbued with a knowledge of the Hindu astronomy before they became acquainted with that of the Greeks, is evident from their translation of Ptolemy's Syntaxis. It is known that this great work of the Greek astronomer first became known in Europe through the Arabic version. In the Latin translation of this version, the ascending node is called "nodus capitis", i.e., "node of the head", and the descending node, nodus caudee, "node of the tail"—which are pure Hindu appellations. This tact with other evidence, clearly shows the influence of Hindu astronomy on that of the Arabians. Taking all these facts into account, the supposition that these people were the inventors is altogether untenable."

v2.c15.s1.55

"As regards the resemblance between the Greek and Hindu methods of calculating the true places of planets, I think that only hints could have passed from one people to the other, and that at an early period; for on the supposition that the Hindus borrowed from the Greeks at a later period, we find it difficult to see precisely what it was that they borrowed; since in no case do numerical data and results in the systems of the two peoples exactly correspond. And in regard to the more important of such data and results—as for instance, the amount of the annual precession of the equinoxes, the relative size of the sun and the moon as compared with the earth, the greatest equation of the centre for the sun—the Hindus are more nearly correct than the Greeks, and in regard to the times of the revolutions of the planets they are very nearly as correct. There has evidently been very little astronomical borrowing between the Hindus and the Greeks. And in relation to points that prove a communication from one people to the other, I am inclined to think that the course of derivation was the opposite to that supposed by Colebrooke—from east to west rather than from west to east; and I would express my opinion in relation to astronomy, in the language which this eminent scholar uses in relation to some coincidences in speculative philosophy and religious dogmas, especially the doctrine of metempsychosis, found in the Greek and Hindu systems, which indicate a communication from one people to the other: "I should be disposed to conclude that the Indians were, in this instance, teachers rather than learners.""

v2.c15.s1.56

Thibaut

v2.c15.s1.57

The author now presents the views of Dr. Thibaut. In his Introduction to the Pañcasiddhāntikā (page 53) he observes :—

v2.c15.s1.58

"Taken together the five Siddhāntas appear to enable us to form a fairly accurate notion of the transition of old Indian astronomy into its modern scientific form. The Paitāmaha Siddhānta, in the first place, is the representative of the prescientific stage of astronomical knowledge. The Vasiṣṭha Siddhānta, while apparently more advanced than the Paitāmaha Siddhānta, yet seems to have been decidedly inferior to the sastric Siddhāntas. We, therefore, shall most probably not be mistaken in assigning it to the period marking the transition from the old purely indegenous systems to those works which were constructed altogether on the basis of Greek Science. The three remaining Siddhāntas fall under one category, all of them, however much they differ in details, representing the modern phase of Hindu astronomy which is completely under the influence of Greek teaching. The general features of that phase are too well known to require restating in this place. We may, I think, discern certain features in which the Romaka and Pauliśa Siddhāntas agree, while at the same time differing from the Sūrya Siddhānta. In the Sūrya Siddhānta only modern Hindu astronomy has fully assumed that type which it has since preserved....That the similarities observed between the Greek and Hindu systems are due to a transfer of the elements of the former to India will at present be hardly called into doubt; and it certainly appears highly probable that the Pauliśa and Romaka Siddhāntas were the earliest Sanskrit works in which the new knowledge imported from the west was embodied. It certainly is no fortuitous coincidence that one of these two siddhāntas whose names point to the west (the Romaka) used the tropical solar year and calculated its ahargaṇa for the meridian of Yavanapura; and that the other (the Pauliśa) expressly stated the difference in longitude of Yavanapura and Ujjayini*. While thus the general question as to the sources of scientific Hindu astronomy admits of one answer only, doubts begin to suggest themselves as soon as we proceed to ask from what particular Greek works the early Siddhānta writers may have borrowed and to what time the first transmittance of astronomical knowledge has to be assigned. Prof. Whitney has expressed the opinion that the absence from the Hindu system of any of the improvements introduced into Greek astronomy by Ptolemy seems to favour the conclusion that the original transmission of astronomical knowledge into India took place before Ptolemy, which would account for many differences in detail between the Hindu system and the teaching of the Syntaxis. Now with this view we certainly may agree so far as to consider it altogether improbable that the Hindu system should have based directly on Ptolemy's work. Assuming the Hindus to have been acquainted with Ptolemy's work, how shall we explain the numerous discrepancies in essential items of doctrine such as, for instance, the different dimensions assigned to the epicycles of the planets by the Hindus and Ptolemy? But nevertheless it would be hazardous to conclude therefrom that the beginnings of scientific Hindu astronomy go back to a time earlier than that of Ptolemy. The whole question indeed is rendered incapable of decisive treatment by the fact that our knowledge of Greek astronomy anterior to Ptolemy is so very imperfect.

First 76 of 166 passages. Read on

Linked texts (26)