causes, be half a degree too far advanced, and from the fecond, it will be too little advanced by as many feconds as there are years. When the number of years becomes as great as that of the feconds in 30', that is, when it is equal to 1800, the two errors will deftroy one another, and the tables will give the place of the fun perfectly exact. Were we, therefore, to afcertain the age of the tables by Mr Bentley's rule, we should commit an error of 1800 years; from which we may judge of the credit due to that rule as a guide in chronological researches.

This is the rule, however, by which he judges, as far as his argument is purely astronomical, of the antiquity of the Surya Siddhanta. We must confess that we are not much disposed to trust to so precarious a guide. With respect to the evidence derived from other sources, from the written or the traditionary history of Hindostan, we abstain from any opinion at present, and leave it as a discussion more properly belonging to the antiquary than the astronomer.

We shall now state, very briefly, our reasons for thinking, whatever may be true of the books of the Indian astronomy, that the astronomy itself is of great antiquity. After what we have said in his vindication, we shall not be afraid to trust ourselves to the guidance of the historian of astronomy, though we admit that the extent to which he has pushed some of his arguments may require a certain deduction to be made.

The precession of the equinoxes is one of the celestial phenomena which has been found of the greatest use in researches like the present. It was by means of it that Sir Isaac Newton determined the date of the expedition of the Argonauts, the great hinge of his chronological system. The very same means of investigation, offers itself in the present question. M. Le Gentil brought with him from India the delineation of a zodiac, on which the constellations and the principal fixed stars are marked with considerable accuracy. The Indian zodiac is moveable; it begins with a certain point in the starry heavens, which is supposed to move forward from the point of the vernal equinox, at the rate of 54" annually. Now,. in the zodiac of Le Gentil, the star Aldebaran has the longitude of 53° 20′ reckoned from the beginning of it. But, according to the Brahmens, at the commencement of the Cali Yug, or in the year 3102 before the Christian era, the beginning of the zodiac was 54° west of the vernal equinox, and therefore Aldebaran which was 53° 20' east of the former point, was 40' to the westward of the latter, or of the vernal equinox. Now, let us see, according to our astronomy, where Aldebaran actually was at the same epoGg 4

cha

cha. The longitude of that star, or its distance eastward from the vernal equinox, in the year 1750, according to the best observations, was 66° 17' 47"; and therefore, reckoning back, or westward from thence, 50 annually, (which is the mean rate of the precession of the equinoxes), we shall find that 3102 years before Christ, Aldebaran was 1° 32' west of the vernal equinox. The Indian computation made the same star 40 west of the same point: the difference is only 52', which is very ing considerable, and answers in time to about 60 years. This coincidence is the more remarkable, that the Brahmens by their own rule of allowing 54" for the annual precession, could not have assigned the same place to Aldebaran, by four or five de grecs, if they had calculated back from a modern observation. This gives a high probability to the supposition, that the zodiac in question represents the state of the heavens for the beginning of the Cali-Yug; at least, it must be allowed, that we have as good authority for believing so, as for holding the sphere of Chiron and Musæus to have been constructed, and the expedition of the Argonauts to have taken place, 1263 years before the Christian era.

Let us next inquire how the places of the fun and moon, as given by the tables of Trivalore for the beginning of the CaliYug, agree with computations made from the most correct tables of our modern aftronomy. If the author of the former tables calculated back to the distance of more than four thousand years from a modern obfervation, we may be well affured that he has afforded fufficient data for detecting the impofition. Nothing but aftronomy in its most perfect state, enriched with the conclufions derived from the theory of gravitation, is capable of afcending fo far into the ages that are paft; and, unless both had copied from nature, there is furely no probability that the fimple and imperfect methods of the Brahmen fhould coincide with the refined calculus of the European aftronomer,

M. Bailly calculates from the tables of Trivalore, that at their epoch answering to midnight between the 17th and 18th of Feb ruary of the year 3102 before our era, the mean place of the fun was 10 3° 38' 13". The fame calculated from La Caille's tables is os 1° 5' 57", to which must be added, 1o 45′ 22′′, on account of an inequality in the precetion of the equinoxes difco vered by La Grange, (Mem. Acad. Berl. 1782, p. 287.) making altogether 10s 2° 51' 10", not more than 47' different from the Indian Tables. This fecond coincidence adds much to the probability that the Indian tables give the places of the heavenly bodies, from observations not much more recent than the ancient epoch to which they profefs to be adapted.

The

The moon's motion affords another remarkable verification of these refults. The place of the moon calculated from Mayer's tables for the inftant of the beginning of the Cali-Yug, as above defined, to the meridian of Benares, is 10' 0° 51′ 16′′. This is on the fuppofition, that the moon's mean motion has been always at the fame cate as at the beginning of the laft century. But it is known that the moon's motion was flower in former ages; and, on counting back, is found uniformly retarded, at the rate of 9" in a century. This quantity accumulating as the fquares of the times, amounts, in 4801 years, to 5° 45' 44", which, added to the mean place already found, gives 10s 6° 37'. But the fame calculated from the Trivalore Tables is 10s 6o o', fo that the difference does not amount to two thirds of a degree. This coincidence, if we confider that the allowance for the retardation of the moon in past ages is an element quite unknown to the Brahmens, can be referred to no source but actual obfervation.

Let us now make the fame experiment with the tables of the Greek and Arabian aftronomers, by deducing from them the places of the fun and moon, for the epoch of the Cali-Yug. If we take the tables of Ptolemy, and go back from the era of Nabonaffar to that just mentioned, including the difference between the meridians of Alexandria and Trivalore, we fhall find the longitude of the fun 10° 13° 59' 28", and that of the moon 10° 17° 52' 7", each differing more than 11° from the places that have just been calculated.

If we next appeal to the tables of the Tartar prince ULUGHBEIGH, constructed in the year 1437 at Samarcand, not far from India, and deduced from a comparison of the Arabic and the Greek obfervations, we find that in place of the fun for the beginning of the Caly-Yug, there is an error of 1o 30', and in that of the moon of no less than 6°.

On confidering all these circumstances, the coincidence on the one hand, and the difference on the other, what is the conclufion that any man of plain fenfe and tolerable impartiality will be inclined to draw? When he finds the calculus of the Indian Brahmens more accurate than that of the astronomers of Greece and Arabia, and agreeing in its delineation of the state of the heavens, at a remote epocha, with the improved aftronomy of modern Europe, can he doubt that it is from having had access to records which went back to that epocha, that this fuperior accuracy is derived? The aftronomers of Greece, and even of Tartary, had every advantage above thofe of Hindoftan, except what might be derived from the antiquity of fcience; and yet they have fallen into great errors, which the latter have entirely avoided. Is it

not

not, therefore, to the antiquity of their science alone, that the aftronomers of India are indebted for this proud diftinction?

The arguments here stated muft, we think, be acknowledged to give great probability to the opinion, that the art of aftronomical obfervation is of high antiquity in India, and goes back not lefs than 3000 years before the Christian era. We must not, however, fuppofe that this conclufion extends to the books or tables of this aftronomy, as they now exift. A fcience muft always be older than the books that treat of it. This is particularly the cafe with aftronomy, which must have been cultivated for many ages before any thing entitled to the name of an astronomical table could poffibly exift. Our argument goes no further than to prove, that obfervations were made and recorded at such a remote date as has just been mentioned; and that those observations were fubfervient to the conftruction of the tables now exifting in India. It is material to obferve, that this is the true state of the question; and that our argument does not immediately concern the date of the prefent books of aftronomy, or the age of the authors by whom they were compofed. The tables, many of them, do not profess to be very ancient; those of Kistnabaram are not said to be older than 1491; and the tables of Trivalore, the most accurate of all, as far as we know, may be no older than Mr Bentley supposes.* All this, however, is quite compatible with the greater antiquity of the fcience. The works that have now been mentioned, and indeed all the aftronomical books in India, of which we have any information, are obviously derived from others more perfect and more extenfive than themselves, and must be regarded as an abridgement or compendium of a science that has existed in a fuller and more enlarged form. What the revolutions were by which this change has been effected, is not the fubject of the prefent inquiry, and falls not within our province to difcufs. But it is proper to obferve, that our pofition may be true; and the affertions of Mr Bentley, concerning the age of the authors of the books we have been treating of, and alfo of the Surya Siddhánta, may also be perfectly juft. The fcience and the books mult by no means be identified; and it is by doing this improperly that fo

much

The tables of Siam

*The dates of the actual compofition of the tables were fully understood to be modern before Mr Bentley wrote. were referred by Caffini to the year 638 of our era; thofe of Kittnabaram by M. Bailly to 1491; and thofe of Narfapoor to 1569. In thofe of Trivalore, there is a date, as the fame aftronomer obferves, that comes down to 1282 of our era.

1

much room has been given for controversy, in a question, where, if not the truth, yet furely the probability, is very clearly to be distinguished.

When M. Bailly's account of the Indian aftronomy made its appearance, the Surya Siddhanta was hardly known in Europe. The inftitution of the Afiatic Society, which has been of fuch benefit to all that regards the antiquities of India, could not fail to make us fpeedily acquainted with a work that was held in the highest estimation over all the Eaft. The antiquity of it has been conceived to be very great, as it is reckoned the most ancient astronomical treatise of the Hindoos; but, according to Mr Bentley, that antiquity extends to no more remote period than the year 1068 of our era. The main argument on which this determination is founded, feems to us fubject to confiderable difficulty. (Afiatic Refearches, vol. VI. p. 544, and 568, &c.; also vol. VIII. p. 216.) It fuppofes, what is by no means certain, that the Hindoo aftronomers deduced the mean motions of the planets from a comparison of a real obfervation with one that was purely fictitious. This is nowhere proved by Mr Bentley, though taken as the basis of all his computations. It is more likely that the Brahmens deduced thofe motions as all other astronomers have done, from a comparison of two or more observations made at a great distance of time. The first mentioned method could not affift them in the outfet; and before they could employ it at all, they must have made use of that which has been laft mentioned. For, fuppofe that the Hindoo aftronomer was difpofed to proceed in the manner now defcribed, and that, knowing the place of the fun and moon at a particular inftant, by his own obfervation, he affumed, as a fact, that these bodies were in conjunction in a certain point of the heavens 648000 years ago. In order to deduce any confequence from this fuppofition, he must know how many days are in 648000 years, and also how many revolutions of the moon are contained in that period. But whence does he derive this information? It is the very thing which he is fupposed to be in fearch of; fo that we have here a real begging of the question, a petitio principii, such as a theorist, fitting in his cabinet, has often enough been guilty of, but which no practical artist was ever in danger of committing. We have therefore demonstrative evidence, that neither the foundation of the Hindoo, nor of any other fyftem, was laid on the principle which is here referred to. If indeed that principle was ever employed, it must have been in adjusting and altering the refults that had been obtained from an actual comparison of obfervations;

* Afiatic Researches, vol. VI. p. 539.

*

and