Let us next confider the criterion which Mr Bentley himself proposes for determining the age of a fyftem of astronomical tables, from the confideration of the tables themselves, independently of teftimony, tradition, or any external evidence. Such a criterion is precifely the thing wanted on the prefent occafion, but we can by no means approve of that particular one which he endea vours to establish. It is founded on this maxim, that the time of the construction of any fet of tables must be that at which they agree befl with the heavens. Hence, when such tables are given, and we wish to determine their antiquity, we have only to compute from them, the places of the fun and moon, &c. for different times confiderably distant from one another: to compare these places with thofe given by the beft modern tables, and the time when they approach the nearest to one another, is to be taken for the time when the tables were constructed. As it must be an object, in all aftronomical tables, to reprefent the ftate of the heavens tolerably near the truth at the time when they are compofed, it must be allowed that this rule is not deftitute of plaufibility. On examination, however, it will be found very fallacious, and fuch as might lead into great mistakes.

Astronomical tables are liable to errors of two different kinds, that may sometimes be in the fame, fometimes in oppofite directions. One of them concerns the radical places at the epoch from which the motions are counted; the other concerns the mean motions themfelves, that is to fay, the mean rate or angular velocity of the planet. Of thefe the first remains fixed, and its off et at all times is the fame; the fecond again is variable, and its effect increafes proportionally to the time. If, therefore, they are oppofite, the one in excefs, and the other in defect, they mun partly destroy one another; and the one increafing continually, will at length become equal to the other, when there will, of confequence, be no error at all; atter which the error will fall on the oppofite fide, and will increase continually. Here, the moment of no error, or that when the tables are perfectly correct, is evidently diftant from the time of the conftruction of the tables, and may be very long, either before, or after that period. Suppofe, for example, that, in conftructing tables of the fun's motion, we are to fet off from the beginning of the prefent century, and that we make the fun's place for the beginning of the year 1801 more advanced by half a degree than it was in reality. Suppose, alfo, that the mean motion fet down in our tables is erroneous in a way oppofite to the former, and is lefs than the truth by 1" in a year. The place of the fun then as affigned from the tables for every year, fubfequent to 1800, will, from the firft of the above

causes,

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 fhould 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 inconsiderable, 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 degrees, 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 Museus 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 moft correct tables. of our modern afronomy. If the author of the former tables calculated back to the diftance 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 molt perfect ftate, enriched with the conclufions. derived from the theory of gravitation, is capable of afcending so far into the ages that are paft; and, unlefs 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 anfwering to midnight between the 17th and 18th of February of the year 3102 before our era, the mean place of the fun was 105 3° 38' 13". The fame calculated from La Caille's tables is 10s 1° 5' 57', to which must be added, 1° 45′ 22′′, on account of an inequality in the preceffion of the equinoxes difcovered by La Grange, (Mem. Acad. Berl. 1782, p. 287.) making altogether 10 2° 51' 1", 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 obfervations 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 results. The place of the moon calculated from Mayer's tables for the instant of the beginning of the Cali-Yug, as above defined, to the meridian of Benares, is 10 0° 51' 10". This is on the supposition, that the moon's mean motion has been always at the fame rate as at the beginning of the last 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 6° 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 paft 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 1° 30′, and in that of the moon of no less than 6o.

On confidering all thefe circumftances, 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 aftronomers 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 accefs 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 Hindostan, except what might be derived from the antiquity of science; 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 ftated 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 less than 3000 years before the Chriftian 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 aftronomical table could poffibly exift. Our argument goes no further than to prove, that obfervations were made and recorded at fuch a remote date as has just been mentioned; and that thofe obfervations were fubfervient to the conftruction of the tables now exifting in India. It is material to obferve, that this is the true ftate 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 profeís to be very ancient; those of Kistnabaram are not faid 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 fuppofes.* 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 extensive than themselves, and must be regarded as an abridgement or compendium of a fcience that has exifted in a fuller and more enlarged form. What the revolutions were by which this change has been effected, is not the subject 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 muft by no means be identified; and it is by doing this improperly that fo much

The dates of the actual compofition of the tables were fully understood to be modern before Mr Bentley wrote. The tables of Siam were referred by Caffini to the year 638 of our era; thofe of Kiftnabaram 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.