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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, iş 10% 0° 51' 16". This is on the fuppofition, that the moon's mean motion has been always at the same ate as at the beginning of the last century. But it is known that the moon's motion was flower in former ages; and, on count. ing back, is found uniformly retarded, at the rate of o" in a century. This quantity accumulating as the squares of the times, amounts, in 4801 years, to 5° 45'44", which, added to the mean place already found, gives los 60 37'. But the same calculated from the Trivalore Tables is 10$ 6° 0', so that the difference does not amount to two thirds of a degree. This coincidence, if we congder that the allowance for the retardation of the moon in past ages is an element quite unknown to the Brahmens, cán be referred to no source but actual observation. · Let us now make the fame experiment with the tables of the Greek and Arabian astronomers, by deducing from them the places of the sun and moon, for the epoch of the Cali-Yug. If we take the tables of Ptolemy, and go back from the era of Nam bonaffar to that just mentioned, including the difference between the meridians of Alexandria and Trivalore, we shall find the longi. tude of the sun 10% 13° 59' 28", and that of the moon 105 170 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 observations, 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 6°. · On considering all these circumstances, the coincidence on the one hand, and the difference on the other, what is the conclusion that any man of plain sense 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 superior accuracy is derived ? The astronomers of Greece, and even of Tartary, had every advantage above those 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

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

The arguments here stated must, we think, be acknowledged to give great probability to the opinion, that the art of astronomical observation is of high antiquity in India, and goes back not less than 3000 years before the Christian era. We must not, however, suppose that this conclusion extends to the books or tables of this astronomy, as they now exist. A science must ale ways be older than the books that treat of it.. This is particularly the case with astronomy, which must have been cultivated for many ages before any thing entitled to the name of an astronomical table could possibly exist. Our argument goes no further than to prove, that observations were made and recorded at such a remote date as has just been mentioned; and that those observations were subservient to the construction of the tables now existing in India. It is material to observe, that this is the true state of the question; and that our argument does not immediately concern the date of the prefent books of astronomy, or the age of the authors by whom they were composed. 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 science. The works that have now been mentioned, and indeed all the astronomical 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 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 subject of the present inquiry, and falls not within our province to discuss. But it is proper to observe, that our position may be true ; and the affertions of Mr Bentley, concerning the age of the authors of the books we have been treating of, and also of the Surya Siddhanta, may also be perfectly juft. The science and the books must by no means be identified; and it is by doing this improperly that so

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* The dates of the actual composition of the tables were fully un. derstood to be modern before Mr Bentley wrote. The tables of Siam were referred by Cassini to the year 638 of our era ; those of Kittnabaram by M. Bailly to 1491; and those of Narsapoor to 1569. In those of Trivalore, there is a date, as the same astronomer observes, that comes down to 1282 of our era.

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

When M. Bailly's account of the Indian astronomy made its appearance, the Surya Siddhanta was hardly known in Europe. The institution of the Asiatic Society, which has been of fuch benefit to all that regards the antiquities of India, could not fail to make us speedily acquainted with a work that was held in the highest estimation over all the East. The antiquity of it has been conceived to be very great, as it is reckoned the most ancient astro. nomical 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, seems to us subject to considerable difficulty. (Afiatic Researches, vol. VI. p. 544, and 568, &c.; also vol. VIII. p. 216.) It supposes, what is by no means certain, that the Hindoo altro. nomers deduced the mean motions of the planets from a compari. son of a real observation 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 those 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 assist them in the outset; and before they could employ it at all, they must have made use of that which has been last mentioned. For, suppose that the Hindoo astronomer was disposed to proceed in the manner now defcribed, and that, knowing the place of the sun and moon at a particular instant, by his own observation, he assumed, as a fact, that these bodies were in conjunction in a certain point of the heavens * 648000 years ago. In order to deduce any consequence from this supposition, 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 supposed to be in search 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 system, 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 results that had been obtained from an actual comparison of observations;

and

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

and would then only have the effe&t already pointed out, of retarding the progress of astronomical improvement.

In some parts of the argument, we acknowledge, however, that Mr Bentley's reasoning is less exceptionable. The mean motions of the moon, and of the planets that are liable to secular equations of very long periods, and of which the law is known, are very proper for affording the means of judging when the Hindoo determinations of those motions were made. The disquisition, however, to which this leads, is a very delicate one, and appears to us to require the solution of some analytical problems of confiderable difficulty. Were we, from the statement which Mr Bertley has given of the moon's mean motion from the Surya Siddlánta, (where it is considerably flower than in the present age), to form a grofs estimate of the age of that book, we should be disposed to refer it to a more remote antiquity than any that has been yet ascribed to the astronomy of India. But on this eftimate we can place no reliance, as it is made without the previous investigations which have just been hinted at.

Many collateral arguments might be brought from other quarters to support the antiquity of the Indian astronomy. Beside the mean motions, several other elements in the tables have the appearance of belonging to a very remote period. The obliquity of the ecliptic, the length of the solar year, the aphelion of Jupiter, the equation of Saturn's centre, and the mean motion of both these planets, correspond well with the commencement of the Caly-Yug. Another element, the equation of the sun's centre, to which the Hindoo tables assign a magnitude considerably larger than it has at present (2° 10' 32", instead of 1° 55') is regarded by M. Bailly as leading to the same conclusion. It is indeed certain, that the irregularity just referred to was greater in former ages than it is in the present; and that the earth's orbit is tending more and more to circularity, when, for a time at least, the equation just mentioned will entirely vanish. LA PLACE, however, has taken notice of a circumstance which escaped the observation of his brother academician, and which tends to invaa lidate the conclusion which he drew from the above mentioned irregularity. The equation to the sun's centre, as given in the Hindoo tables, includes in it that equation or irregularity of the moon's motion, known by the name of the Annual Equation. This happens, because it is the object of those tables to exhibit the relative motion of the sun and moon, at the time of the eclipses of these luminaries. They, therefore, have very naturally united together the irregularities that belong to each of the bodies, and have considered the amount as belonging only to one of them, by

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which their relative motion is equally well represented, and, apparently, with more simplicity. The blending together of these two irregularities, has therefore produced a greater equation of the sun's centre than is admitted in our astronomy, where they are separately considered. This observation, therefore, takes away the force of one of M. Bailly's arguments, though we must say that, nevertheless, it does not materially affect his general conclusion. We have stated this the more particularly, both because impartiality required that we should conceal nothing that affected the argument either way, but because we think that, after twenty years, during which the Astronomie Indienne has been before the public, this is the only argument contained in it, that, on fair and solid grounds, can be said to have lost any of its force.

Beside the arguments that tend immediately to prove the antiquity of the astronomy of the Hindoos, there are others that do so indirectly, by marking it as a system distinct from those that are known to have existed in Greece and Arabia, the only countries, it would appear, from which India can have borrowed. We had occasion already to remark the great difference between the tables of Trivalore and those of Ptolemy, and of Ulugh-Beigh, when we calculated from them the places of the sun and moon at the beginning of the Cali-yug. We might remark the same sort of dissimilitude on comparing them either with the Arabic or the Persian tables, so that thty seem essentially distinguished from all the systems of ancient astronomy, of which any distinct records have been preserved.

In several of the other astronomical methods, not contained imdiately in the tables, the same appearance of originality is discovered. Such is the rule by which the Brahmen of Trivalore, who ins structed Le Gentil, computed the length of the day, at the different seasons of the year. That ruie consisted in an approximation to a trigonometric result, made by a method quite peculiar, and applicable only to very low latitudes. The trigonometry contained in the Surya Siddhanta, of which Mr Davis has given so curious an account, is very different from any thing of the same sort that we meet with in other quarters. The theorem from which the investigation of the sines is deduced in that trigonometry, has been pointed out (Edin. Trans. vol. IV.), and is a proposition that was known to the Greek geometers, but not applied by them in a way at all similar to that explained in the Surya Siddhanta. The remark on which the computation in that work proceeds, that each number in the tables is related in the same way to the two that go before it, is abundantly subtle, and escaped the mathematicians of Europe, till within two centuries of the present time.

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