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thirds of a degree, which, for so remote a period, and considering the acceleration of the moon's motion, for which no allowance could be made in an Indian calculation, is a degree of accuracy that nothing but actual observation could have produced.

To confirm this conclusion, Mr. Bailly computes the place of the moon for the same epoch, by all the tables to which the Indian astronomers can be supposed to have ever had access. He begins with the tables of Ptolemy; and if, by help of them, we go back from the æra of Nabonassar to the epoch of the Kaly-Yug, taking into account the comparative length of the Egyptian and Indian years, together with the difference of meridians between Alexandria and Tirvalore, we shall find the longitude of the sun, 10° 21′ 15′′ greater, and that of the moon 11° 52′ 7′′ greater, than has just been found from the Indian tables. At the same time that this shews how difficult it is to go back, even for a less period than that of 3000 years, in an astronomical computation, it affords a

proof altogether demonstrative, that the Indian astronomy is not derived from that of Ptolemy.

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The tables of Ulugh Beig are more accurate than those of the Egyptian astronomer. They were constructed in a country not far from India, and but a few years earlier than 1491, the epoch of the tables at Krishnapouram. Their date is July the 4th, at noon, 1437, at Samarcand; and yet they do not agree with the Indian tables, even at the above-mentioned epoch of 1491. But for the year 3102 before Christ, their difference from them in the place of the sun, is 1°30′, and in that of the moon 6; which, though much less than the former differences, are sufficient to prove, that the tables of India are not borrowed from those of Tartary.

“The Arabians employed in their tables the mean motions of Ptolemy; the Persians did the same, both in the more ancient tables of Chrysococca, and the later ones of Nassireddin. It is therefore certain, that the astronomy of the Brahmins is neither

derived from that of the Greeks, the Arabians, the Persians, or the Tartars. This appeared so clear to Cassini, though he had only examined the tables of Siam, and knew nothing of many of the great points which distinguish the Indian astronomy from that of all other nations, that he gives it as his opinion, that these tables are neither derived from the Persian astronomy of Chrysococca, nor from the Greek astronomy of Ptolemy; the places they give at their epoch to the apogee of the sun and of the moon, and their equation for the sun's centre, being very different from both.*

"A formula + for computing this inequality" (in the moon's motion) "has been given by M. de la Place, which though only an approximation, being derived from theory, is more accurate than that which Mayer deduced entirely from observation ; and if it be taken instead of Mayer's, which

* See Trans. of the Royal Society of Edinburgh, vol. ii. p. 155, &c.

+ Ibid. p. 160.

last, on account of its simplicity, I have employed in the preceding calculations, it will give a quantity somewhat different, though not such as to affect the general result. It makes the acceleration for 4383 years, dated from the beginning of the Kaly-Yug, to be greater by 17′ 39′′ than was found from Mayer's rule; and greater, consequently, by 16' 32", than was deduced from the tables of Krishnapouram. It is plain, that this coincidence is still near enough to leave the argument that is founded on it in possession of all its force, and to afford a strong confirmation of the accuracy of the theory, and the authenticity of the tables.

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That observations made in India when all Europe was barbarous or uninhabited, and investigations into the most subtle ef fects of gravitation, made in Europe near five thousand years afterwards, should thus come in mutual support of one another, is perhaps the most striking example of the progress and vicissitude of science, which the history of mankind has yet exhibited.

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This, however, is not the only instance of the same kind that will occur, if, from examining the radical places and mean motions in the Indian astronomy, we proceed to consider some other of its elements; such as, the length of the year, the inequality of the sun's motion, and the obliquity of the ecliptic, and compare them with the conclusions deduced from the theory of gravity by M. de la Grange. To that geometer, physical astronomy is indebted for one of the most beautiful of its discoveries, viz.-That all the variations in our system are periodical; so that, though every thing, almost without exception, be subject to change, it will, after a certain interval, return to the same state in which it is at present, and leave no room for the introduction of disorder, or of any irregularity that might constantly increase. Many of these periods, however, are of vast duration. A great number of ages, for instance, must elapse, before the year be again exactly of the same length, or the sun's equation of the same magnitude, as

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