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.

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

at present. An astronomy, therefore, which professes to be so ancient as the Indian, ought to differ considerably from ours in many of its elements. If, indeed, these differences are irregular, they are the effects of chance, and must be accounted errors; but if they observe the laws, which theory informs us that the variations in our system do actually observe, they must be held as the most undoubted marks of authenticity." "'*

Professor Playfair then proceeds to examine this question, as M. Bailly has done; and we are persuaded, if the reader will impartially peruse the investigations of these learned men, he will be satisfied that the differences alluded to, are neither the effects of chance, nor can be accounted errors.

After examining the duration given to the year by the Brahmins at the period of the Kaly-Yug, Mr. Playfair proceeds:

"The equation of the sun's centre is an

* See Trans. of the Royal Society of Edinburgh, vol. ii. p. 160, &c.

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element in the Indian astronomy, which has a more unequivocal appearance of belonging to an earlier period than the KalyYug.* The maximum of that equation is fixed, in these tables, at 2° 10′32′′. It is at present, according to M. de la Caille, 1° 55', that is 15' less than with the Brahmins. Now, M. de la Grange has shewn, that the sun's equation, together with the eccentricity of the earth's orbit, on which it depends, is subject to alternate diminution and increase, and accordingly has been diminishing for many ages. In the year 3102 before our æra, that equation was 2° 6' 28" less only by 4', than in the tables of the Brahmins. But, if we suppose the Indian astronomy to be founded on observations that preceded the Kaly-Yug, the determination of this equation will be found to be still more exact. Twelve hundred

* M. Bailly, in his remarks on the length of the years, supposes some of the observations of the Brahmins to have been made during a period often mentioned by them, of 2,400 years before the Kaly-Yug.

years before the commencement of that period, or about 4300 before our æra, it appears, by computing from M. de la Grange's formula, that the equation of the sun's centre was actually 2° 8′ 16′′; so that if the Indian astronomy be as old as that period, its error with respect to its equation is but 2′.*

The obliquity of the ecliptic is another element in which the Indian astronomy and the European do not agree, but where their difference is exactly such as the high antiquity of the former is found to require. The Brahmins make the obliquity of the ecliptic 24°. Now M. de la Grange's formula for the variation of the obliquity, gives 22′32′′, to be added to its obliquity in 1700, that is, to 23° 28′ 41′′, in order to have that which took place in the year 3102 before our æra. This gives us 23° 51′ 13′′,

which is 8′ 47′′ short of the determination of the Indian astronomers. But if we sup

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* See Trans, of the Royal Society of Edinburgh, vol, ii. p. 163.