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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:

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* 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 2o 8′ 16′′; so that if the Indian astronomy be as old as that period, its error with respect to its equa

tion 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

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

pose, as in the case of the sun's equation, that the observations on which this determination is founded, were made 1200 years before the Kaly-Yug, we shall find that the obliquity of the ecliptic was 23° 57′ 45′′, and that the error of the tables did not much exceed 2'.

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Thus do the measures, which the Brahmins assign to these three quantities, the length of the tropical year, the equation of the sun's centre, and the obliquity of the ecliptic, all agree, in referring the epoch of their determination to the year 3102 before our æra, or to a period still more ancient. This coincidence in three elements, altogether independent of one another, cannot be the effect of chance. The difference, with respect to each of them, between their astronomy and ours, might singly, perhaps, be ascribed to inaccuracy ; but that three errors, which chance had introduced, should be all of such magnitude as to suit exactly the same hypothesis concerning their origin, is hardly to be conceived. Yet there is no other alterna

tive, but to admit this very improbable supposition, or to acknowledge that the Indian astronomy is as ancient as one or other of the periods abovementioned.

"In seeking for the cause of the secular equations, which modern astronomers have found it necessary to apply to the mean motion of Jupiter and Saturn, M. de la Place has discovered, that there are inequalities belonging to both these planets, arising from their mutual action on one another, which have long periods, one of them no less than 877 years; so that the mean motion must appear different, if it be determined from observations made in different parts of those periods. Now I find' (says he) by my theory, that at the Indian epoch of 3102 years before Christ, the apparent and annual mean motion of Saturn was 12° 13′ 14′′, and the Indian tables make it 12° 13′ 13′′. In like manner, I find that the annual and apparent mean motion of Jupiter at that epoch, was 30° 20′ 42′′, precisely as in the Indian astronomy."

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"Thus have we enumerated no less than

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