the comparatively recent date of the extravagant pretensions made by Hindu astronomers is simply this. In European astronomy, the mean motions of the heavenly bodies are computed from a comparison of observations, made at a distant period, with those recently taken. The unavoidable errors of observation will be thus spread uniformly over the whole intervening time: and the mean motions will be obtained with considerable accuracy. A still further degree of precision is obtained by introducing corrections first pointed out by the theory of gravitation, and confirmed by subsequent observation. Now it appears that the Hindus, in the formation of their artificial systems, proceed upon a different principle. They assume a given position of the heavenly bodies at a very distant epoch; and then compute such mean motions as would give the position of the bodies at the time for which the tables were computed. If the epoch be sufficiently remote, and the assumed configuration approximately correct, the mean motions thus computed will differ by a very small quantity from the true mean motions, or from the mean motions which are presumed to be accurately determined by the European method. But the error which arises from this source affords the means of computing the very time when it was first committed. The

motions will have been assumed so that the computed place nearly agreed with the observed place at the time when the tables were constructed. But, if the tables be erroneous, the coincidence will no longer exist, when the computation is made for any other æra. And the amount of the accumulated error will be greater in proportion as the time is more remote. By noticing, therefore, the difference between the places of the heavenly bodies as computed by the European and Hindu methods, for different epochs, if the results indicate a continually increasing error both before and after a particular period, the time at which the tables were computed will be approximately obtained. For it will be the time at which the positions computed by the tables agree most nearly with the true positions previously known.

The antiquity of the system may also be discovered, if the total error, at any given time be known, and also the error in the mean annual motions which are assigned respectively to the heavenly bodies.

The degree of accuracy which is thus attainable will evidently vary with the number of independent calculations, and with the reliance which can be placed upon our own tables. But when many such calculations agree in pointing out the same time, a degree of cer

tainty is obtained, from which no reasonable mind can withhold its assent.

This principle being applied to the tables of the Hindus, which have been appealed to, as establishing the great antiquity of their astronomy, and the consequent authority of their own claim to immense antiquity, it has been shewn that none of their artificial systems are ancient; the earliest extending only to the beginning of the sixth century of the Christian æra: and that the dawn of astronomy in India can be traced back only to about fourteen centuries before the coming of Christ.

The same conclusion has been drawn respecting the date of a different method of computation.

In the calculation of eclipses of the sun, as now practised in India by the Brahmins, who appear generally ignorant of the principles upon which their computation is founded, it is necessary to add a certain correction for precession. And this correction is such, that it would have been nothing about five hundred years after the Christian æra. From this circumstance alone it was concluded that the peculiar method of calculation was introduced at that period.x

x Montucla, Histoire des Mathematiques, Part II. Liv. 1. f. 3. See Le Gentil, Voyage dans les mers des Indes: and Mem. de 1'Academie, 1772.

But, whether the astronomical computations of the Hindus are derived, as is pretended, from real observations made full three thousand years before the Christian era, or not, the chronological system founded upon them is evidently artificial. The very inspection of them is sufficient to satisfy the enquirer, that they are the production of an ingenious but fanciful people, well skilled in numerical computation, and undeterred by periods of any length. That the ages of the world, marked by great natural catastrophesy should be arranged in periods according to a fixed numerical law—that the length of human life should at the end of each be diminished in a determinate ratio—to say nothing of the corresponding alteration of the moral character of mankind in every age, and the various degrees of illumination which are supposed to have been præternaturally imparted, are suppositions so evidently imaginary that to mention them is to confute them. When it is further considered that the Hindus are beyond all others skilful in committing the most notorious forgeries to give a colour to their fanciful schemes,

y Les Indiens disent que chacun de leur ages a fini par un deluge. See Bailly, Astronomie Indienne et Orientale. Discours Prelim. p. cii. ciii. Sir W. Jones on the Gods of Greece, Italy, and India: Asiat. Researches, Vol. I.

the degree of importance, which has sometimes been attached to their pretensions, will be found far greater than they really de

serve.

It is, besides, very remarkable, that the same astronomical systems, which have been held forth as opposing the Mosaic chronology, actually confirm it. The date ascribed to the commencement of their age, called the Kali Yuga, in their more modern systems of astronomy, has been shewn, with as much accuracy as the subject allows, to be that which the Septuagint version of the Scriptures ascribes to the general deluge: and is the same which was used by the Arabians, and also adopted in the celebrated astronomical 'ables constructed by order of Alphonsus king of Sevile. In the system of chronology also which existed among the Hindus two hundred years before Christ, their history was divided into astronomical periods, at the beginning of which they then placed the creation of the world. And the

See Bailly, Astron. Indienne: Discours Prelim. Part II. p. xxxvi. Upon this point Montucla thus expresses himself: "II resterait a determiner lesquels des Indiens ou des Hebreux sont les originaux ou les copistes. Si nous croyons a l'inspiration des livres saints, nous ne devons pas etre embarasses. Mais dans ce siecle philosophique, qui oserait, sans se vouer au ridicule, appuyer sur une pareille raison?" Hist. des Math. Part II. Liv. UI. Vol. I. p. 428

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