regulation of the calendar, the rules given in the Vedas prescribed that a month should be doubled in the middle and at the end of the quinquennial period; which consequently consists of three common lunar years and of two, containing, each, thirteen lunations: the year is divided into six seasons, and each month into two half months; the day also, is said to consist of 30 hours, a division which, according to Achilles Tatius, was in use among the Chaldeans, and each hour, of 60 minutes. The zodiac is, moreover, divided into 27 signs, and the first is said to include the cluster of stars denominated Crittica which is supposed to signify the Pleiades: this supposition however, is at variance with the general opinion concerning the place at which the Hindu zodiac commenced, but it is probable that the latter did not become fixed till long after the age of which we are speaking. In a note, Mr. Colebrook observes that the cycle of 5 years is mentioned by the name of Yuga in Parasara's Institutes, and it is there stated to be the basis of calculation for greater cycles; from this, the cycle of 60 years [12 × 5], so much used in the east, was probably formed, and subsequently, from the latter arose the cycle of 3600 years [60 x 60], which was denominated the Yuga of Vacpati; sixty of these, or 216,000 years, constitute the Yuga of Prajanatha, and the double of this last is the value of the Cali-yuga.

The cycles of 60 years, and 3600 years, here mentioned are identical with the Sossos and Saros of the Chaldeans, and from them, the Hindus may have formed some of their longer periods by the aid of their own observations on the celestial phenomena; in like manner, the restitutions of the moon's inequalities of motion may have been adopted by the latter people from those discovered by the former before the time of Aristotle. The Hindu periods, though not the same in quantity as those which have been preserved by Geminus, and which we consider as the bases of the lunar theory of Hipparchus, are precisely the same in kind; and may easily have been formed from the others, according to their own estimates of the length of the solar year and of the age of the world, by the learned astronoIsagoge, cap. 18, in Petav. Uranol. Asiat. Res. vol. VIII.

a

mers of India who are mentioned by Brahma Gupta, and whom Mr. Colebrook supposes to have lived about the times of Hipparchus and Ptolemy. According to the Narsapour tables, 800 [sidereal] years contain 292,207 days; and from this it is evident that the Hindu sidereal year was equal to 365.25875 days. Besides the cycle of 19 years, in which are contained 235 lunations, the Hindus had two periods; the one of 12,362 days, and the other of 21,857 days, in which respectively, they found that the moon had made 453, and 800 sidereal revolutions; and three periods in which she made, as they supposed, an exact number of revolutions with respect to the apogeum; the first of these was equal to 248 days, and contained 9 revolutions; the second to 3031 days, and contained 110 revolutions; the third to 12,372 days, in which were 449 revolutions; and these cycles were, most probably, employed subsequently in the construction of the tables of the movements of the sun and moon, which, in the last century, and after many reformations, were received in Europe. With respect to the planetary periods, Mr. Colebrook is of opinion that the Hindus merely surmised that the nodes and apsides of those celestial bodies were in movement, from analogy with the corresponding motions of the moon's orbit: he conceives that they were unable to verify their conjecture by observation, and that they have merely assigned arbitrary numbers to the supposed revolutions, in order to bring the places right, or nearly so, conformably to their assumption of a great conjunction of the planets with their nodes and apsides, in a certain point of the ecliptic, at a very remote period.

a

In a paper on the Hindu systems of astronomy there is given a table of the restitutions of the solar, lunar, and planetary inequalities, according to the periods ascribed to Brahma-Gupta ; from which it appears that in a Calpa, or in 4320 millions of years, the apsides of the solar orbit made 480, and the equinoctial points 199,669 complete revolutions [the mean movement of the latter must consequently have been supposed equal to 597 yearly]; that, in the same time, the moon made

a Asiat. Res. Vol. VIII.

57,753,300,000 synodical revolutions; her apsides, 488,105,858; and her nodes, 232,311,168 revolutions. Mr. Davis finds, from the treatise ascribed to Brahma-Gupta, and also from the Siddhanta Siromani, that the number of days contained in a Calpa was supposed to be 1,577,916,450,000; whence consequently, the length of the sidereal year must have been considered equal to 365.25844 days.

Like Hipparchus, the Hindus determined the inequalities of the moon's motion by means of eclipses; and, hence, their theory is destitute of the equation of evection which was discovered by Ptolemy from observations made at the quadratures; this discovery, by some chance, never found its way into the astronomy of India and, in all probability, an attachment to the ancient method of observing prevented the people of India from attempting a comparison of the observed and calculated places of the moon when she was in any other position than the syzygies. We have said that they once had a value of the precession equal to that assigned by Ptolemy; and it is to be observed that, like him, in computing the true places of the planets, they suppose the conjunctions and oppositions to be referred to the mean place of the sun, instead of the true place, and the mean longitudes of Mercury and Venus to be the same as that of the sun. Lastly, in the tables of Triavelore and of Siam, the apogeum is supposed to be fixed in space, and in all these respects, there is a close conformity with the astronomy of Ptolemy; though there is no reason to doubt that all the above circumstances belong equally to the age of Hipparchus, if not to one still earlier. But the remaining elements belong to an astronomy of a later day than that of Ptolemy, and it is probable that the Hindus received the works of the latter astronomer only through the medium of the Arabian writers and, of course, accompanied by all or many of the changes which they had introduced in the science; their solar equations differ from those of the Greeks and Arabians, as if they had been formed by taking arithmetical means between the values assigned by both these people; they discovered, or adopted from the latter, the particular movements of the apogea of the Sun, Jupiter and Mercury, which Ptolemy considered as fixed in space, and their

precession of the equinoctial points is actually that of Albategnius: nor can it be doubted that the lunar tables of the Hindus were formed posteriorly to the time of Ptolemy, because the mean motions of the moon with respect to the apogeum, the nodes and the sun, are, in these tables, found to be more rapid than in those of the Greek astronomers: and these movements are known to increase with the lapse of time. We may observe, therefore, that though the elements of the Hindus tables have not been formed immediately from those of the Greeks and Arabians, which, indeed, is proved by Mr. Playfair from the want of coincidence in the assigned places of the sun and moon at the supposed epoch of the Triavelore tables with the places determined by computation from the tables of Ptolemy and Ibn Jounis; yet there is nothing to prevent us from concluding that the astronomy of India, originally that of the ancient people of Western Asia, has received successive corrections from the discoveries made by natives and foreigners, and has been remodelled at various periods, down to the end of the seventeenth century.

With the Mohammedan power, the science of India declined and, notwithstanding the patronage afforded by the emperors Akbar and Aurengzebe, and the magnificent observatory erected at Benares by the rajah Jay Sing, it has not, since, been revived in that country.

CHAPTER XVI.

THE ANCIENT ASTRONOMY OF CHINA.

A conjunction of the planets taken as an epoch by the Chinese.--The commencement of the Chinese year at one time coincided with that of the Hindus. A regulation of the seasons by the Emperor Yao.-Ancient observations made in China with the gnomon.-Destruction of the Chinese writings. The Chinese histories contain catalogues of celestial phenomena. Alleged resemblances of the Chinese sphere and those of the Hindus and Egyptians.-Divisions of time in use among the Peruvians and Mexicans.

b

THE astronomy of China may vie with that of India in the remoteness and obscurity of its origin; and, like the latter, it is supposed to have commenced with a primitive epoch at which the sun, moon, and several planets were in conjunction. In a Chinese work alleged to have been composed about the year 204 Before Christ, this conjunction is said to have been observed or predicted by the Emperor Tchuen-hi, and to have taken place in the constellation Xi; and the writer asserts that 143,127 years had elapsed between the time of the conjunction and that in which he lived"; now M. Bailly disregarding that pretended interval of time, has found by computation that Mars, Jupiter, Saturn and Mercury were together, on the morning of February 28, Julian reckoning, in the year 2449 B. C. in a part of the heavens situated, in longitude, between the eighth and twenty-fifth degree of the sign Pisces, a space which must have been, then, comprehended between the star « Arietis and the Pleiades: and hence it is inferred that this portion of the zodiac must have coincided with the Chinese constellation Xi. The same astronomer found, also, that a conjunction of the sun and moon took place on the same day, in the nineteenth degree of the sign Aquarius, or near the star Piscium; these he conceives, therefore, to have been the phenomena alluded to, which is not improbable since historians have placed in the a Martini Historia Sinica, Tom. I. Astr. Ind. Chap. IX. sect. 2.