which she makes nearly 235 revolutions; and it is curious to find at Siam, the knowledge of that cycle, of which the invention was thought to do so much honour to the Athenian astronomer Meton, and which makes so great a figure in our modern kalendars."*

"Cette règle suppose donc, une période de 19 années, semblable à celle de Meton et du nombre d'or; et Dom. Cassini ajoute, que la période Indienne est plus exacte le cycle ancien du nombre d'or."†

que

It is evident that the Hindūs must have known the use of the gnomon at a very remote period. Their religion commands that the four sides of their temples should correspond with the four cardinal points of the heavens; and they are all so constructed.

The rules by which the phenomena of eclipses are deduced from the places of the

* Playfair, in Trans. of the Royal Society of Edinburgh, vol. ii. p. 144.

+ Astronomie Indienne et Orientale, p. 4, 5.

sun and moon, have the most immediate reference to geometry; and of these rules, as found among the Brahmins at Tirvalore, M. le Gentil has given a full account. We have also an account by Father Du Champ of the method of calculation used at Krishnapouram.

"It is a necessary preparation, in both of these, to find the time of the sun's continuance above the horizon at the place and the day for which the calculation of an eclipse is made; and the rule by which the Brahmins resolve this problem, is extremely simple and ingenious. At the place for which they calculate, they observe the shadow of a gnomon on the day of the equinox, at noon, when the sun, as they express it, is in the middle of the world. The height of the

gnomon is divided into 720 equal parts, in which parts the length of the shadow is also measured. One third of this measure is the number of minutes by which the day, at the end of the first month after the equinox, exceeds twelve hours; four-fifths of this excess is

the increase of the day during the second month; and one-third is the increase of the day during the third month.

"It is plain that this rule involves the supposition, that when the sun's declination is given, the same ratio every where exists between the arch which measures the increase of the day at any place, and the tangent of the latitude; for that tangent is the quotient which arises from dividing the length of the shadow by the height of the gnomon. Now, this is not strictly true; for such a ratio only subsists between the chord of the arch, and the tangent above mentioned. The rule is therefore but an approximation towards the truth, as it necessarily supposes the arch in question to be so small as to coincide nearly with its chord. This supposition holds only for places in low latitudes; and the rule which is founded on it, though it may safely be applied in countries between the tropics, in those which are more remote from the equator, would lead into errors too considerable to escape ́observation.

"As some of the former rules have served to fix the time, so does this, in some measure, to ascertain the place, of its invention. It is the simplification of a general rule, adapted to the circumstances of the torrid zone, and suggested to the astronomers of Hindustan by their peculiar situation.”*

The precession of the equinoxes, or motion from west to east of the points where the ecliptic crosses the plane of the earth's equator, is reckoned in their tables at fiftyfour seconds of a degree in the year: it is found to be at present only fifty and a third seconds in the year. From this motion of fifty-four seconds, they have evidently formed many of their calculations. They have a cycle or period of sixty years, each of which has its particular name; another of 3,600 years, and one of 24,000. From the annual motion given by them of fiftyfour seconds of longitude in the year, fiftyfour minutes of longitude make sixty years,

* See Trans. of the Royal Society of Edinburgh, vol. ii. p. 170.

fifty-four degrees 3,600, and the entire revolution of 360 degrees makes their great period, or annus magnus, of 24,000 years, which is often mentioned by them.

The point at which the sun is on the 20th or 21st of March, is called, as with us, the vernal equinox; that at which he arrives on the 20th or 21st of September, the autumnal equinox; on both occasions festivals are observed, but at the vernal equinox, with greater joy and ceremony, in order to salute the return of the sun to the northern tropic, and celebrate the commencement of their favourite season, Visanta, or the spring.

The Hindus, whether in matters of accounts or science, make their calculations with a surprising degree of quickness and precision, especially when we consider the methods they sometimes employ. M. le Gentil gives an account of a visit he received, soon after his arrival at Pondicherry, from a Hindu, named Nana Moodoo; who, though not a Brahmin, had found means to learn some of the princi