in the daily revolution of the whole celestial sphere, advanced from west to east by different motions proper to themselves. These motions formed what was called lunations, and solar years. The Moon appeared to complete about twelve of these periodical motions while the Sun accomplished but one: hence, to establish a correspondence between the motions of these two celestial bodies, the solar year was divided into twelve parts, or months, comprising as many lunations. These first arrangements were but approximations, which were afterward corrected and improved, in proportion as observations became more exact*. Most I conceive it incumbent on me here to give accurate notions of the solar and lunar revolutions, as they are at present understood from the collective observations of the ancients and moderns. Three kinds of solar years, and four kinds of lunar months, are now distinguished. The three solar years are: the tropical year, or the interval at the end of which the Sun returns to a given point of the ecliptic, to the same colure, or to the same solstice, &c.; consisting of 365 days, 5 hours, 48 minutes, and 48 seconds: the sidereal year, or term at which the Sun returns to a given fixed star, of 365 days, 6 hours, 9 minutes, and 10 seconds: and the anomalistical year, or the period in which the sun returns to the same apsis, of 365 days, 6 hours, 15 minutes, 46 seconds. By the word year simply we always understand the tropical year; the others require to be distinguished by their respective epithets. The four kinds of lunar months are: the periodical, or the interval marked by the return of the Moon to the first point of Aries, which is of 27 days, 7 hours, 43 minutes, 5 seconds: the sidereal or term of it's return to a given fixed star, of 27 days, 7 hours, 43 minutes, 12 seconds: the synodical, or term of it's return to the Sun, Most of the ancient nations regulated the measure of time by the course of the Sun; but some others by that of the Moon. The babylonians began the day with sunrise; the athenians, with sunset; ią either of which modes, the times of the Sun's conti nuance above the horizon of a given place varying every day, on account of the inclination of the ecliptic to the equator, some difficulty was experienced when it was requisite to compare them. The egyptians reckoned their day from midnight to midnight, and divided it into a certain number of equal parts, or hours of equal lengths, to which any time that is wanted to be known may easily be referred. This practice has been adopted in several other countries. It is followed in France, in England, in Spain, for the purposes of common life. Copernicus, and the astronomers his contemporaries, likewise employed it in their calculations: but for about two hundred years astronomers have found it more commodious, to fix the commencement of the day at noon. The Sun, the cause of heat and of fertility, brings on the alternate seasons, and regulates both seedtime and harvest; so that mankind have always been obliged to conform to this invariable law of nature. Other labours may admit a more arbitrary distribution of the employment of time. Among the jews the Sun, of 29 days, 12 hours, 44 minutes, 3 seconds: and the anomalistical, or term in which it returns to it's apogee, of 27 days, 13 hours, 18 minutes, 34 seconds. It is obvious, that in comparing the lunar month with the solar year, the synodical month must always be understood. Moon Moon served to regulate various civil and religious affairs, by the quick succession of it's revolutions, and by it's different phases. A view of ancient astronomy would form an important object of curiosity, and of philosophical reflection, could we ascertain with presision, and exhibit at any length, the progress made by the nations, who cultivated this science; and no doubt a great variety of views, researches, and attainments in it would be observed, according to the climate of the country, the genius of the people, and the spirit of the government. But, deprived of this by the want of historical records, we are reduced to offer the reader only imperfect notions of the astronomical labours of the ancients, abstaining even from conjectures, unless founded on satisfactory probabilities. At the time when the greeks carried their victorious arms into Asia, the chaldeans, according to Simplicius*, quoted a series of observations for 1903 years, which were collected at Babylon by Callisthenes, a scholar of Aristotle, to whom he sent them by command of Alexander. We have no direct and positive proof of the accuracy, or even of the reality of all these observations: nay more, there are authors contemporary with Alexander, whose testimony appears formally to contradict the account of Simplicius. Be this as it may, we can scarcely doubt, that the ancient chaldeans were well acquainted with Simplicius was a peripatetic philosopher, who lived in the fifth century, and of whom we have Commentaries on Aristotle, and on Epictetus. the the motions of the Sun and Moon. The most ancient historians, in particular Geminus, of whom I shall speak more at large hereafter, affirin, that they had gone so far as to form several very ingenious lunisolar periods, and nearly approaching the truth: and these, they add, were the result of astronomical computations, founded on a great number of accurate observations. Among others the period called Saros is mentioned, which, after 223 lunations, brought back the Moon almost to the same position with respect to it's node, it's apogee, and the Sun. I shall not enter into a discussion of these periods, the bases of which frequently appear very uncertain. The chaldean astronomy does not begin to offer any certain and positive results till the era of Nabonassar, the first king of the babylonians. This answers to the year 747 before Christ. Ptolemy, who flourished about the year 140 of our era, and who, as we shall see hereafter, was one of the greatest astronomers of the alexandrian school, employed in his calculations three observations of lunar eclipses made by the chaldeans in the years 27 and 28 of the era of Nabonassar. They were particularly addicted to observations of this kind, and the same Ptolemy mentions four others, the last of which answers to the year 380 of the era of Nabonassar, or 367 before Christ. The revolution which subjected the kingdom of Babylon to the persian yoke was not fatal to astronomy: Lunisolar periods are spaces of time, after which the Sun and Moon, or two remarkable points of their orbits, such as the apogee, the nodes, &c., being supposed to set out from the fame point in the heavens, would meet there again. the the persians themselves became astronomical ob servers. As early as the reign of Darius Ochus, they reckoned time by solar revolutions, and had established a calendar of a very simple form, which is mentioned with praise by some ancient authors, A. c. 516. The state of ancient astronomy in Egypt is very obscure. We only presume, with much probability, that it was considerably advanced. Diogenes Laertius expresses himself on this subject as follows. The egyptians say, that Vulcan, whom they make the son of Nilus, was the first who treated on philosophy, the professors of which they call magi and prophets. From him to Alexander, king of Macedon, they reckon forty-eight thousand, eight-hundred, and sixty-three years; during which there were a hun dred and seventy-three eclipses of the Sun, and eight hundred and thirty-two of the moon.' Introduction to the Lives of the Philosophers. The proportion of 173 to 832 is about that of the number of solar and lunar eclipses, which happen at one place in the same portion of time; so that in this respect the narrative of Diogenes may be exact, But astronomical calculation demonstrates, that al, these eclipses may have happened in an interval of twelve or thirteen hundred years; of course the number 48863 is obviously fabulous. We can only conclude therefore, that the period of the first egyp tian observations cannot be dated more than sixteen or seventeen hundred years before the christian era, More certain proofs however of the skill of the egyptians in astronomy exist. The accurate manner, |