school; they flourished about the year 300 before the Christian æra. Their observations of the principal stars of the zodiac, enabled Hipparchus to discover the precession of the equinoxes, and Ptolemy, from their observations of the planets, founded his theory of those bodies.

The next astronomer which the school of Alexandria produced, was Aristarchus, of Samos. The most delicate elements of astronomy were the subjects of his investigation. He observed the summer solstice, the year 281 before the Christian æra. He determined the magnitude of the apparent diameter of the sun, which he found equal to the 720th part of the whole circumference, a quantity forming a mean between the two limits which Archimedes assigned, a few years afterwards, to this diameter, by an ingenious method, according to which the solar diameter appeared to him greater than the 200th part of a right angle, and less than the 164th part. But what reflects the greatest honour on the genius of Aristarchus, is the method by which he endeavoured to determine the distance of the sun from the earth. He observed the angle contained between the sun and the moon, at the moment he judged half of the lunar disk to be illuminated by the sun, and having found it just 96°.7, he concluded that the sun was eighteen or twenty times farther from us than the moon. Notwithstanding the inaccuracy of this result, it extended the boundaries of the universe much farther than had been done before. Aristarchus revived the opinion of the Pythagorists, relative to the motion of the earth. But as his writings have not been transmitted to us, we are ignorant to what extent he carried this theory in his explanation of the celestial phenomena. We only know that this judicious astronomer, having reflected that the motion of the earth produced no change in the apparent position of the stars, placed them at a distance incomparably greater than the sun. Thus it appears, that of all the ancient astronomers, Aristarchus had formed the most just notions of the magnitude of the universe.

The celebrity of his successor, Eratosthenes, is principally due to his measure of the earth, and his observations on the obliquity of the ecliptic. Having, at the summer solstice, remarked a deep well, whose whole depth was illuminated by the sun, at Syene, in Upper Egypt, he compared this with the altitude of the sun, observed at the same solstice at Alexandria. He found the celestial arc, contained between the zeniths of these two places, equal to

the 50th part of the whole circumference, and as their distance was estimated at 500 stadia, he fixed at 250 thousand stadia the length of the whole terrestrial circumference. The uncertainty that exists, as to the value of this stadium, does not permit us to appreciate the exactness of this measurement.

Aristotle, Cleomedes, Possidonius, and Ptolemy, have given four other evaluations of the circumference of the earth, equivalent to 400, 300, 240, 180 thousand stadia. The simple relations of these measures to each other, leave room to conjecture, that these different quantities are translations of the same measure in different stadia. The Alexandrian stadium was 400 great cubits, of the same length as the nilometer of Cairo, which, according to Freret, has not been altered for a great number of centuries, and may be traced back to the time of Sesostris; its magnitude is equal to 1.7119 feet, according to some measures lately made with great precision, which gives 684.76 feet, for the value of the stadium of Alexandria. As it is probable this stadium was that of Ptolemy, the circumference of the earth, according to that astronomer, would be 123,256,800 feet, which differs but little from our actual measurement, which fixes it at 123,178,320 feet*.

If the measures of Possidonius, Cleomedes, and Aristotle, are identical with that of Ptolemy, the corresponding stadia are 513.570, 410.856, and 308.142 feet. Now, in comparing a great number of ancient itinerary distances with the actual known distances, we find in antiquity these different stadia so precisely, as to render the identity of these four measures of the earth extremely probable, it is therefore very probable that they all depend on some ancient and very exact measure, either executed with great care, or in which the errors were fortunately compensated, as has since happened in the measure of a degree by Fernal, and even in that by Picard. It is true we know, that Possidonius himself measured an arc of the terrestrial meridian; and his operation, as far as we can judge from the details that have been transmitted to us, was very inexact; but there is reason to think he only proposed to verify some ancient measures of the earth, and that he found them to agree nearly with his own.

* Ten millions of metres, according to the new measurement of the French National Institute; the metre being equal to 39.37100 English inches.-Editor.

The observation of Eratosthenes, on the obliquity of the ecliptic, is very valuable, inasmuch as it confirms the diminution of it, determined, à priori, by the theory of gravitation. He found the distance between the tropics less than 53.06, and greater than 52.96, which gives us a mean *26.50, for the obliquity of the ecliptic. Hipparchus found no reason to alter this result by his observations.

But of all the astronomers of antiquity, the science is most in. debted to Hipparchus of Bithynia, for the great number and extent of his observations, by the important results he obtained, by comparing them with those that had been formerly made by others; and for the excellent method which he pursued in his researches. He flourished at Alexandria about 140 years before our æra. Not content with what had already been done, he determined to recominence every thing, and not to admit any results but those founded on a new examination of former observations, or on new observations, more exact than those of his predecessors.

Nothing affords a stronger proof of the uncertainty of the Egyp tian and Chaldean observations on the sun and stars, than the necessity which compelled him to recur to the observations of the Alexandrine school, to establish his theories of the sun, and of the precession of the equinoxes. He determined the length of the tropica! year, by comparing one of his observations of the summer solstice, with one made by Aristarchus of Samos forty-five years before; he found it 365.24667 days. This is in excess about four minutes and a half. But he remarks himself on the little reliance that can be placed on a determination from solstitial observations, and on the advantage of employing observations of the equinoxes. Hipparchus recognized that there elapsed 187 days from the vernal equinox, to that of the autumn, and 178 days only from this last equinox to that of the spring. He observed, likewise, that these intervals were unequally divided by the solstices, so that 94 days and a half elapse from the vernal equinox to the summer solstice, and 92 days and a half from this solstice to the autumnal equinox.

To explain these differences, Hipparchus supposed the sun to move uniformly in a circular orbit; but, instead of placing the earth in the centre of it, he supposed it removed the 24th part of the radius, and fixed the apogee at the sixth degree of Gemini.

* 23.51

From these data he formed the first solar tables to be found in the history of Astronomy. The equation of the centre, which they suppose was too great, it is very probable, that a comparison with eclipses, in which this equation is augmented by the annual equation of the moon, confirmed Hipparchus in his error, and perhaps even led him into it. He was mistaken also in supposing circular the elliptic orbit of the sun, and that the real velocity of this body was constantly uniform. The contrary is now demonstrated by direct measures of the sun's apparent diameter; but such observations were impossible at the time of Hipparchus, whose solar tables, with all their imperfections, are a lasting monument of his genius, which Ptolemy, three centuries after, respected, but did not attempt to improve.

This great astronomer next considered the motions of the moon ; he measured the length of its revolution by comparing eclipses, and determined both the eccentricity and inclination of its orbit; he ascertained the motion of its nodes and of its apogee; and from the determination of its parallax endeavoured to conclude that of the sun, by the breadth of the cone of the terrestrial shadow, in an eclipse at the moment it was traversed by the moon, which led him nearly to the same result as had been obtained by Aristarchus. He made a great number of observations on the planets, but too much the friend of truth to explain their motions by uncertain theories, he left the task of this investigation to his successors. A new star which appeared in his time induced him to undertake a catalogue of the fixed stars, to enable posterity to recognize any changes that might take place in the appearances of the heavens. He was sensible also of the importance of such a catalogue for the observations of the moon and the planets. The method he employed was that of Arystillus and Timochares, and which we have already explained in the First Book. The reward of this long and laborious task was the important discovery of the precession of the equinoxes; in com. paring his observations with those of these astronomers, he discovered that the stars had changed their situation with respect to the equator, but had preserved the same latitude with respect to the ecliptic, so that to explain these different changes, it is sufficient to give a direct motion to the celestial sphere round the poles of the ecliptic, which produces a retrograde motion of the equinoxes with respect to the stars. But he announced his discovery with some

reserve, being doubtful of the accuracy of the observations of Arystillus and Timochares. Geography is indebted to Hipparchus for the method of determining places on the earth by their latitude and longitude, for which he first employed the eclipses of the moon. Spherical trigonometry, also, owes its origin to Hipparchus, who applied it to the numberless calculations which these investigations required. His principal works have not been transmitted to us; they perished in the conflagration of the Alexandrine library, and we are only acquainted with them through the Almagest of Ptolemy.

The interval of near three centuries which separated these two astronomers, produced some observers, as Agrippa, Menelaus, and Theon. We may also notice in this interval the reformation of the calendar by Julius Cæsar, and the precise knowledge of the ebbing and flowing of the sea. Possidonius observed the law of this phenomenon, which appertains to astronomy by its evident relation to the motion of the sun and moon, and of which Pliny the naturalist has given a description remarkable for its exactness.

Ptolemy, born at Ptolemais in Egypt, flourished at Alexandria about the year 130 of our æra. Hipparchus had conceived the project of reforming astronomy, and establishing the science on new foundations. Ptolemy continued this labour, too vast to be accomplished by a single individual, and has given a complete treatise on this science in his great work entitled the Almagest.

moon.

His most important discovery is the evection or libration of the Astronomers previously had only considered the motion of this body relative to eclipses; by following it through its whole course, Ptolemy recognized, that the equation of the centre of the lunar orbit, was less in the sysigies than in the quadratures; he determined the law of this difference, and ascertained its value with great precision. To represent it, he made the moon to move upon an epicycle carried by an eccentric, according to a method attributed to Appolonius the geometrician, and which had before been employed by Hipparchus,

It was a general opinion of the ancients, that the uniform circular motion being the most simple and natural, was necessarily that of the heavenly bodies. This error maintained its ground till the time of Kepler, and for a long time impeded him in his researches. Ptolemy adopted it, and, placing the earth on the centre of the