of the stars from east to west, and on the changes observed in the position of these stars, when we travel nearly under the same meridian toward the north, or toward the south. And soon the comparison of the apparent change in the stars with the corresponding lengths of the distance passed over on the Earth suggested the idea of measuring the circumference of the globe by means of observations of the stars. Aristotle, the most ancient author of whom we have any writings on this subject, expresses himself as follows in his second book De cælo, chap. XIV.

In eclipses of the Moon the line that bounds the eclipsed part is always a curye: and as the Moon is eclipsed by the shadow of the Earth, it is certain, that this appearance is caused by the circumference of the Earth, which is spherical. Indeed it is evident from the appearances of the stars, that the Earth is round. It's extent too cannot be very considerable: for, if we travel ever so little either toward the North or toward the South, the horizon manifestly varies in such a manner, that the stars over our heads are altered, not being the same to those who travel north, as to those who travel south.'..... Aristotle adds: those mathematicians, who have attempted to determine the magnitude of the Earth's circumference, say, that it is 400000 stadia.'

By those mathematicians, we have every reason to presume, Aristotle means the pythagoreans, who considered the Earth as a star, and made it revolve around the centre of the World, so as to produce the alterations of day and night; an opinion, which Aristotle himself attempts to refute in the preceding chap

ters.

ters. He clearly speaks only as an historian, when he mentions the measure of the Earth. Horace furnishes us with a proof, that this measurement is to be ascribed to the pythagoreans; for in the 28th ode of the 2d book he calls the pythagorean philosopher Archytas, who had been Plato's master, the measurer of the Earth.

Eratosthenes, librarian of the alexandrian museum, is the first of the ancients, from whom we have a measurement of the Earth by a method consistent with the principles of geometry and astronomy. A. C. 280. This measurement, admired in it's time as a prodigy of human sagacity, has been transmitted to us by Cleomedes: Cycl. Theor. book I, chap. 10. Eratosthenes was informed, that, at the time of the summer solstice, the Sun at noon was vertical to the city of Syene, situate on the borders of Ethiopia, under the tropic of Cancer. A well is particularly mentioned to have been constructed in this city, which was illuminated throughout it's whole depth by the Sun at noon on the day of the solstice. He knew likewise, or at least he imagined, and he was not far from the truth, that Alexandria and Syene were both under the same meridian. On these data he constructed a concave hemisphere at Alexandria, from the bottom of which arose a vertical style, terminating at the centre of curvature of the hemisphere. Then, supposing the city of Syene to be in the vertical direction of the style, he observed, that the arc, included between the foot of the style and the extremity of it's shadow projected on the concavity of the hemisphere by the meridian

Sun

Sun at the solstice, was equal to a fiftieth part of the whole circumference. Hence he inferred, that the arc of the Heavens comprised between Alexandria and Syene must be the same; and that the distance between the two cities must likewise be a similar arc,. or a fiftieth part of the whole circumference of a great circle of the Earth. Now on measuring this distance, or the length of this arc, it was found to be 5000 stadia, which gave 250000 stadia for the length of the entire circumference of the Earth, and 694 stadia to a degree. Some later astronomers, desirous of avoiding the fraction, and supposing, that it was impossible to answer for the accuracy of the measure to five or six stadia in a degree, extended this length to 700 stadia, which give 252000 stadia for the measure of the whole circumference..

There is another ancient measure of the Earth reported likewise by Cleomedes, which is that of the philosopher Posidonius, who was contemporary with Pompey. A. c. 60. This philosopher, having observed, or been informed, that the star Canopus did but just appear on the horizon at Rhodes; while at Alexandria, which he placed under the same meridian, it rose a forty eighth part of the circumference of the heavens above it, which answers to a forty eighth part of the circumference of the Earth: and supposing, that the distance between Rhodes and Alexandria was 5000 stadia; he reckoned 240000 stadia for the entire circumference of the globe, or 666 to a degree. But it was soon after found, that these two determinations exceeded the truth, because Posidonius had made the distance of Rhodes from Alexandria much

greater

greater than it really was. Strabo, who wrote his geography in the time of Augustus, asserts, that Eratosthenes had measured this distance, and found it to be only 3750 stadia: whence we should have only 180000 stadia for the length of the entire circumference of the Earth, and 500 stadia for that of a degree.

It remains for us to ascertain the proportion of the stadium to some of our present measures, that we may be enabled to compare the length assigned to a degree by the ancients with what it has been determined to be by the moderns.

Some authors affirm, that both Eratosthenes and Posidonius employed the greek stadium, which is 607 feet and a half english measure; others, the egyptian stadium, which is 731 feet and a half. Supposing it to have been the greek stadium, the first measure of a degree by Eratosthenes would be 421875 feet; the second, 425250: the first by Posidonius, 404999 ; and the second, 303750. Of these four different measures three are more or less erroneous in excess, while the fourth errs by deficiency; the degree being 365640 feet, or thereabout, according to the measures of the moderns. Supposing the egyptian stadium to have been used, the first three err greatly by excess; but the fourth, giving 365672 feet, differs little from the modern measures. But this agreement can be no more than the effect of chance, or a false estimation of the stadium; for the methods of Eratosthenes and Posidonius were not susceptible of great precision, and cannot be compared with the modern in this respect. The discussion of this sub

ject,

ject, on which the reader may consult several excellent memoirs among those published by the Academy of Belles-Lettres, I shall pursue no farther; but return to the general history of astronomy, at the time of Alexander.

The impulse, which this prince had given to the astronomy of the greeks, was powerfully seconded by the encouragements and liberalities of the new kings of Egypt, who sought out the men most illustrious for their learning in all parts of the World, and invited them to the museum of Alexandria. A. C. 300. It was here, during the space of twenty six years, reckoning from the year 295 before Christ, that Aristillus and Timocharis made an immense series of observations, as well on the position and number of the fixed stars, as on the motions of the planets: and these observations afterward served as the basis, on which Ptolemy founded his theory.

About the same time flourished Aristarchus of Samos, who rendered himself illustrious in astronomy by several interesting opinions or discoveries. He observed a solstice in the year 281 before Christ, according to Ptolemy's calculations, which fixes with. precision the age of this astronomer, respecting whom historians, not well informed, express themselves doubtfully. We have a very simple method of his, if not very accurate, for determining the ratio of the distances of the Moon and the Sun from the Earth. It con-. sists in observing the moment, when the plane of the circle, which, in the different phases of the Moon, separates; the dark from the enlightened part, is directed towards the eye of an observer on the Earth,

and