ERA OF THE GREEK AND ALEXANDRIAN SCHOOLS. 9 



The most interesting circumstances connected with the early history of the Alexandrian 

 school are the attempts made to determine the distance of the earth from the sun, and the 

 magnitude of the terrestrial globe. Aristarchus of Samos is the author of an ingenious 

 plan to ascertain the former. Suppose the centre of the circle s to represent the centre of 

 the sun, M that of the moon, and at E the position of an observer on 

 the surface of the earth. It is easy to perceive that, when the moon 

 has half her disc illuminated by the sun, a line drawn from E to 

 M will be perpendicular to another line drawn from s to M, 

 making with each other a right angle. The plan of Aristarchus 

 was, that the angular distance s E M should at that time be 

 taken, which is possible, because both the sun and moon may then 

 be seen at once above the horizon, from whence the ratio of E s 

 to E M may be determined. He obtained the general result, that 

 the distance of the sun from the earth is about nineteen times as 

 great as that of the moon from the earth. We now know that 



the distance is much greater ; but notwithstanding the inaccuracy of the result, the 

 method employed is undoubtedly just, and reflects the highest honour upon the genius of 

 its proposer. He failed in practice, owing to the difficulty of ascertaining the exact time of 

 the bisection of the moon's disc, and the imperfect instruments then in use for the mea- 

 surement of angular distances. The determination of the sun's distance from the earth, 

 with any thing like precision, is only of recent date, and has .been effected by means of 

 which the ancients could have had no conception. Aristarchus held the Pythagorean 

 doctrine of the motion of the earth in space, and gave the right answer to the formidable 

 objection long afterwards made to it, that of the non-existence of an annual parallax. The 

 answer recognised the earth's orbit as being an insensible point in comparison with the 

 vast distance of the fixed stars. The boundaries of the universe were thus extended to 

 his mind far beyond any limits conceived by his predecessors. There is great obscurity 

 resting upon his life. The era of his birth and death is unknown ; but he was alive B. c. 

 280, as an observation of the solstices made by him at that date has been preserved. The 

 Greek text of his only surviving work, " On the Magnitudes and Distances of the Sun 

 and Moon," was edited in this country by Dr. Wallis in 1688. He estimated the apparent 

 diameter of the sun at 30', about 2' too little. 



The attempt to determine the magnitude of the earth was made by Eratosthenes, and 

 we have reason to believe this was the first attempt ever made to solve the problem, as 

 certainly it was to do it upon a true principle. Syene, in Upper Egypt, then 

 a flourishing city, now Assouan, has acquired an interest from its connection 

 with this experiment. It was supposed to lie exactly under the tropic of 

 Cancer, as it had been observed that, on the day of the summer solstice, at 

 noon, a well there was enlightened to the bottom, while vertical bodies threw 

 no shadow for the space of about three hundred stadia around it. At 

 Alexandria, therefore, which was conceived to lie under the same meridian, 

 on the same day at noon, when the sun was believed to be vertical at Syene, 

 Eratosthenes measured his zenith distance, or the value of an arc of the 

 meridian between the two cities. Let E be the centre of the earth, A Alex- 

 andria, s the sun, and s' Syene. The celestial arc contained between the 

 zeniths of the two places, Alexandria and Syene, was found to be equal to g^th of the 

 circumference of a circle, that is, to 7 12'. Now, admitting the earth to be of a spherical 

 form, Eratosthenes would obtain the measure of its circumference, by multiplying fifty 

 times the distance between the cities. This distance was ascertained by order of the 

 government to be 5000 stadia, and consequently the result obtained for the length of the 



