28 SCIENCE OF THE GREEKS. PT. I. 



he should have a line which would describe a circle round 

 the earth from pole to pole, as the equator marks a circle 

 round the earth midway between the two poles. This 

 second line he drew from Alexandria, and it passed right 

 through Syene, now called Assouan, one of the southern 

 cities of Egypt ; and thus he knew that Alexandria and 

 Syene were on the same meridian of longitude. 



Now he found that at Syene the sun was exactly over- 

 head at mid-day, at the time of the summer solstice. He 

 knew this by means of a gnomon, or upright pillar (B, Fig. 2), 

 which was used by the Greeks to measure the height of the 

 sun in the sky. At Syene this pillar cast no shadow at noon 

 of the summer solstice, proving that the sun shone straight 

 down upon the top of it ; and this was further proved by 

 the sun shining down to the bottom of a deep well, which 

 it would not do unless it were directly overhead. But at 

 Alexandria the gnomon did cast a shadow, because, as 

 Alexandria was farther north and the earth is round, the 

 sun there was not directly overhead. Now, as light travels 

 in straight lines (see p. 21), a line drawn from the extreme 

 point of the shadow cast by the pillar or gnomon up to the 

 top of the pillar itself would, if carried on, run straight into 

 the sun, and thus the angle between this line and the pillar 

 showed at what angle the sun's rays were falling at Alex- 

 andria. By measuring this angle, Eratosthenes found that 

 Alexandria was T V tn of the whole circumference of the earth 

 north of Syene, where the rays were perpendicular. 



You can form an idea of this from the accompanying 

 diagram, Fig. 2. Let the large circle represent the earth ; 

 B the gnomon at Syene, and A the gnomon at Alexandria. 

 The length of the shadow c D of the gnomon A, will bear the 

 same proportion to the circumference of the small circle 

 (drawn from the top of the gnomon as a centre), that the 



