is more than 6612°, the sun passes in summer into the region of the circumpolar stars which never set (chapter i., § 9), and therefore during a portion of the summer the sun remains continuously above the horizon. Similarly in the same regions the sun is in winter so near the south pole that for a time it remains continuously below the horizon. Regions in which this occurs (our Arctic regions) were unknown to Greek travellers, but their existence was clearly indicated by the astronomers.
36. To Eratosthenes (276 B.C. to 195 or 196 B.C.), another member of the Alexandrine school, we owe one of the first scientific estimates of the size of the earth. He found
Fig. 16.—The measurement of the earth.
that at the summer solstice the angular distance of the sun from the zenith at Alexandria was at midday 150th of a complete circumference, or about 7°, whereas at Syene in Upper Egypt the sun was known to be vertical at the same time. From this he inferred, assuming Syene to be due south of Alexandria, that the distance from Syene to Alexandria was also 150th of the circumference of the earth. Thus if in the figure s denotes the sun, a and b Alexandria and Syene respectively, c the centre of the earth, and a z the direction of the zenith at Alexandria, Eratosthenes estimated the angle s a z, which, owing to the great distance of s, is sensibly equal to the angle s c a, to be 7°, and hence inferred that the arc a b was to the circumference of the earth in the proportion of 7° to 360° or 1 to 50. The distance between Alexandria and Syene
