3 6] The Measurement of the Earth 39 



is more than 66 1, 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. 1 6. The measurement ot the earth. 



that at the summer solstice the angular distance of the 

 sun from the zenith at Alexandria was at midday J^th 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 ^th 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 i to 50. The distance between Alexandria and Syene 



