A HISTORY OF SCIENCE 



a given case may be but an inch in length, while an- 

 other circle is so large that its corresponding arc is 

 measured in millions of miles; but in each case the 

 same number of so-called degrees will represent the re- 

 lation of each arc to its circumference. Now, Eratos- 

 thenes knew, as just stated, that the sun, when on the 

 meridian on the day of the summer solstice, was 

 directly over the town of Syene. This meant that at 

 that moment a radius of the earth projected from 

 Syene would point directly towards the sun. Mean- 

 while, of course, the zenith would represent the pro- 

 jection of the radius of the earth passing through 

 Alexandria. All that was required, then, was to 

 measure, at Alexandria, the angular distance of the 

 sun from the zenith at noon on the day of the solstice to 

 secure an approximate measurement of the arc of the 

 sun's circumference, corresponding to the arc of the 

 earth's surface represented by the measured distance 

 between Alexandria and Syene. 



The reader will observe that the measurement could 

 not be absolutely accurate, because it is made from the 

 surface of the earth, and not from the earth's centre, 

 but the size of the earth is so insignificant in com- 

 parison with the distance of the sun that this slight 

 discrepancy could be disregarded. 



The way in which Eratosthenes measured this 

 angle was very simple. He merely measured the 

 angle of the shadow which his perpendicular gnomon 

 at Alexandria cast at mid-day on the day of the 

 solstice, when, as already noted, the sun was directly 

 perpendicular at Syene. Now a glance at the dia- 

 gram will make it clear that the measurement of 



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