ALEXANDRIAN OR HELLENISTIC PERIOD 



ihis angle of the shadow is merely a convenient 

 means of determining the precisely equal opposite 

 angle subtending an arc of an imaginary circle passing 

 through the sun ; the arc which, as already explained, 

 corresponds with the arc of the earth's surface rep- 

 resented by the distance between Alexandria and 

 Syene. He found this angle to represent 7 12', or 

 one-fiftieth of the circle. Five thousand stadia, 

 then, represent one-fiftieth of the earth's circum- 

 ference; the entire circumference being, therefore, 

 250,000 stadia. Unfortunately, we do not know 

 which one of the various measurements used in 

 antiquity is represented by the stadia of Eratos- 

 thenes. According to the researches of Lepsius, how- 

 ever, the stadium in question represented 180 meters, 

 and this would make the earth, according to the meas- 

 urement of Eratosthenes, about twenty -eight thousand 

 miles in circumference, an answer sufficiently exact to 

 justify the wonder which the experiment excited in an- 

 tiquity, and the admiration with which it has ever 

 since been regarded. 



Of course it is the method, and not its details or 

 its exact results, that excites our interest. And be- 

 yond question the method was an admirable one. Its 

 result, however, could not have been absolutely ac- 

 curate, because, while correct in principle, its data were 

 defective. In point of fact Syene did not lie precisely 

 on the same meridian as Alexandria, neither did it lie 

 exactly on the tropic. Here, then, are two elements of 

 inaccuracy. Moreover, it is doubtful whether Eratos- 



;henes made allowance, as he should have done, for 

 the semi-diameter of the sun in measuring the angle 



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