ALEXANDRIAN SCIENCE. 



39 



in Southern Egypt, vertical bodies at the time of the summer solstice 

 cast at noon no shadows, or, in other words, the sun was at this time 

 exactly overhead in Syene. Now, Eratosthenes measured at Alexan- 

 dria the length of theltedow cast by the gnomon at midday on the 

 summer solstice, that is, at the very moment when he supposed the sun 

 to be vertical at Syene. The annexed diagram, Fig. 12, will serve to 

 explain how the magnitude of the earth was inferred from the observa- 

 tion. Let the circle ASD represent the earth, c its centre, s the 

 vertical gnomon at Syene, A that at Alexandria, the dotted lines re- 

 presenting the direction of the sun's rays ; and these are practically 

 parallel, because the distance of the sun is immensely great in com- 

 parison with the distance between them. Now, from the length of the 

 shadow A c of the gnomon, the angle A b c is determined, that is, the 

 angular distance of the sun from the zenith or point of the heavens 

 vertically over Alexandria. It will be evident to the merest tyro in 

 geometry that this angle is equal to 

 that between the lines s c and A c, 

 subtended by the arc A s. The angle \ \ 



was found by Eratosthenes to be in- 

 cluded by one -fiftieth part of the 

 whole circumference. The whole cir- 

 cumference of the earth must there- 

 fore be fifty times the distance be- 

 tween Alexandria and Syene, which 

 Eratosthenes estimated at 5,000 sta- 

 dia, and he thus found for the earth's 

 circumference 250,000 stadia, or 

 about 31,250 miles, an estimate not 

 very greatly wide of the truth, al- 

 though, as we now know, there were 

 several sources of error in the data. 

 Syene", Tor instance, is not on the me- 

 ridian of Alexandria, as Eratosthenes 

 supposed, but 30' to the east of it. 



Eratosthenes also made a very good determination of the obliquity 

 of the ecliptic by observing the altitude of the midday sun at the 

 summer and at the winter solstice, half the difference between these 

 angles being the obliquity, that is, the inclination of the earth's plane 

 of axial rotation to the plane of its orbit. 



Another great name in the list of Alexandrian men of science is 

 that of foiCHiMEDES (B.C. 287 212). His birthplace was .Syracuse, 

 but he came as a young man to the capital of the Ptolemies, and 

 studied majlxejn^ics under the pupils of Euclid of Alexandria, for by 

 that time the great master had himself passed away. Archimedes re- 

 turned to his native city, \v 'iere he soon had opportunities of applying 

 his science in practice. Indeed, it is chiefly by the great services 



FIG. 12. 



