OBSERVATION AND EXPERIMENT 73 



ciples with respect to fluids at rest discovered by Archimedes 

 as amongst the capital contributions to the science of all times ; 

 for while his successors, of the last two centuries especially, 

 hav^e added to hydromechanics the large and vastly more difficult 

 branch of hydrokinetics, they have found no change essential 

 in his laws of hydrostatics. 



Equally important, also, in its far-reaching connections was 

 the work of Eratosthenes in determining the size of the earth. 

 This work required an hypothesis as to the shape of the earth 

 and appropriate observations. Supposing the earth to be spher- 

 ical, an assumption which Eratosthenes knew well how to justify, 

 he saw that to determine its size it is only necessary to apply 

 the rule of three to the measured length of an arc of a meridian 

 and to the measured difference of the latitudes of the ends of 

 such arc. He observed that at the city of Syene, which is about 

 500 miles south of Alexandria, the sun shone vertically down- 

 wards into deep wells at noon on the day of the summer solstice, 

 showing thus that at that place and time the sun was in the 

 zenith. On the same day at Alexandria he observed, by means 

 of the gnomon, that the sun at noon was south of the zenith by 

 one-fiftieth of a circle, or 7°. 2. The distance between the two 

 points was found by the royal road masters of the country to 

 be 5,000 stadia, thus giving for the complete circumference of 

 the earth 250,000 stadia. Although the measurements thus 

 made by Eratosthenes were very crude and undoubtedly subject 

 to large errors, we see in them the beginnings of some of the 

 most refined geodetic operations of the present day. Unfor- 

 tunately for us, also, the measurement of the distance is ex- 

 pressed in a unit whose relation to modern units is only roughly 

 known. ^ 



But commendable as was the work of his predecessors and 

 contemporaries, the work of Hipparchus rises to a still higher 



1 As illustrating the slow growth of ideas with respect to precision, it may be re- 

 lated that when the Arabians, in the ninth century undertook, for the same purpose, 

 the measurement of a meriodinal arc on the plain Singiar, in Mesopotamia, they 

 were not more successful in preserving for posterity the standard of length used by 

 them. This standard is said to have been the " black cubit, which consists of 27 

 inches, each inch being the thickness of six grains of barley." 



