THE BEGINNINGS OF SCIENCE 43 



just in proportion as his body was immersed did the 

 water run out of the tub. From this he caught the 

 method to be followed in the solution of his problem 

 and immediately followed it up. He jumped out of 

 the tub in his joy and ran home naked through the 

 streets, crying in a loud voice ' Eureka/ meaning 'I 

 have found it,' for he had found the method 1 for 

 which he was searching." 



Another story as to Archimedes is told by Plutarch. 

 While conversing with Hiero, Archimedes explained 

 the principle of the lever by an illustration. He said 

 that, given a lever and another world like our earth on 

 which to stand, he could move our earth itself. Hiero 

 was struck with amazement, and asked Archimedes 

 to give a demonstration by moving some large weight 

 on this earth. The latter arranged to draw out of the 

 dock of the king's arsenal a heavily loaded ship which 

 was otherwise only to be moved by many men with 

 great effort. To accomplish this he used a system of 

 pulleys and unaided drew the boat out of its dock. 



How this " technical Yankee of antiquity," as he 

 has been called by an eminent German historian, 



1 Suppose Archimedes weighed the crown first in air and then in 

 water. When hung from the balance arm so as to be immersed 

 in water it weighed less than before by an amount equal to that of 

 the displaced water. Hence subtracting the two gave the weight of 

 the displaced water. Now suppose he performed the same oper- 

 ations on a lump of gold. He would have found that the weight 

 of the gold in air was 19.3 times the weight of the displaced water. 

 If he used a lump of silver he found this ratio to be only 10.5. Hence 

 if the crown was pure gold it should weigh 19.3 times as much in 

 air as the water it displaced. On the other hand, if it was of pure 

 silver this ratio would be 10.5. If it was a mixture of the two 

 metals the ratio would lie between these two values. 



