INTRODUCTION. XXXI 



problem, till, going one day into the bath, he perceived that the 

 water rose in the bath in proportion to the bulk of his immersed 

 body ; it occurred to him at that moment that any other sub- 

 stance of equal 'size would have raised the water just as much, 

 though one of equal weight and of less bulk could not have 

 produced the same effect. He immediately felt that the solu- 

 tion of the king's question was within his reach, for taking two 

 masses, one of gold and one of silver, each equal in weight to 

 the crown, and, having filled a vessel very accurately with 

 water, he first plunged the silver mass into it, and observed the 

 quantity of water that flowed over ; he then did the same with 

 the gold, and found that a less quantity had passed over than 

 before. Hence he inferred that, though of equal weight, the 

 bulk of the silver was greater than that of the gold, and that 

 the quantity of water displaced was, in each experiment, equal 

 to the bulk of the metal. He next made a like trial with the 

 crown, and found it displaced more water than the gold, and 

 less than the silver, which led him to conclude that it was 

 neither pure gold nor pure silver. 



This discovery by Archimedes, which after all is but the 

 application of the well-known axiom, that two bodies cannot 

 occupy the same space at the same time, has been considered 

 one of the most fortunate in the annals of science, for it has 

 led to great advances in the arts, and become the foundation of 

 chemical analysis ; just in the same way that his development 

 of the properties of floating bodies has formed the rudiments 

 of naval architecture, how much soever this branch of con- 

 structive mechanics may boast of its modern improvements. 



In the Tenth Chapter, specific gravities and the methods of 

 weighing solid bodies in fluids are treated of; and the principle 

 here to be demonstrated is, 



That when a solid body is immersed in a fluid of dif- 

 ferent specific gravity from itself, the weight which the 

 body loses will be to its whole weight, as the specific 

 gravity of the fluid is to the specific gravity of the solid. 



In this chapter we have a full developement of that fine thought, 

 which rendered the truth of experiment an overmatch for the 

 craft of Hiero's goldsmith ; and the examples we have pro- 



