340 Introduction to the Study of Science 



by the spring balance. The force which the water exerts in sustaining 

 the weight, whether the object sinks or floats, is called the buoyant 

 force of water. 



Put the stone into the overflow can just as you did the block in 

 the first experiment. Catch and weigh the overflowing water. What 

 relation do you find between the weight of the water displaced and the 

 buoyant force of the water as shown in the last experiment ? 



The principle of buoyancy. The object has clearly lost in 

 the water the weight of its own volume of water. A general 

 statement of the fact is given : " The buoyant force of water 

 (and you may find it holds true for any liquid) is equal to the 

 weight of the water displaced." For a body that floats evi- 

 dently displaces water equal in weight to itself, that is, the 

 entire weight of a floating body is apparently lost in water. 



Archimedes' discovery. There is a tradition that Archi- 

 medes, living in Syracuse, Sicily, was requested by King Hiero 

 to ascertain whether or not silver had been substituted by a 

 jeweler for gold in his crown. As the king would not permit 

 Archimedes to drill into the gold crown, and as the crown was 

 too irregular in shape to measure for volume, another method 

 had to be devised. The scientist gave much thought to the 

 problem. One day when taking a bath he perceived that his 

 body was buoyed up by the water ; in fact it seemed to lose 

 weight when submerged in water. The significance of this 

 discovery in relation to his great problem was recognized at 

 once. He saw clearly how he could determine the weight of 

 the gold in the crown and whether or not any substitution of a 

 lighter metal had been made. He was so delighted with his 

 discovery that he rushed home from the bath, shouting " Eureka ! 

 Eureka ! " a Greek word meaning " I have found it." 



He weighed the crown in air, then in water. The difference 

 between the two weights was equal to the weight of the water 

 displaced. From the weight of the displaced water he com- 

 puted its volume, which he knew to be equal to the volume of 

 the crown. With these data he determined the weight per 



