IN POPULAR PHYSICS. 33 



56*. A hollow ball of iron weighs 1O Ibs. : what must be 

 its volume to float in water ? 



10 Ibs. = 160 oz. As a cubic ft. of water weighs 1,000 oz., 

 the ball must displace such a part of a cu. ft. of water as 160 

 oz. is of 1,000 oz., or .16 cu. ft. 



37. Suppose that Hiero's crown was an alloy of silver 

 and gold, and weighed 22 oz. in air and 2O% oz. in water. 

 What was the proportion of each metal ? 



"Multiply the specific gravity of each ingredient by the 

 difference between it and the specific gravity of the compound. 

 As the sum of the products is to the respective products, so is 

 the specific gravity of the body to the proportions of the in- 

 gredients. Then, as the specific gravity of the compound is to 

 the weight of the compound, so is each of the proportions to 

 the weight of its material." American Cyclopedia. 



Second method : 



Let A = mass of crown = 22 



" B = sp. gr. " = 14.66 



" x = mass of gold 



" x' = sp. gr. " = 19.26 



" y = mass of silver 



" y 1 = sp. gr. " 10.5 



then 



and since 



mass 

 volume = 



specific gravity' 

 we have 



A _x y f 



B"-tfV 



whence we find (approximately), 



Gold = 13.95 

 Silver = 8.05 



1 2 1 38. Wliy ^vill oil f which floats on water, sink in 

 alcohol ? 



The specific gravity of absolute alcohol is only .79 ; hence 

 even the dilute alcohol of commerce is lighter than most speci- 

 mens of oil. 



