EXAMPLES. 87 



51. A ring consists of gold, a diamond, and two equal 

 rubies ; it weighs 44J grs., and in water 38f grs. ; when one 

 ruby is taken out, it weighs 2 grs. less in water. Find the 

 weight of the diamond, the specific gravity of gold being 

 16J, of diamond 3, of ruby 3. Ans. 5 grs. 



52. If the price of pure whiskey be $4 per gallon, and its 

 specific gravity be .75, what should be the price of a mixture 

 of whiskey and water which on gauging is found to be of 

 specific gravity .8? Ans. $3.20. 



53. How deep will a paraboloid sink in a fluid whose spe- 

 cific gravity is n times that of the solid, the axis being 

 vertical and equal to a, and the vertex upwards ? 



Vn Vn 1 

 Ans. a = 



Vn 



54. A cubic inch of metal, whose specific gravity is m, is 

 formed into a hollow cone, and immersed with its vertex 

 downwards. Determine the ratio of the altitude to the 

 exterior radius of its base, when the surface immersed is a 

 minimum. 



