EXAMPLES. 63 



Let the density of the material of the parallelepiped be p 

 times that of the fluid ; then (Art. 25, Cor.), 



p : 1 :: y : h; 

 .: y = hp, 



which in (1) gives 



which is the measure of the stability required. 



COR. 1. To determine the limits of stability depending 

 upon the dimensions and density of the solid, let 8 = 0, 

 and (2) becomes 



-p) = 0; (3) 



or, ^ = V&P (1 p). 



If p = I, we have 



\ = W6 = 1.225, 



n 



and hence in this case the parallelepiped floats in stable, 

 indifferent, or unstable equilibrium, according as the breadth 

 is >, =, or < 1.225 times the height. 



COR. 2. Solving (3) for p, we get 



11 /' 2P 

 = 2 2V ~3T*' 



which is real when = is = or < A/6 ; *' &> when the 



ratio of the breadth of the solid to the height is equal to, or 



