48 THE EQUILIBRIUM OF ELASTIC SOLIDS. 



1. When A, = A,, the equations of compression become 



"3m'~ '' 



(27). 



When A, = A, = o, then 



x r 



The compression of a cylindrical vessel exposed on all sides to the same 

 hydrostatic pressure is therefore independent of m, and it may be shewn that 

 the same is true for a vessel of any shape. 



2. When a^/t^a, 1 ^,, 



x 

 Sr 



3m 



(28). 



In this case, when o = 0, the compressions are independent of /A. 



3. In a solid cylinder, a, = 0, 



p = q = h 1 . 



S 



The expressions for ^ and - - are the same as those in the first case, when 



X i 



h t . 



When the longitudinal pressure o vanishes, 



x 



. 

 3m' 



