﻿Isotropic Spheres under Uniform Surface- Pressure. 167 

 In (e .a .c) we have 



» . t « 3 / 1 1 e"\ 



s ° = -*p>7=Am + ^?)> • • • • < 26 > 



«*— fcjc?J. (») 



*-£>* 8 /^(l-$) (28) 



= -^^(l+^l) (29) 



S00 



c 3 3c 



»-±**7=?i? < 3 °) 



C' J 



The existence of the common factor 8p.~o o will be 



noticed. 



We shall consider the phenomena relating to the pressures 

 p and p' separately. By reference to Table I. we know the 

 signs of the strains and stresses in the simple shell (e.a. a), 

 and when the signs of Spb and 8p c are determined from (16) 

 and (17) we know the signs of the increments to the strains 

 and stresses in (b . a . a) and (e . a . c). 



§ 5. If first pressure be applied over the inner surface only, 

 or p' be zero, the signs of 8p& and 8p e are shown in the 

 following Table II. for the cases most likely to arise in 

 practice. 



Table II. 



p only existing. 



\'n x — n + + — — 

 \k x -k + + - - 



8p b — — — + + -f (except when e/c and 



b/a both very small.) 



8p c + + + - - - 



The columns of signs are to be taken each separately. The 

 first column, for instance, gives the signs of 8p b and 8p c when 

 n r — n and k x — k are both positive. It seems hardly practi- 

 cable to lay down concise general rules for what happens 

 when n 1 — n and k x — k have opposite signs, but the results in 

 any specified case may be derived of course from (16) and 

 (17). 



