﻿168 Mr. C. Ohree on the Local Alteration of 



If next pressure be applied over the outer surface only, or 

 p be zero, we obtain the results embodied in Table III. 



{ 



Table III. 

 p' only existing. 



n l — n 4- + — — 

 k x —k + + - 



o> + + + 



Bp c — — — + -f + (except when e/c and 



b/a both very small). 



From Tables II. and III. we see that if n t — n and k l — fc 

 be both positive, or if one be positive and the other zero, 

 Bp b is negative and Bp c positive when p only exists ; whereas 

 hpb is positive and Bp c negative when p' only exists. This- 

 signifies that if pressure be applied at either surface of a shell 

 the intercalation of a layer of greater k, n raises the radial 

 pressure at the surface of the layer nearest to the surface 

 where the pressure is applied, and lowers it at the other. In 

 other words, as we retire from the surface of the shell where 

 the pressure is applied the radial pressure falls more slowly — 

 i. e. has a less steep gradient — throughout the material on 

 both sides of the layer of greater k, n than previous to the 

 alteration of the layer, and makes up for this by an accelerated 

 rate of falling throughout the layer itself. 



The phenomena when one of the two n 1 — w and k x — k is 

 negative and the other zero are exactly opposite to the above, 

 and the same is also in general true when n x —n and k x — k 

 are both negative ; but in the latter event an exception may 

 arise when e/c and b/a are both very small, especially when 

 the altered layer differs considerably from the remainder. 



Effects on Dilatation. 



§ 6. The effect on the dilatation due to the existence of the 

 altered layer claims special attention. When n x —n and k 1 — k 

 are both positive, or one positive and the other zero, we see, 

 by reference to equations (21) and (27), and to Tables II. 

 and III., that BA is negative in both (b . a . a) and (e.a.c) 

 when p only exists, and is positive in both when p only exists. 

 Thus it follows by (6) that BA is opposite in sign to A in both 

 (b . a . a) and (e.a.c). In other words, the presence of the 

 layer of greater k, n reduces numerically* the dilatation — 



* To avoid complexity the statement in the text is limited to suit the 

 general case where the changes 8 A are not large enough to cause a re- 

 versal of sign in the dilatation. Such a reversal occurs, however, in one 



