46 THE EQUILIBRIUM OF ELASTIC SOLIDS. 



By comparing this equation with the last, we find 



(L L\<b + (L AW^ + ^ 



\9/t 3m/ dr \9ft 3m/ \dr dr) 

 Integrating, 



Since o, the longitudinal pressure, is supposed constant, we may assume 



Cl ~ 



c, 



i+'-i 



9/x 37?i 

 Therefore qp = c t 2p, therefore by (21), 



dr r r ' 

 a linear equation, which gives 



The coefficients c, and c, must be found from the conditions of the surface 

 of the solid. If the pressure on the exterior cylindric surface whose radius is a, 

 be denoted by h lt and that on the interior surface whose radius is a a by ^,, 



then p = h 1 when r = a, 

 and p=h t when r = a a 

 and the general value of p is 



P= V'-a/ ' ^ a? 11 "? ^ 22)> 



,'A, a*h ct/a,' A., j 



.(24). 



r* a a '-< ! 



This last equation gives the optical effect of the pressure at any point. The 

 law of the magnitude of this quantity is the inverse square of the radius, as in 



