52 THE EQUILIBRIUM OP ELASTIC SOLIDS. 



Since the forces which act on the particle in the direction of the radius 

 must balance one another, or 



2qdrd0 +p (rd0y = lp + ^ drj (r + dr)*e, 



therefore y"~P = <j ~f~ ( 3 ^). 



Substituting this value of q p in the preceding equation, and reducing, 



rJ.n rlfi 



therefore 



Integrating, 



But 



and the equation becomes 



^_ 



dr^ J r r 



therefore p = c t -j + ^ . 



Since p = h^ when r = a l , and p h t when r = a tt the value of p at any 

 distance is found to be 



_ afh^afh, _ ofo* _V-A . . 



o, ,- + i^gL i- / 38 \ 



a^-a,' i* a,' -a,' 



8F .. 8r a.'hi afh. 1 _ 0,'ci,' ^, A, 1 



^_ Q ^_ * ^L J . j__. 



==- O - - "^ 8 g 



Whenr=a l; ^ = ^"^ I+f^'Az*-. i 1 



r a. a, u. a, a t m. 



, (39). 



~ a, 1 a,' \ /u, 2wi/ a,' a, 1 \ji 2m/ 



When the external and internal pressures are equal 



, SF ^ 

 h l = h t =p = q, and -=^.- = v 4(J / 



Jr /^ 



