2 GWYTHER, Conditions of Stresses in a Heavy Body. 



Then, we shall have for the elements of the strain, 

 cu 

 or 



r\ ex ex" J 



I / , CV hv\ 

 r \ ex c^ / 



_ I / c'z/ _ / _ ,iJ0W\ 

 r \lxl<^ ex) ' 



sin / I lu . liv 

 r \\ - x^ li^ hr 



sin y / V'v ev eu' 



sin / I'v _6v _(3«\ 

 r \ ?'r?ix ^x ex/ ' 



and A = — + ^{ 2n+2X — -{l -X )■-—, + ■::—]. 



cr r V ex Ixr b<p / 



And, for the rotations, 



1 / / nCW c'V \ 



2wi = - ( 2XW - (l - X^)^:r~ - r-^ I ' 



r\ tx exctj)/ 



sin d / I ei( cw \ ■ a r^ 



2(1). = I , — -r^^ -^v ] = 2 smO . Gg 



r \i - x^ c<f> dr / 



sin / c^v Iv , hi\ ■ ^ „ 



2W3= (^_^+ +_ =2SinO . Bs, 



r \ ercx ex tx/ 



whence 



or ox e(j) 



The general equations of elastic motion under gravity 

 become 



cr r Kcx e<p ) 



I . \cA , f I cw, , „ >) / ev\ 



