AND DEFORMATION OP A THIN ELASTIC SHELL. 531 



< 65 > 

 (66 > 



. (67) 



Of these (67) gives V when U and w are known. The solution of (66) consists of 

 two parts one, the complementary function which satisfies (66) when w = ; the 

 other, the particular integral which satisfies (66) when w is a solution of (65). We 

 may show first that this particular integral is proportional to ( 1 jt 2 ) (div/dp) \ 

 take it to be X (1 /**) (dwjd^}. 



For, writing (65) in the form 



a.v a 2 . dw 



~ &*? ~ 2/t(l - /i) - 



and difierentiating, we have 



and the left-hand side is found by using (66) to be 



so that X(l /x 2 ) (dw/dn) ^ a particular integral of (66), if 



*cY2cX = (2 + jc)/(l -f c) = 2 + K* - K2/2X, 

 which are both satisfied by 



Thus, 



is a particular integral of (66). 



3 Y 2 



