192, 193] Stresses in the Medium 167 



By Green's Theorem, 



. rrrd fiv 



= * JJJ te & 



[[[VVdV, , . C[[dV d f dV\ 



JJJ w & d ydz = ~ in * vte J 



Now 



rr/*8F 8 /dv\ , , , rrr, a /ary . 



1 11 aT a~ bf~ dxdydz = U dxdyd 



JJJ dy dy \fa/ JJJ * dx \dy J 



- 



so that the last equation becomes 



and there is a similar value for 



Substituting these values, equation (108) becomes 



8F8F 



X= - 



4?r j v2// Vw/ ^ 



8F8F 



o 



[_V 8a; / \ 9y / V 



Since we have at every point of the surface of a conductor 



8F 8F 8F 



a* !__. ........................ (109) 



/ m n 



it follows that the integral over each conductor vanishes, leaving only the 

 integral with respect to cZS, which gives 



X = - (lP xx + mP xy + nP m ) dS, 



where ^ = - (Z 2 - F 2 - 2 ), 





