202 Proceedings of the Royal Irish Academy. 



(2) The case where the point P considered in the dielectric is at a distance 

 from the conductors large compared with their linear dimensions and mutual 

 distances. Here the character of the distribution of the matter, whether 

 electrical or gravitational, becomes indifferent, and the electrical problem 

 tends to the case discussed previously for a point charge, or for the 

 gravitational to a single atom of matter. The same forms of strain and 

 displacement hold for finite distances of P in the gravitational problem, 

 for the case discussed previously of a homogeneous sphere ; in the electrical, 

 for the case of an insulated" spherical conductor. The displacements are 

 now radial, and given by w = Bx, v = Ry, w = Bz, where 



The stress-components are now given by 



ar_ dB\ 

 r dr /' 



A= 2^[B+- -tA. 



C =2^{B^- —y 

 yz dB 



G=2,B^^^, 

 r dr 



xi = Ziixt — — - — . 



r dr 



The components of stress on any element plane 



cos -4, cos^, cos C 

 are then 



X = %xB cos ^ + 2u - -^— ^x cos A^ 11 cos B -v z cos G), 



Y = 2nB COS B + 2a - -7-^ (x cosA + ycosB+ z cos C), 

 r- ^ r dr 



7 dP 



Z = 2fxB cos C ^ 2fx - -j^ {x cos ^ + y cos ^ + « cos C). 

 This will represent a stress normal to the element plane (1) where the 



