122 Proceedings of Royal Society of Edinburgh. [ sess . 
Thus w may be regarded as a function of the independent variables 
(£, €, i {/, and we shall have 
p S(S8K,e = S 8+LawZ, = 8S Vl aw V ! 
07T r 
by equations (13) and (8) above. 
Thus 
sw = -fffSSrjfi V jSS)® - (SS V + JY VftX^-^awV Jdfe 
or 
W=fjfSS Vl (§VXV 1 ® + i// awV 1 )d< : . . . ( 79 ). 
Hence we see that 
g = - |V£)A®- dwA (80) 
% = [kVX)Vi& + *awVv-L» .... (81), 
and that these forces per unit volume and surface respectively can be 
supposed due to a stress <j> given by 
(^a)=-|YM-^(0 (82). 
From this we see that the stresses in the electric field can only be 
determined when for the particular strain existing at any point 
forty-two scalar functions of that strain are known, viz., the six 
coefficients of specific inductive capacity and their thirty-six dif- 
ferential coefficients with respect to the six coefficients of pure 
strain. 
The two parts of the stress cf> (1) that which is independent of 
the variation of specific inductive capacity with strain, and (2) 
that which depends on this variation are conveniently considered 
separately. 
The first is more general than Maxwell’s, because we have not, 
as he does in this connection, assumed that X is parallel to (S'. It 
consists of a tension in the direction bisecting the positive directions 
(or negative directions) of both X and (5*, of magnitude JT£)T(§, 
an equal pressure in the direction bisecting the positive direction of 
either and the negative direction of the other, and a pressure at 
right angles to both, of magnitude — JS^)(S or w. This stress, of 
course, reduces to Maxwell’s when X is parallel to (£• 
The other part of the stress — flw = can be only 
