jEther and Electrons . 701 



for the cut and reunited medium in which 6 is constrained 

 to have some different value. Thus we may legitimately 

 define the meanings of <f), yjr, .... in. any specification of 

 strain for which 6 does not vanish by saying that the con- 

 figuration (6. cf>, i/r, . . . .) is geometrically related to 

 (0, 0, 0, ... .) precisely as the con figuration (0, <£, yfr, . . . .) 



is related to (0, 0, 0, ). 



Consider now particularly the state of the medium when it 

 has been cut and strained and reunited, and then left to itself. 

 In this state 6 is different from zero, but <£, yjr, . . . . all 

 vanish in virtue of our definition of 0. Again, the state of 

 strain which is defined by (0, 0, 0, . . . .) and with which we 

 have now to deal, is due to no forces except mutually equili- 

 brating tractions at the reunited surfaces ; such tractions 

 giving rise to no virtual work in any infinitesimal displace- 

 ment which does not involve relative motion of the surfaces 

 in question. In other words, the strain (6. 0, 0, . . . .) is due 

 to applied forces which give rise to no virtual work in any 

 infinitesimal strain specifiable in terms of <£, yfr, . . . . ; so 

 that we have 



= <$> = V= i 



corresponding to > , (3) 



6z£(); G = cj> = f= . . . . ) 



where <1>, M*, . . . . are the (generalized) forces, corresponding 

 respectively to (f>, yfr, . . . ., which have to be applied to the 

 medium in order to maintain equilibrium. In other words, 

 if TV is the potential energy of strain, 



<£ = aw/d<£ 3 ^=aw/at> (i) 



All that has been said so far is independent of any limita- 

 tion regarding the magnitude of the strains involved. We 

 shall now suppose the strains to be so small that W is ade- 

 quately represented by a homogeneous quadratic function of 

 the coordinates of the medium ; that is to say, we can write 



W = (a homogeneous quadratic function of cf), ijr. . . . .) 



+ iA<9 2 + B 1 <9c/> + B 2 6ty+ (5) 



Differentiating in turn with respect to </>, ijr. . . . ., we find 



when fl^O; 0=^ = ^ = . . . . 



® = B l 0; ¥ = B 2 0, .... j v } 



