170 Mr. G. H. Livens on the Mechanical 



Larmor, where the medium is isotropic and the law of 

 induction linear, this is probably true ; but the present 

 argument shows that it is the electrical displacement in 

 Maxwell's sense that more properly defines degrees of 

 electrical freedom in the dielectric medium. 



The fact that in the aggregate for the whole field the 

 above expression for SW vanishes, which Helmholtz is at 

 such pains to secure and which results from the characteristic 

 equation for D, viz. 



div D=p, 



merely verifies that there is on the whole no resultant force 

 on the infinitely extended system. 



The second term in the expression for the forcive just 

 deduced is exactly analogous to the corresponding term 

 depending on the polarization of the elementary theory of 

 Maxwell. It is only to be noticed that the whole circum- 

 stances summed up in the vector D are subject to the virtual 

 displacement, of the matter, whereas in Maxwell's theory the 



part — E of this vector denning conditions in the aether 



does not partake of motions of the matter, the remainder 



P=D — -7— being the only portion that so moves. Herein 



lies the second cause of discrepanc} r between the two theories, 

 and it would appear that the method described by von Helm- 

 holtz must be radically unsound : it would be valid if there 

 were only one medium under consideration, of which W 

 is the energy function ; but there is here in the same space 

 the aether with its stress and the polarized matter with 

 its reacting mechanical forces, and there is no means of 

 disentangling from a single energy function in this way the 

 portions of energy which are associated with these different 

 effects. 



To sum up, we may say that the theory of electric stress 

 formulated by Helmholtz, Hertz, Cohn, and others is funda- 

 mentally at fault. In its correct analytical form it involves 

 physical assumptions which have been long regarded as 

 wholly untenable, besides leading to an impossible type of 

 dielectric body forcive. We are therefore virtually thrown 

 back to Maxwell's original and simple theory, which is the 

 only one that has really proved to be consistent with all the 

 facts, among which it must not be forgotten to include those 

 fundamental ones concerning the electrodynamic properties 



