THEORY OF ELECTROMAGNETISM. 
709 
It might be thought that equation (4) could not be true in general unless a was 
a scalar in general. This, however, is not the case. From equation (4) it certainly 
follows that VU va\Jv = 0, but this, by virtue of the dependence of a on strain is merely 
an equation of condition satisfied by the strain. The equation \y\Jv] a + b = aUv a may 
indeed be written 
M«_6 = — TJWLJV.(6), 
which is, of course, more general than equation (5), since here a is not assumed a 
scalar. It may be noted that V dtia d%' = mfV dta d%, so that the two conditions, 
VUVa'UV = 0 and YJJvaTJv = 0, are identical. 
101. It should be remarked here that on the present theory the term just introduced 
would have no thermal effect in steady fields, and, therefore, no connection with the 
Peltier effect. (See § 85 above.) 
We have been obliged to suppose l s no longer zero. Before discussing the modifica¬ 
tions this entails in the general results above, the last application in the present paper 
of those results will be made. 
This is the place where it would be proper to discuss electrolysis in connection with 
the present theory. This I do not propose to do, because the mathematical machinery 
of this paper would require some important modifications to enable us to deal with 
such subjects as diffusion, the motion of the ions, &c., and because the subject is a 
very large one, and would, perhaps, unduly extend the length of the present paper. 
F. The Transference of Energy through the Field. 
102. On the present theory, in which the principle enunciated in equations (24), 
(25), § 36, required strong confirmation, it was necessary to show that it agreed in 
every particular with the generally accepted views as to frictional forces being 
derivable from a dissipation function in Lord Rayleigh’s sense, and also with the 
much more certainly established truths treated of in the theory of conduction of heat. 
The only way to establish this last seemed to be to show that as a result of the 
principle there was a time flux of intrinsic energy, one term of which was what, in the 
theory of conduction of heat, is .called the time flux of heat. This led to the necessity 
of finding the time flux of intrinsic energy in general. We are thus brought on to 
ground which has hitherto been regarded as belonging exclusively to Professor 
Poynting —the transference of energy through the field. 
103. Let us now examine how far the results of the present theory are consistent 
with those of Professor Poynting. Let L be a flux such that 
E - P. = [f SL <K.(1), 
5 F 
MDCCCXCIT.—A. 
