77 2 
MR. A, McAULAY ON THE MATHEMATICAL 
indeterminate one ; thus, for example, if the energy inside a closed surface remains 
constant we cannot, unless we know the mechanism of the system, tell whether this 
is because there is no flow of energy either into or out of the surface, or because as 
much flows in as flows out. The reason for this difference between what we should 
expect and the result obtained in this paper is not far to seek.” He then goes on to 
point out' 1 ' how, so far from P being necessarily the time flux of energy, P + We 
where e is any vector, such that at surfaces of discontinuity [VUVe] a + b = 0, might 
equally well be taken as the time flux of energy. It so happens that (assuming v 
continuous) L — P is such a vector, so that the difference between the result arrived 
at in this paper and Professor Poynting’s is just such a case as Professor Thomson 
warned us to expect. 
We cannot then say that either L or P is the time flux of energy, but only that if 
we assume either the one or the other (P being supplemented with P s ) to be the flux, 
the real changes of intrinsic energy will be accounted for. 
106. Notwithstanding Professor Thomson’s warning, many subsequent writers seem 
to have taken Professor Poynting’s theories for established facts. The following 
statement of Professor Poynting especially seems to have grown to be accepted 
almost universally as a commonplace truth [‘Phil. Trans.,’ 1884, Part II., p. 361] :— 
“ I think it is necessary that we should realise thoroughly, that if we accept 
Maxwell’s theory of energy residing in the medium, we must no longer consider a 
current as something conveying energy along the conductor. A current in a conductor 
is rather to be regarded as consisting essentially of a convergence of electric and 
magnetic energy from the medium upon the conductor, and its transformation there 
into other forms.” Now, if we take L as the true time flux of energy, we see that 
one way in which we must regard a current is precisely the way Professor Poynting 
denies us, namely, “ as something conveying energy along the conductor.” In fact, 
from the term vC in L, we see that in this respect, as in so many others, a current and 
the potential are the exact analogue of a liquid current and its pressure. Without 
doubt, the view that L is the true flux is simpler for steady fields than the view that 
P is. This statement is not so obvious—perhaps on the whole not true—for varying 
fields. 
It is easy to contrast in detail the two views in all the particular cases Professor 
Poynting considers. This may, therefore, be omitted here. 
G. The General Effects of the Existence of l s . 
107. The general equations above established must now be modified on account of l s . 
In considering electrolysis on the present theory it would be necessary to suppose 
l s to contain D or C or both, as well as d. For the sake of simplicity we shall not 
* This is not put quite in the form Professor Thomson puts the case. 
