FUNDAMENTAL FORMULATIONS OF ELECTRODYNAMICS. 
243 
some authors, 1)ut which is not satisfied by the results of our jjreseiit discussion. 
The vector determining tlie flux of electromagnetic energy has been seen to be 
8 = V [E. H'] 
and that determining the momentum is 
M = — [E, HI. 
In the absence of magnetic media and convective dielectric polarisations these two 
expressions satisfy the equation 
M=is. 
but under the most general circumstances this relation is not satisfled. 
We have so far conducted the discussions as though the quantity derived as a 
momentum is unique and definite, whereas, as a matter of fact, this is far from being 
the case. We saw that the idea of the momentum arose from certain outstanding 
terms which remamed when attempting to reduce the electromotive forces to a 
representation by a stress system. Now we can give a number of difterent forms to 
this reduction and each one carries with it a diflerent expression for the electro¬ 
magnetic momentum. We can, for instance, write 
J. 
47rc 
[EH] = 
1 
Attc^ 
1 
dX 
Attc^ [_ dt ’ 
H 
and the second term in this expression when differentiated with respect to the time 
might be included in the stress specification. This would leave a new expression for 
the electromagnetic momentum which is 
LLc 
Cg \ 47r L dt 
a form which would probably be suitable for use in connexion with a theory in which 
the radiation phenomena are represented by Macdonald’s form of the theory. 
This is not the only alternative to the usual theory for we can construct similarly 
any number of others. It appears, however, that the usual presentation is probably 
the simplest possible one, and this is a great advantage in its favour ; but subsequent 
developments of the theory may require a modification, and then it is as well to 
remember that there are other forms of the theory perfectly consistent with the 
general relations of the electromagnetic field, both as regards its general and 
dynamical aspects. 
