FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
459 
sentecl by the action of E and H in A on the new interfacial matter and current. 
That is, the E and H in the region A may be done away with altogether, because 
their abolition will immediately introduce the fictitious matter and current equivalent, 
so far as B is concerned, to the influence of the region A. Similarly E and H in B 
may be abolished without altering them in A. And, generally, any portion of the 
medium may be taken by itself and regarded as being subjected to an equilibrating 
system of forces, when treated as a rigid body. 
§ 24. When c and p do not vary in space, we do away with the forces — ^E 2 Vc 
and — -lEPVg, and make the form of the surface and volume translational forces 
agree. We may then regard every element of p or of cr as a source sending out 
from itself displacement and induction isotropically, and every element of J or G- as 
causing induction or displacement according to Ampere’s rule for electric current and 
its analogue for magnetic current. Thus 
H 
_ + VJu 
4<7rr“ 
(163) 
where iq is a unit vector drawn from the infinitesimal unit volume in the summation 
to the point at distance r where E or H is reckoned. Or, introducing potentials, 
E = - -curl 2-A, .(164) 
4 irr 4tirr 
H = — V2 ^ + curl .(165) 
Aiirr 4 ttv 
These apply to the whole medium, or to any portion of the same, with, in the 
latter case, the surface matter and current included, there being no E or H outside 
the region, whilst within it E and H are the same as due to the matter and current 
in the whole region (“matter,” p and c r ; “current,” J and G). But there is no 
known general method of finding the potentials when c and p. vary. 
We may also divide E and H into two parts each, say E x and due to matter 
and current in the region A, and E 2 , H 3 due to matter and current in the region B 
3 n 2 
