FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
443 
The Electromagnetic Flux of Energy in a stationary Medium. 
§ 16 . First let the medium be at rest, giving us the equations 
curl (H - ho) = J = C + D, .(94) 
- curl (E - e„) = G = H + B 
(95) 
Multiply (94) by (E — e 0 ), and (95) by (H — h 0 ), and add the results. Thus, 
(E — e 0 ) J + (H — h 0 ) G = (E — e 0 ) curl (H — h 0 ) — (H — h 0 ) curl (E — e 0 ), 
which, by the formula (25), becomes 
e 0 J + IpG = EJ + HG + div V (E — e 0 ) (H — h 0 ) ; 
or, by the use of (82), (83), 
e 0 J + h 0 G = Q + U + T + div W, .(96) 
where the new vector W is given by 
W = V (E - e 0 ) (H - h,,) 
(97) 
The form of (96) is quite explicit, and the interpretation sufficiently clear. The left 
side indicates the rate of supply of energy from intrinsic sources. These (Q + h : + T) 
shows the rate of waste and of storage of energy in this unit volume. The remainder, 
therefore, indicates the rate at which energy is passed out from the unit volume; and 
the flux W represents the flux of energy necessitated by the postulated localisation of 
energy and its waste, when E and H are connected in the manner shown by (94) 
and (95). 
There might also be an independent circuital flux of energy, but, being useless, 
it would be superfluous to bring it in. 
The very important formula (97) was first discovered and interpreted by Professor 
Poynting, and independently discovered and interpreted a little later by myself in an 
extended form. It will be observed that in my mode of proof above there is no 
limitation as to homogeneity or isotropy as regards the permittivity, inductivity, and 
conductivity. But c and g should be symmetrical. On the other hand, k and g do 
not require this limitation in deducing (97)." 
* The method of treating Maxwell’s electromagnetic scheme employed in the text (first introduced 
in “Electromagnetic Induction and its Propagation,” ‘The Electrician,’January 3, 1885, and later) 
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