450 
MR. O. HEAVISIDE ON THE FORCES, STRESSES, AND 
I argued that 
W = V(E-e 0 ) (H-h 0 ) . (129) 
was the probable form of the Poynttng flux in the case of a moving medium, not 
VE^, because when a medium is endowed with a uniform translational motion, the 
transmission of disturbances through it takes place just as if it were at rest. With 
this expression (129) for W, we have, identically, 
VEjH, - Veil - Ve (J h - Veh 0 = W - VeH - VEh.(130) 
Therefore, by (128) and (130), we get 
2% = VeH + VEh + q (U + T),.(131) 
to represent the negative of the stress flux of energy, so that, finally, the fully 
significant equation of activity is 
e ut J 0 + h 0 G 0 = Q + U -f f + Fq + Sa + div ^V (E — e 0 ) (H h 0 ) + q (U + T)J 
- div [VeH + VEh + q (U + T)]. (132) 
This is, of course, an identity, subject to the electromagnetic equations we started 
from, and is only one of the multitude of forms which may be given to it, many being 
far simpler. But the particular importance of this form arises from its being the 
only form apparently possible which shall exhibit the principle of continuity of energy 
without outstanding terms, and without loss of generality; and this is only possible 
by taking J 0 as the proper flux for e 0 to work upon/"' 
* In the original an ei’roneons estimate of the value of (0/3 1) (U c + T F ) was used in some of the 
above equations. This is corrected. The following contains full details of the calculation. We require 
the value of (0/06) Uc, or of fE (dc/dt) E, where 3c/3i is the linear operator whose components are the 
time-variations (for the same matter), of those of c. The calculation is very lengthy in terms of these 
six components. But vectorially it is not difficult. In (27), (28), we have 
D = cE - i.c,E + j.c,E + k.c g E 
= (i.Cj + j.c 3 + k.c 3 )E, 
if the vectors c,, c 3 , C 3 , are given by 
Cj = ic n + jc 13 + kc 13 , c 2 = ic 31 + jc 33 + kc 23 , 
We, therefore, have 
c :’, — + jc 32 + kr 33 . 
(132a) 
0c. 
ob 
ci 
0j , 0k 
E 2* E - E ( 0^ C 1 + 0^ >C 2 + dt ,Cs E + E (i- + j- g/ + k - 
0C t . 0Co 0C 3 
'dt 
0 ^ 
(1326) 
The part played by the dots is to clearly separate the scalar products. 
Now suppose that the eolotropic property symbolised by c is intrinsically unchanged by the shift of 
the matter. The mere translation does not, therefore, affect it, nor does the distortion; but the rotation 
