454 
MR. 0. HEAVISIDE OH THE FORCES, STRESSES, AND 
If S be the torque, it is given by 
therefore 
VSN = P N - a x = E.DN - D.EN + &c. 
VN (VED + VHB) ; 
S = VDE + VBH .... 
(139) 
But the matter is put more plainly by considering the convergence of the stress 
flux of energy and dividing it into translational and other parts. Thus 
div 2ft? = Fq + (E.DV.q - U div q) + (H.BV.q - T div q),.(140) 
where the terms following Fq express the sum of the distortional and rotational 
activities. 
Shorter Way of going from the Circuital Equations to the Flux of Energy, Stresses, 
and Forces. 
§ 21. I have given the investigation in §§ 17 to 19 in the form in which it occurred 
to me before I knew the precise nature of the results, being uncertain as regards the 
true measure of current, the proper form of the Poynting flux, and how it worked in 
harmony with the stress flux of energy. But knowing the results, a short demonstra¬ 
tion may be easily drawn up, though the former course is the most instructive. Thus, 
start now from 
curl (H - ho) = J 0 , 
- curl (E — e 0 ) ~ G 0 , 
(141) 
on the understanding that J 0 and Gr 0 are the currents which make e 0 J 0 and h 0 G 0 
the activities of e 0 and h 0 the intrinsic forces. Then 
where 
e 0 J 0 F h 0 G,j = EJ 0 + HG 0 + div W,.(142) 
W = V(E —e 0 )(H —ho);.(143) 
and we now take this to be the proper form of the Poynting flux. Now develop 
EJ (I and HG 0 thus :— 
EJ () F HGq = E (C + D + q/> + curl h) + H (K F B + q<x — curl e), by (93) ; 
= Q x + U F tic + Eq/; + E curl VDq 
+ Q 3 + T 4- T (jl + Hqo- + H curl VBq, by (88) aud (91) ; 
= Qi + U + ti c + Eqj> + E (D div q + qV.D - q div D - DV.q) 
+ Q 2 F T + T M + Hq<7 + H (B div q + qV.B - q div B - BV.q), by (26), 
= Q a + U + U c + 2U div q + E.qV.D — E.DV.q 
+ magnetic terms, 
= (Qi + U + div qU) + (U div q - E.DV.q) + (U c - qV.U + E.qV.D) 
F magnetic terms...(144) 
