438 
MR. 0. HEAVISIDE ON THE FORCES, STRESSES, AND 
P N = n-^ V curl D. N, 
F = — n-^ curl 2 D. 
(63) 
Thirdly, if we have both Jc = — § n and n — n x , then 
P N = 2 n curl VDN, 
F = — 2 n curl 2 D, 
(€ = n curl D), 
(64) 
i.e., the sums of the previous two stresses and forces. 
§13. As already observed, the vector flux of energy, due to the stress, is 
— 2a q = — a,// = — (a l2l + a 2 g a - + o^).(65) 
Besides this, there is the flux of energy 
q (H + T) 
by convection, where U is potential and T kinetic energy, Therefore, 
W = q(U+ T) .(66) 
represents the complete energy flux, so far as the stress and motion are concerned. 
Its convergence increases the potential energy, the kinetic energy, or is dissipated. 
But if there be an impressed translational force f its activity is fq. This supply of 
energy is independent of the convergence of W. Hence 
fq + Q + u = T + div [q (U + T) — 2a^].(67) 
is the equation of activity. 
But this splits into two parts at least. For (67) is the same as 
(f + F) q + Sav 2 = Q + U + T + divq (U + T),.(68) 
and the translational portion may be removed altogether. That is, 
(f + F) q = Q 0 + U 0 + T 0 + div q (U 0 + T p ),.(69) 
if the quantities with the zero suffix are only translationally involved. For 
example, if 
*+’-'! . (7o> 
as in fluid motion, without frictional or elastic forces associated with the translation, 
then 
