FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
439 
(f + F)q = /J q^ = T + divqT .(71) 
if T = the kinetic energy per unit volume. The complete form (69) comes 
in by the addition of elastic and frictional resisting forces. So deducting (69) from 
(68) there is left 
2ftV 2 = Qi + lb + i\ + div q (U x + T x ),.. (72) 
where the quantities with suffix unity are connected with the distortion and the 
rotation, and there may plainly be two sets of dissipative terms, and of energy (stored) 
terms. Thus the relation 
€=(„, +% | + »4)criD.(73) 
will bring in dissipation and kinetic energy, as well as the former potential energy of 
rotation associated with n y . 
That there can be dissipative terms associated with the distortion is also clear 
enough, remembering Stokes’s theory of a viscous fluid. Thus, for simplicity, do away 
with the rotating stress, by putting € = 0, making P N and Q, N identical. Then take 
the stress on the i plane to be given by 
P 1 = („ + ^ j + .| 8 ) ( VD 1+ V 1 D ) - i { p + ,(. i + ^ ( + .| ? )a i vD}, . . (74) 
and similarly for any other plane ; where P = — Jc div D. 
When fx = 0. v = 0, we have the elastic solid with rigidity and compressibility. 
When n — 0, v = 0, we have the viscous fluid of Stokes. When v = 0 only, we 
have a viscous elastic solid, the viscous resistance being purely distortional, and 
proportional to the speed of distortion. But with n, fx, v, all finite, we still further 
associate kinetic energy with the potential energy and dissipation introduced by 
n and /x. 
We have 
SPVg = Qo + Uo + Tg 
for infinitesimal strains, omitting the effect of convection of energy ; where 
T 2 = M-f(divqP + V 2l (V 2l + V iq ) + Vg 3 (V ?2 + V,q) + V 23 (Vg 3 + V 3 q)], .... (75) 
Q 2 = ^ [-I(divq)2 + V ?1 (V 2l + V 1 q)+V ?8 (V Sa + V 8 q) + Vg 8 (V 2s + V 8 0], ■ • • • (76) 
U 2 = in _ A (div D)2 + VD y (VD t + YjD) + VD 2 (VD, + V 3 D) + VD 3 (VD 3 + V 3 D)]. (77) 
