FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 447 
Comparison of the third with the second form of (105) defines the generalised mean¬ 
ing of c when c is not a mere scalar. Or thus, 
tj e = E*d = i^(ED) e 
= 2 + IjCggEj 2 "t 2 ^33®3 2 "t CijEiEj + C 33 E 2 E 3 + C 31 EjE s ,.(106) 
representing the time-variation of U due to variation in the c’s only. 
Similarly 
T = HB - i H/'(H = HB - T,,,.(107) 
with the equivalent meaning for p generalised. 
Using these in (104) we have the result 
e 0 J + h 0 G = (Q + U + T) + q (E/j + B>) + (i EcE + £ H/iH) - (eJ + liG) + div YE^. . (108) 
Here we have, besides (Q + U + T), terms indicating the activity of a transla¬ 
tional force. Thus E p is the force on electrification p, and Eqp its activity. Again, 
Sc 
Wt 
= c + qV.e; 
so that we have 
and, similarly, 
> 
S c _ 1 
c = s - 4 V.o, j 
S/t 
» = j 
the generalised meaning of which is indicated by 
su c , 
- -gy + |EcE = - IE (qV. c) E = - qVU, 
where, in terms of scalar products involving E and D, 
a 
+ \TSLiJSL = - qVT^ 
(109) 
. . ( 110 ) 
- qYU, = - \ (E.qV.D - D.qY.E).(Ill) 
This is also the activity of a translational force. Similarly, 
S.t h 
• (H2) 
is the activity of a translational force. Then again 
- (eJ + hG) = - JYqB - GVDq = q (VJB + VDG) 
(113) 
