FLUXES OF ENERGY IN THE ELECTROMAGNETIC FIELD. 
437 
F = (n + wj V 2 D + (k + 3 n — «i) V div D;.(57) 
or, in another form, if 
P = - k div D, 
P being the isotropic pressure, 
F = — VP + n (V 2 D + ^ V div D) — n x curl 2 D,.(58) 
remembering (23) and (53). 
We see that in (57) the term involving div D may vanish in a compressible solid 
by the relation n x — k + ^ n ; this makes 
n + n-y = k + f n, — n = k — § n, .. . . (59) 
which are the moduli, longitudinal and lateral, of a simple longitudinal strain ; that 
is, multiplied by the extension, they give the longitudinal traction, and the lateral 
traction required to prevent lateral contraction. 
The activity per unit volume, other than translational, is 
2Q,Vg = (n — (VfD.Vjj + V 2 D.Vg 2 + V 3 D.Vg 3 ) 
+ (n + n{) (VD 1 .Vj 1 + VD 2 .Vg 2 + VD 3 .Vg- 3 ) 
+ (k — § n) div D div q 
= n (V^.Vjj + V.jD.V^o + V 3 D.Vg 3 + VD 1 Vg , 1 + VD 2 Vg 3 + VD 3 Vg 3 ) 
+ Qi ~ I n ) div D div q + n Y curl D curl q;.(60) 
or, which is the same, 
2QVg = ]fik (div D) 2 + \n x (curl D) 2 
+ i»{(VD x ) 9 + (VD 2 ) 2 + (VD 3 ) 2 + VDj.V^ + VD 2 .Y 2 D + VD 3 .t? 3 D} -> (div D) 2 ], . (61) 
where the quantity in square brackets is the potential energy of an infinitesimal 
distortion and rotation. The itadicised reservation appears to be necessary, as we 
shall see from the equation of activity later, that the convection of the potential 
energy destroys the completeness of the statement 
2qv 3 = u, 
if U be the potential energy, 
In an elastic solid of the ordinary kind, with n x — 0, we have 
P N = n (2 curl VDN + VN curl D), 
F = —* n curl 2 D 
(62) 
In the case of a medium in which n is zero but n x finite (Sir W. Thomson’s 
rotational ether), 
