498 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
If the medium in the field is a perfect dielectric there is no true conduction, and the 
currents^', q', r' are only variations in the electric displacement, or, by the equations of 
Total Currents (A), 
(65) 
n'-f 
q'=f, 
* dt 
, dh 
V ~Jt 
But these electric displacements are caused by electromotive forces, and by the equations 
of Electric Elasticity (E), 
P =Jcf\ Q^Jcg, R =kh (66) 
These electromotive forces are due to the variations either of the electromagnetic or 
the electrostatic functions, as there is no motion of conductors in the field ; so that the 
equations of electromotive force (D) are 
dF_d^ 
dt dx ’ 
dG_cW 
dt dy 
rfH dW 
K ~ “ dt~ dz ‘ 
(67) 
(94) Combining these equations, we obtain the following : — 
KS- vaF )+ 4 'K?+S)=°’ 
i (|-VG) +V (-? + ^)=0, • 
*(§-V*H) + 4^ + S) = 0. 
. . ( 68 ) 
If we differentiate the third of these equations with respect to y, and the second with 
respect to z, and subtract, J and T - disappear, and by remembering the equations (B) of 
magnetic force, the results may be written 
&V 2 /aa = 4 iryj pa, 
d 2 
A;V>/3=4^^2^/3, 
d 2 
ArV>y = 4*-^^py. 
(69) 
(95) If we assume that a, (3, y are functions of lx-\-my-\-nz — Vt=w, the first equa- 
tion becomes 
7 d 2 a 
k (*dw* 
(70) 
v=±V^‘ <*> 
The other equations give the same value forV, so that the wave is prqpagated in either 
direction with a velocity V. 
