502 PROFESSOR CLERK MAXWELL ON THE ELECTROMAGNETIC FIELD. 
The equations of electric currents (C) remain as before. 
The equations of electric elasticity (E) will be 
P = W/, | 
Q=4 l (82) 
R=4 7rc 2 h, J 
where 4 4w5 2 , and 4 tt(? are the values of k for the axes of x, y, z. 
Combining these equations with (A) and (D), we get equations of the form 
(104) If l , to, n are the direction-cosines of the wave, and V its velocity, and if 
lx-\-my-\-nz— Vt=w, (84) 
then F, G, H, and Y will be functions of w ; and if we put F', G', H', Y' for the second 
differentials of these quantities with respect to w , the equations will be 
(v ! -b , (~+^))f , + ^G'+^H'-?V'P'=0, 
(^-' ! C-+i)) ff +7i’+xG'-»w=«' 
If we now put 
(85) 
V 4 — "V" 2 -f- c 2 v) -f- r nv l yj(c 1 v -f- tt 2 X) -j - vikv[dk~k -f- 1 > "^)|’ 
we shall find 
F'V 2 U-ZT"VU=0, 
with two similar equations for G' and H'. Hence either 
. ( 86 ) 
. (87) 
Y = 0, (88) 
U=0, (89) 
or 
VF' = ZT", YG'=to^ and YB.'=nY' (90) 
The third supposition indicates that the resultant of F', G', H' is in the direction 
normal to the plane of the wave ; but the equations do not indicate that such a disturb- 
ance, if possible, could be propagated, as we have no other relation between M'' and 
F', G', H'. 
The solution Y=0 refers to a case in which there is no propagation. 
The solution U = 0 gives two values for Y 2 corresponding to values of F'. G', H', which 
