96  Conway—On the Reflection of Electric Waves by a Moving Plane Conductor. 
ne . oF eZ, eB ba 
2 | essere ee eae) ee is ee rier 0 st Pe Lees oS 
‘a E UE oye A te eK = Be By 
0a 0a Oa Oa 5 OW 
~ a” Be oy ” be oy 0g” 
BY ler, Oy i 3 
tis, a. 7 scp ee eget Ox 
ot 0a ” dy 02 On ; 
Let us now integrate these six equations with respect to z throughout the 
: 0 : : : : 
thickness of the shell. |w-—~0z, for example, will vanish, since the quantity 
ap” 
under the sign of integration remains finite, whilst the range of integration 
is very small; also we have J tidz=I, &e. Of the other quantities, only 
those which contain a differentiation with respect to 2 will not vanish. Then, 
since the forces vanish within the surface, we have for their values on the 
surfuce 
—wV?X +4rI,=— B, 
—wV*VY+4rI,=a, 
= wV-?*Z + Ant, = 0, 
wa=— XY, 
WSS AX, 
vy = O- 
The first three of these equations determine the currents which screen the 
action of the external varying field. The second three are the necessary 
boundary conditions. 
Take axes of z and y in the face of the conductor, and the axes of 2 
pointing into the dielectric medium. Let the distance of the origin from a 
fixed plane parallel to the face of the conductor be denoted by 
h( = (0). 
