440 Mr Bevan, Reflexion and Transmission of Light 
We get 
x(p 
71 V 2 \ V 2 
_ ^ = f mX) + n (nX - IZ)} 
mpj p 
=— {tp.x-mx}, 
Y 7 
Z (p- —) + z (— - \ = 
V mu/ \mn 2 mu 2 — <W 
^-{tlKZ-nllX J. 
So that, multiplying by L , ilf, W and adding, we obtain 
n e- 
0. 
\mp* mp 2 — a 2 / 
As we suppose a, 2 is not = 0 we must have, for the propagation 
of waves without change of type, N — 0 or Z— 0. 
If Z = 0 we have 
IX + mY = 0, from (1), 
so that the electric force is perpendicular to the direction of pro- 
pagation. 
Consider light incident normally on the metal. I and m = 0. 
Writing 
we have 
and therefore 
ne* . 
V = A, 
mp 
AX = - VnM, 
AY = VnL, 
V 2 
A n 2 = 0, 
P 
or 
ir = 
Ap 
V 2 
— TX2 \ P 
The velocity of propagation is 
ne- 
m 
V (3). 
For normal incidence we get the same expression for the 
velocity if we take N = 0. 
We have then in the metallic charged layer a wave trans- 
mitted with the velocity given by (3). 
