transmitted through a Metal of a Current in the Metal. 389 
a current made to pass through the. plate in the direction of 
the intersection of the plate and the plane of incidence. We 
have seen that the surface effects are of an order too small to be 
measured, so that we shall have to consider a change of phase 
which is introduced by the alteration of the velocity of the light 
when in the metal. 
If A BCD is the course of the light through the plate without 
any current, the course when the 
current flows will be slightly 
different. But the alteration in 
v 1 being small the change in the 
phase of the light introduced by 
the difference of path through the 
metal will be too small to be 
taken into account, at any rate for 
incidence such that BC makes an 
angle not nearly with the 
normal BN. 
If the angle CBN is r, then the difference of phase introduced 
by the current owing to the change in the velocity of the light 
through the metal is 
d_ 
dv 2 
t sec r 
8v, 
V' being the velocity in the metal with no current, and r being 
regarded as unaltered by the current. 
Using the same approximations as before, this is 
t sec r pkcj) 
V' 2 f*{\ + k 2 )(a + n 2 k 2 ) I 
c pkt sec r n ' 2 V 
= (l +k 2 ) (a + n' 2 k*)$ jp ' 
The fraction this is of the time of oscillation is therefore, since 
we have also a = n! 2 (1 — k 2 ), 
(pkt sec r V 
n\l+k 2 ) 27 rp' 
^ being the angle of incidence, this becomes 
XPl 
t / _A *_ 
V sin 2 a- 1 +F 
47rcrp 
= A 
XPl 
ap 
28—2 
