transmitted through a Metal of a Current in the Metal. 385 
Then 
af — l 2 — vi 2 + v 2 2 = 0 
7,0 xPl A 
67 - + 2 = U 
■W. 
m being equal to 0. 
If we put P = 0 in equation (4) we obtain the change of 
phase T due to the metal without the current flowing into it. 
The additional change of phase due to the current is 
sr s 
ov l ov 2 
where 
T — - tan -1 
2 nv 2 
p n* — — v 2 
and Svx, &v 2 are the changes in v u v 2 due to the retention in 
equations (4) of the term 
XPl 
crV ‘ 
We have then from (4) 
ViSi’x = v 2 $v 2 , 
v x $v 2 4- vf>Vx = g -p -= </> say. 
And therefore 
Bv x = cf) 
Sv 2 = </> 
iV + 
We obtain then 
2ni> 1 <f) ( n 2 — i^ 2 + 3i7 2 2 ) 
(^i 2 + ^ 2 2 ) {(w 2 — vx 2 - vff + 4nV}‘ 
From this expression, using (4) with P = 0, we obtain 
flr = 2 n Vi<t> t/ 2 (1 ~ <*) + 2Z7 2 2 } 
pf {( 1 - a) 2 + h 2 } (vx 2 + vf) ‘ 
From equations (4) 
v i = i[( a 7 2 “ ^ 2 ) + V{(^7 2 ~ + h 2 7 4 }], 
= i[“ ( a 7 2 “ ^ 2 ) + V(( a 7 2 - 1 2 ) 2 + & 2 7 4 }]- 
Now a = n 2 (1 — k 2 ), 
h = - 2n /2 &, 
where w' and are the quantities corresponding to the refractive 
index of the metal and the absorption coefficient, and from Drude’s 
