390 Mr Bevan, The Influence on Light, etc. 
and this, when P, cr and X are in electromagnetic units, 
. XP sin $r 
= A . 
<7 
c 
Now X=— where G is the Hall coefficient, so the change of 
<T 
phase is finally, where P is in volts and cr in ohms, 
pn 
= A sin Sr— s- . 10 
P 
Now — is the current through unit area in amperes, so if 
G is the current through unit breadth of the metal strip 
G = P 
t cr 
The change of phase is therefore 
sin Sr k j 
4lT 
k 
i+fV 
1 _ GO 
sin 2 ^ cr 
10 -10 of a wave-length. 
And this effect is again too small to be measurable, since the 
plate to transmit any light must be very thin, and so the current 
G cannot be made large. 
To conclude, we have shown that the effect of the current 
in the metal is to cause an alteration in the constants of the metal 
but this alteration is too small for the effect to be measurable 
(taking 10 -2 of a wave-length as the minimum change of phase 
which can be detected). The alteration also of the plane of 
polarisation, or rather the major axis of the ellipse of polarisation, 
of reflected light is similarly too small to be detected, so that as 
far as any measurable effects are concerned, the metal’s optical 
properties would not be altered by the current. 
The cases considered have been worked out with certain 
approximations which will not be valid for some metals, silver, 
sodium, etc., but it is easy to see that in these cases the changes 
will still be of the same order of magnitude as in the cases 
considered. In all cases the thickness of metal through which 
light can be passed being only a few wave-lengths, there is no 
possibility of a small difference of velocity producing a large 
enough change of phase to admit of measurement. 
