transmitted through a Metal of a Current in the Metal. 381 
Suppose a corpuscle has mass m, charge e, and that an elastic 
force pi; acts on it, where f is its displacement in the direction of 
the X axis, /c a frictional coefficient, then the equations of motion 
for the corpuscle are 
m ^ = eX- K f t - p£ etc., E = (X, Y, Z). 
For corpuscles which are not acted on by a harmonic force we 
have 
m dP =eX ~ K dt • 
Writing 
= or. 
47 rm 
A 
47 re 2 J 
P P P 
where N is the number of charges e per unit volume, then we 
obtain 
,[■-«'*/ 7 \ v, / 47 t&N 
a ib — 1 -I - f ^ \ ~f* So 
i+.M 
T T 1 ' 
27 TK 47T 2 
l m 
k r r- ' 
where r is the period of the luminous waves and S x refers to 
corpuscles of the first type, S 2 to corpuscles of the second type. 
(Drude, loc. cit .) 
For the modification to be introduced when a current is flowing 
in the metal we first consider S 2 . This sum will be unaltered by 
the constant external force since the equations are linear both for 
the motion of the corpuscle due to the light field and the electric 
force producing the current. There will then be no change 
in S 2 . 
We have mentioned the possibility of some of the corpuscles 
of the first type changing character owing to the electric force 
driving the current, and becoming corpuscles of the second type. 
But as Ohm’s Law holds very accurately we see that the number 
of corpuscles passing over from one type to the other is small 
compared to the whole numbers in the two types provided the 
temperature of the metal does not change, so that there will not 
be much change in the values of a and b and any variation in 
these constants will be of the order of variations from Ohm’s Law. 
If now E', H' represent the electric and magnetic forces due 
to the light and ’E 1 I 1 1 the part due to the battery producing the 
current, the total electric flux is 
*7E / E "X 
(a + ib) + (c + id) [E', H, + H'] + — 1 + - [E, , H, + H'], 
at <7 <j 
E x being constant. 
