through thin metallic films. 
121 
10 -4 and 10 -5 cm. ; thus the free path is large compared with 
molecular dimensions, indeed it is so long that it is possible to 
make metallic films whose thickness is much less than the mean 
free path of the corpuscle in bismuth. Let us consider the case of 
a metallic film whose thickness is comparable with X — the mean 
free path of the corpuscle in an unlimited mass of metal. The 
limitation imposed by the thickness of the film will diminish the 
free path. I find that if d is the thickness of the film and if we 
suppose the direction of motion of the particles uniformly dis- 
tributed then when d is less than X, the mean free path X' is given 
by the equation 
. 7 (3 1. X) 
*= d {i + 2 lo ^[; 
When d = \ V = ~ 
4 
d = 2\, V = *- 
O 
d = S\, V = 
Jo 
Thus when the thickness is greater than X the mean free path 
changes but slowly with the thickness of the film, but when the 
thickness of the film becomes less than X the free path diminishes 
rapidly as the thickness of the film diminishes. Now the con- 
ductivity of the metal contains the mean free path as a factor, 
hence we see that the conductivity of metallic films ought on this 
theory to diminish slowly as the thickness diminishes, until the 
thickness of the film is reduced to the free path, then any further 
diminution will be accompanied by a rapid diminution in the 
conductivity. From observations of the way the specific resistance 
changes with the thickness we may hope to approximate some- 
what closely to X. 
There is another way in which the effect of the thinness of the 
thin film might be expected to make itself felt. In the Report 
already referred to it is shown that if 8a- is the increase in the 
specific resistance a of a metal produced by a transverse magnetic 
field H, then 
8a _ 1 e 2 X 2 
