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 A, — 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 



When d = \ X' = T X, 



4 



7 

 d = 2\ X' = - X, 



Qj — oK, X = -r-= X, 



]o 



d = 2nX X'-(l-i)v. 



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 Bo- is the increase in the 

 specific resistance <r of a metal produced by a transverse magnetic 

 field H, then 



So- 1 „, e J X s 

 a 12 mf c 1 



