122 Prof. Thomson , On the theory of Electric Conduction, etc. 
where \ is the mean free path. Thus when the film becomes so 
thin that the mean free path is diminished, not merely is the 
specific resistance increased, but the effect of a magnet on the re- 
sistance is very materially diminished. This is strikingly shown by 
Patterson’s experiments 1 , which prove that in thin films of bismuth 
the effect of the magnetic field on the resistance is very small. 
The electrical properties of thin metallic films as investigated by 
Longden and Patterson are qualitatively at any rate in accordance 
with the results of the theory discussed in this paper ; further 
experiments are however needed on films of the various metals 
and with as wide as possible range in thickness to see if the 
numerical results obtained by experiment are in agreement 
with those predicted by theory. 
1 Proc. Camb. Phil. Soc. Yol. xi. p. 118. 
