Properties of Thin Metal Films. 675 



then the conductivity is given by 



l = lnfX* 

 <t 2 m c ' 



This equation holds until the thickness of the film becomes 

 comparable with X. 



When the thickness becomes comparable with X there are 

 three cases to be considered, namely : — 



When t the thickness is 



(i.) greater than 2 \, 

 (ii.) between 2 X and X, 

 (iii.) less than X. 



Assuming that the corpuscles cannot leave the metal. Prof. 

 Thomson has calculated that for (i.) X becomes 



and tor (iii.) \ becomes 



On substituting these values of X in the equation 



1 ^.lnf X 



cr 2 m c' 



we get when 



and when 



t = 2X 



1 = 1 nf\l 



<t 2 m c 8 



t =A 



er 2 m c 4 ' 



that is, that the resistance of the film has increased one- 

 seventh in the first case and one- third in the last. Hence the 

 resistance of the film does not change very much until it 

 becomes equal to the mean free path of the corpuscle. 



From the results obtained for platinum films it will be seen 

 that the resistance began to change rapidly between 7*6 and 

 4 x 10~ 7 cm. 



The value of X calculated from the change of resistance of 

 the film is 6 X 10 — 7 cm. These numbers agree very closely. 



* J. J. Thomson, Rapports presenters cm Cong res International de 

 Physique, vol. iii. p. 138, Paris, 1900. 



t Proc. Camb. Phil. Soc. vol. xi. pt. ii. p. 119 (1901 j. 



2 Y2 



