Resistance of Thin Metallic Films. 475 



which was deposited up to the thickness corresponding to 

 the bend was sufficient to cover the whole plate to a depth 

 of about 60 molecules. If, however, we imagine that the 

 groups which come down contain, say, more than 10 c mole- 

 cules, the groups would not at this stage join up so as to 

 form a continuous film. The molecules would be piled up 

 to a greater height in each group than if they had come 

 down singly, but this greater height in places is only obtained 

 at the cost of the existence of gaps between the groups *. 

 The fact that the resistance does not become absolutely 

 infinite for a definite time of deposit would be explained by 

 the fact that though all the groups would not be in contact 

 at the critical time, certain of them would be, and the 

 current would be able to find paths through the film, the 

 number of such paths diminishing rapidly for smaller times 

 of deposit. 



Though the above theory would explain the sharp bend, a 

 modification of it is more fruitful in explaining the peculiar 

 behaviour which these films show with regard to change of 

 temperature, and it is this modified view which forms the 

 basis of the theory about to be developed. We shall assume 

 that the molecules comedown in groups, which are, however, 

 not so large as those cited above. We shall imagine that 

 they cover the plate for a time of deposit less than that cor- 

 responding to the critical value. We shall imagine, however, 

 that they are not pressed into very intimate contact, and 

 that it is only those electrons which have more than a certain 

 minimum velocity, depending on the closeness of packing, 

 which can travel from one group to the next. We shall 

 suppose that this necessary velocity gets less as the time of 

 deposit increases and the groups are pressed more intimately 

 into contact by the greater molecular forces brought into 

 play. The effect of the electric field has now to be con- 

 sidered as that of accelerating the electrons which are 

 travelling against the field and retarding those travelling in 

 the opposite direction, so that the number of electrons 

 crossing the gaps against the field is greater than the 

 number travelling in the opposite direction. The details of 

 the analysis connected with the problem will be found in 

 the appendix to this paper. It will be sufficient here to 

 refer to the main steps. 



* Since this paragraph was written a paper has come to my notice by 

 M. Houllevique (Comptes Rendus, t. 150. p. 1237), in which the author 

 suggests that the molecules come down in groups. He assumes that 

 the resistance remains infinite until the groups join up, and on this 

 basis calculates the number of molecules in the groups. 



