Resistance of Thin Metallic Films. 493- 



It will be unnecessary to give the full steps in the evaluation 

 of i. The result, after a certain amount of reduction,, 

 neglecting terms of smaller order than QieVY compared 



with unity, and writing I for I e~P d% amounts to 

 i= g™ [|-rinh (feV) + ~ heX x x\(l + « 2 ) e-«=-2a s I 



Discussion of the case where the complicated cell structure 

 cited on page 476 is assumed. 



Let us, as a preliminary problem, consider the case of a 

 gap which is not perpendicular to the resultant field in the 

 metal. Let X x as before be the actual field in the metal, and 

 let us resolve X x into a component X ?l perpendicular to the 

 gap, and a component X s parallel thereto. Suppose for the 

 moment that X* were absent. Then obviously, just as in 

 the above problem, we obtain for the number of electrons 

 crossing the gap per square centimetre per second the result 



. . . . (22> 



where we have neglected the small quantities of the order 

 (heY)\ 



But the number of electrons flowing per square centimetre 

 per second past a plane in the metal parallel to the gap is 



.T7-, — rrX». The continuity of the flow requires that these 

 6{hmy J 



shall be equal, so that we find on equating them 



V=f\X„F(a), (23) 



where F(a) is the quantity defined on p. 479. 



Now this result will not be altered by the presence of the 

 component X s , for the effect of this component is merely to 

 shift the position in which each electron strikes the gap by a 

 small amount parallel thereto. It does not shift all of the 

 electrons equally. If we divide the electrons up into groups, 

 such that the members of each group take the same time to 

 reach the gap after collision, then each of the individual 

 members of any one group will be shifted by the same 

 amount, but by an amount which is different from that by 

 which the members of any other group are shifted. The 



