486 Dr. W. F. Gr. Swarm on the Electrical 



The Departure from Ohm's Law. 



Referring to equation (7) we first observe that in the 

 coefficient of (Xellt) 2 , a 2 may be looked upon as hmu 2 , since 

 7] is negligible in these terms. We next notice that it is only 

 films which have specific resistances well above the normal 

 value in which we may hope to find deviations from Ohm's 



law, for so long as — — in equation (7) is very 



nearly equal to X, - — F(a) must be small, and the deviation 



from Ohm's law due to the fact that a involves the 

 quantity rj, which itself involves V, is consequently small. 



Also, when ~y~F(a) is small, . ^ , is large, and the 



coefficient of the term involving [Helh) 2 is small. The 

 maximum departure from Ohm's law will be attained when 

 s, and consequently F(a), is very large. Indeed, for this 

 case we can obtain an expression for i in a more convenient 

 form. 



If we substitute the value of Xj given by (5) in (4) we 

 see that when e _a2 is very small (i. e. for films of abnormally 

 high resistance), the first member on the right-hand side of (4) 

 becomes all important, and we have 



A 7 



6-« 2 sinh(/^Y) (11) 



4(/im) 



Since for this case (5) gives V = XZ and since a 2 = hmu 2 + 2herf 

 we have, on substituting for A, 



/Y TifXv dl _ hmu2 akn nnh (helX) 



V 3tt* u0 'l\ helX. ' 



We cannot express rj as a function of V unless we know 

 the nature of the intermolecular forces in the gaps, but if 

 w r e make the very reasonable assumption made on page 489 

 we have 



2he v l/AgV\ 2 1/7^X\ 2 



mu 2 ~~ dWv ~~4 \ ?m 2 / 



Hence, on expanding € ~ 2her) and the sinh function, we have- 



