Resistance of Thin Metallic Films. 487 



If hmu* is greater than, say, 3 or 4, the term representing 

 the deviation from Ohm's law approximates to (hellL) 2 /6, and 

 the term arising from the more doubtful assumption with 

 regard to rj becomes less important. The formula then 

 indicates an increase of the conductivity with the field. If 

 X is 1 volt per cm. /*<?X = 14, and we readily see that in 

 order to obtain a one per cent, deviation from Ohm's law on 

 doubling the field, it is necessary that Z = O017. Of course 

 if.X = 100 volts per cm. a value of I equal to 000017 will be 

 sufficient. We thus see that unless the molecules are col- 

 lected into large aggregates containing many molecules, the 

 deviations from Ohm's law to be expected are small. It 

 might happen, however, that a film which had been ruptured 

 in several places by being subjected to a large current, or by 

 being otherwise drastically treated, would act as though the 

 molecules were collected into large groups, and would show 

 deviations from Ohm's law. In fact this possibility is a very 

 likely one. 



It may be noted that by cutting narrow slits in a film, 

 similar to those referred to by Professor R. W. Wood in his 

 paper on "Electron Atmospheres"*, it should be possible to 

 produce artificial conditions of the above kind, and to obtain 

 films showing large deviations from Ohm's law, and generally 

 exhibiting the characteristic properties of films of high 

 resistance, such properties as large negative temperature- 

 coefficients, &c. 



The expression (11) of course applies to a single slit when 

 the slit is sufficiently wide to cause a large increase in the 

 resistance of the film. V is in this case practically equal to 

 the applied e.m.f. Measurements made on a single slit should 

 enable us to calculate h, and so test the theory by obtaining 

 the mean kinetic energy of a gas molecule at the temperature 

 of the experiment, for by differentiating (11) with respect 

 to V and dividing the resulting equation by equation (11) 

 we obtain 



lfdi\ 

 i\dVj 



he (he)*Y 



t&nhheV 2hmu 2 



di 

 If measurements of i and -prf are made for a value of V 



d\ 



so small that heV is small compared with hmu 2 , we can 



neglect the second term on the right-hand side, and so 



determine li. 



* Phil. Mag. [6] xxiv. p. 316 (1912). 



