FAILURE OF OHM's LAW AT HIGH CURRENT DENSITIES. 171 



urements at current densities less than 10^ in order to pick out the 

 square term (provided that it exists), or to improve on the theory. 

 I do not believe that the latter will be possible without taking into 

 account the detailed structure of the atom. At the same time, I 

 believe that the existence of the effect at current densities so much lower 

 than would be expected on the basis of a free path of the order of 10~^ 

 cm. is at least presumptive evidence that this value of the path is too 

 low. 



The appearance of the v^ term in the formula above suggests an 

 essential observation. The measurements, and the results computed 

 from them, do not refer to metal at the same temperature at the differ- 

 ent current densities, but the observations at the higher densities are 

 for the metal at higher temperatures, because of the heating effect. 

 This of course was not eliminated by extrapolating to infinite fre- 

 quency. The change of temperature at the maximum current density 

 was in the neighborhood of 50° for all specimens. If the form of the 

 function were known, it would have been possible to correct for this 

 temperature effect, but in the absence of the knowledge, I thought it 

 better to give the results as obtained without attempting any correc- 

 tion. If conduction is by a free path mechanism, then at higher 

 velocities the departures from Ohm's law are less than at lower ones, 

 (that is, lower temperatures) so that if the corrections had been 

 applied a deviation from Ohm's law even greater than that shown 

 would have been found at the higher current densities. 



We have noticed that the deviations are greater for the thick than 

 for the thin gold. Although the results are not as accurate for the 

 thicker as the thinner leaf, there seems to be no possibility that all the 

 difference can be accounted for by errors of observation. If the free 

 path is long, as I have supposed, an effect in precisely this direction 

 would be expected. For the leaf is considerably less in thickness than 

 the length of the normal path, so that increasing the thickness would 

 have the effect of increasing the average path, and so increasing the 

 departure from Ohm's law. 



The departure is considerably less in silver than in gold of the same 

 thickness. This would mean a shorter path in silver than in gold. 

 In view of the greater conductivity of silver this may mean that the 

 number of free electrons is greater in silver than in gold. It is, how- 

 ever, perhaps dangerous to drive the comparison too far between the 

 different metals, because the much closer approach to normal of both 

 the specific resistance and the temperature coefficient of resistance of 

 silver suggests that the internal conditions may not be comparable. 



