170 BRIDGMAN. 



putation that the correct form of the curve is not algebraic, or at any 

 rate that the first term is not a square term. 



However, merely in order to afford a basis for comparison with 

 previous results, let us assume for the moment that at compara- 

 tively small values of the current the most important term is the 

 square term. My results for 8 X 10"*^ gold show that at a current 

 density of 10^ ftmp/cm- the departure from Ohm's law is certainly not 

 any greater than U)~^. Assuming, in lack of anything better, that the 

 coefficient of the square term is unity, and assuming the square law, 

 this would mean that at a current density of 1 amp/cm^ the departure 

 from Ohm's law is not greater than 10"^^. Maxwell stated the limit 

 as one part in 10^" for the same current density. The law is probably 

 actually much closer than 10~^^ at 1 amp/cm^. 



Another argument against the probability of the square law is the 

 very high values that it would mean for the free path. Let us assume 

 again that the coefficient of the sc^uare term is unity, and substitute 

 numerical values. We have to put 



/Eeiy 

 — =10-^, 



where E is the electric field at a current of 10^ amp/cm^. In accord- 

 ance with the usual assumption of classical theory, which I have 

 attempted to show elsewhere is very probably true,^ we put the 

 energy of the electron equal to the energy of a gas molecule at 

 the same temperature (300" Abs.). We may simplify by writing 

 mv" = 2kT, where k is the gas constant and r absolute temperature. 

 We have to solve the above equation for I, the only unknown. The 

 specific resistance of gold is 2.4 X 10~^. To drive 10^ amp/cm- takes 

 2.4 volts/cm which is 0.08 Abs. E. S. U. Substituting these values 

 gives . 



/ = 4.5 X 10-4 cm. 



It would appear on this basis, therefore, that the free path is of the 

 order of 5 X 10"^ cm. long. This is in the direction that I would like 

 to find the path to differ from the previous results of the classical 

 theory, which gave something of the order of 10~^ cm., for my theory 

 demands a long path and few electrons,^ but I believe that the number 

 above goes rather too far in the desired direction. It is, however, 

 perhaps not impossible that the path should be of the order of 10-^ cm. 

 In default of a better theory, my measurements do not afford the basis 

 for a better calculation. It would be necessary to refine on the meas- 



