EFFECT OF PRESSURE ON CONDUCTIVITY OF METALS. 125 



which is due to the electrons would be expected to have the same 

 pressure coefficient as the electrical resistance (except for a possibil- 

 ity to be mentioned later); the remaining part must be capable of 

 either positive or negative variation under pressure, and must be of 

 the right order of magnitude. 



In the first place, let us consider the possible magnitude of the 

 non-electronic part of heat conduction. The first deduction of the 

 theoretical value of the Wiedemann-Franz ratio, given by Drude, was 

 an elementary one, in which certain simplifying assumptions were 

 made, particularly that the velocities of all the electrons were the 

 same. Later Lorentz gave a more exact discussion, taking account of 

 the ^Maxwell distribution of velocities among the electrons, and ob- 

 tained a value for the ratio only two thirds of that of Drude. The 

 discussion of Lorentz has later been verified by Bohr and others. The 

 elementary value for the ratio is much closer to the experimental 

 values than the more rigorous one, but still lies somewhat low. The 

 failure of the more exact value to agree more closely with the facts 

 has been regarded by some as a blot on the classical theory, but by 

 others is regarded rather as to the credit of the theory, because the 

 Wiedemann-Franz ratio as calculated by the elementary theory was 

 felt to be too close to the experimental value to sufficiently allow for 

 the atomic part of the conduction. 



I shall take this latter point of view, and consider that the value for 

 the Wiedemann-Franz ratio calculated by Lorentz represents the part 

 due to electronic conduction, and that the dift'erence between this 

 theoretical value and the actual value represents the part of the heat 

 conduction that must be accounted for in other ways. This point of 

 view at once imposes certain numerical limits on the changes under 

 pressure that it should be possible to obtain experimentally. For the 

 total change of thermal conductivity under any pressure must never 

 be so great as to more than wipe out the part of the conductivity which 

 was initially ascribed to the non-electronic part. This means that the 

 total decrease of thermal conductivity, after allowing for a change 

 equal to the change of electrical conductivity, must not be greater 

 than the difference between the total initial thermal conductivity, and 

 the part given by Lorentz's expression. In practise this imposes a 

 restriction only when the thermal conductivity increases under pres- 

 sure less rapidly than the electrical conductivity. An examination of 

 the results obtained in this paper will show that this condition is met 

 in all cases. The condition imposed is most restrictive in the case of 

 nickel. Under 12000 kg. its thermal conductivity decreases by 14.5%, 



