﻿of the Electron TJieory of Matter. . 599 



The ratio of the thermal to the electrical conductivity is 



T/* = l^/^--=^™e, . . . (io) 



4 e 2 h 2 s — le- 1 v y 



if R is the constant in the equation pv = B.d reckoned for 

 one molecule of any gas. 



The calculations may be checked by putting s = go . In 

 that case the collisions will be like those between hard elastic 

 spheres. On making the substitution, the formulae for a, 

 T, and T/cr are found to be the same as those obtained 

 by Lorentz, when the difference in the measuring of the 

 constant k is allowed for. 



The fact which makes these calculations of interest is the 

 known experimental result that the value of T/cr is pro- 

 portional to the absolute temperature 6 and is almost 

 constant at constant temperature for all the pure metals 

 that are good conductors of electricity. This value is very 



nearly equal to S-ytf. It follows, in the case of such 



2s 

 metals at an)- rate, that = 3 very nearly : whence 



We therefore conclude that the collisions of the free 

 electrons inside metals do not occur with hard elastic spheres 

 but with centres of force ; and that the force exerted on the 

 electrons varies as the inverse third power of the mutual 

 distance. 



Some of the metals, notably iron and bismuth, have values 

 of T/cr which are considerably above the normal. The 

 question arises as to whether the law of force is different in 

 these cases. I think the most reasonable hypothesis to make 

 is that the law of force is the same in all cases, unless quite 

 definite reasons can be adduced for abandoning such a 

 position. Now the exceptional elements are either such 

 as have very small electrical and thermal conductivities, or 

 are elements which are difficult to obtain in the pure state in 

 a suitable form for experimenting with. In the case of bad 

 conductors the theory will be in error, because we have 

 neglected the transference of heat of the type which occurs 

 in electrical insulators. This would make the calculated 

 values of T/cr less than the observed values. On the other 

 hand, it does not seem advisable to pay much attention 

 to the value of T/cr for metals whose purity is under 

 suspicion, as there is something about alloys — possibly the 



