﻿<300 Prof. 0. W. Richardson : Some Applications 



thermo-electric resistance suggested by Lord Rayleigh — 

 which causes them to have a high value of the ratio. 



It is of interest to note that this is not the only line of 

 reasoning which leads to the inverse third-power law of force 

 for the collisions of electrons in metals. Sir J. J. Thomson* 

 showed, from his calculation of the emission of radiant electro- 

 magnetic energy from hot metals, on the assumption that it 

 was due to the acceleration of the free electrons, that for 

 Stefan's law and Wien's displacement law to be satisfied, it 

 was necessary that the law of force during collisions should 

 be the inverse third. Thomson also obtained a formula for 

 the radiation of given frequency, which resembled Planck's 

 formula in the case of both high and low frequencies. From 

 a comparison of the constants it was possible to deduce the 

 strength of the centres of force. Jeans f has confirmed 

 Thomson's result so far as the inverse third-power law of 

 force is concerned, but has raised the objection that the 

 centres of force are so strong that the electrons would never 

 get as near to them as it is known, on other grounds, that 

 they must be all the time. This objection would not seem to 

 hold if the centres were attractive or, like doublets, attractive 

 in one direction and repulsive in another. The calculations 

 in these cases, however, are much more complicated, as it is 

 necessary to take into account the electrons which are 

 executing closed orbits. 



From the magnitude of the electrical conductivity we may 

 obtain an estimate of the strength K of the centres of force. 

 Putting 5 = 3 in formula (7) we find 



a= ?^nK\m r. — ' ■ ■ • < n ) 



1 sin" 9 « doc 



Jo 



where N is the number of free electrons in 1 c.c. 

 Thus 



37T 3 / 2 n \vm' <r ( • 2 jl j 

 1 sin' 5 <pa ax 



Jo 



where v is the number of molecules in 1 c.c. of a gas at 0° C. 

 and 760 mm. pressure. 

 When 5 = 3, I find 



* Phil. Mag. vol. xiv. p. 217 (1907) ; vol. xx. p. 238 (1910). 

 i Phil. Mag. vol. xx. p. 642 (1910). 



