﻿668 Sir J. J. Thomson : Further Studies on 



We shall suppose that the average velocity due to the 

 electric force is 



9-mv* (4) 



where g is a fraction. This by equation (3) is equal to 



JLencv _ eXlv 



where I is the length of the chain. 



If q is the number of chains parallel to x per unit volume, 

 the number crossing unit area in unit line is equal to 



Xe lv 



and since each chain carries ne units of electricity, the current 

 across unit area is 



^Ke 2 nlv 



Hence a, the specific electrical conductivity, is given by 

 the equation 



e 2 lvnq _ eHvfp ,.. 



where p is the number of electrons per unit volume and / 

 the fraction of them formed into chains. 



On the theory we are considering, these moving chains are 

 responsible not only for the electrical conductivity of metals, 

 but also for the production and absorption of the radiation 

 which fills the space occupied by the metal. They may be 

 regarded as in some ways analogous to Planck's oscillators, 

 the slowly moving ones corresponding to oscillators with a 

 long period of vibration, producing mainly the long wave 

 radiation while the chains with high velocities give out the 

 radiation corresponding to the shorter wave-lengths. We 

 see from equation (3) that, at the same temperature, the 

 chains which have a high velocity contain a small number 

 of electrons and are therefore short, the chains which have a 

 small velocity contain a large number of electrons and are 

 long. Thus the long chains produce the long wave-length 

 radiation, the short chains the short waves. We should 

 expect on this view that the lengths of the various chains in 

 a metal should be distributed according to a law analogous 

 to that which governs the distribution of the energy corre- 

 sponding to waves of different wave-lengths in the radiation 

 from a black body. But according to Wien's Displacement 

 Law, the length-scale of the radiation varies inversely as the 

 absolute temperature ; Xj9 = a constant. Hence we conclude 



