﻿of the Electron Theory of Matter. 607 



components between u x and u x + dui is 



ni^TduS^C \ X ¥(u.v.w. Ul )^- km ^ v2 ^dudvdw. 

 But, as we have seen, this is also equal to 



Thus F(m. ».«).«!) has to satisfy the equation 



Ooo p 

 -oo J - 



ue -km(v?+v*+w2 } ji Y(u.v.w..u 1 )^,2kmu 1 e- kmu ^idudvdtv = 0. 

 tr ... (266) 



G(tt.tf.w.ui) and H(w.'u.w.Wi) satisfy equations which 

 only differ from (266) in that the expression in brackets is 

 replaced by 



in the one case and 



1 -tj / n fhn\ 



— £l [U . V . W . W 1 ) — I } 



r \ ir J 



kmVI 2 e _ kmv{2 



^v» e _ kmw < 



in the other. Each equation is true for all values of w 1? v l9 

 and w l respectively and of k. 



The rate at which the conductor gains heat, and the force 

 acting on it in any direction, owing to the activity of the 

 •electrons, may be represented by integrals of the type 



f 



QrN(w.'y.Mj)— r(u.v.w)~ e(u. v.w)]d$ .dudvdw, (27) 



where Q is kinetic energy in the first case and momentum 

 in the second. All of these vanish, as they should, by virtue 

 of (26 a). 



In an enclosure containing different bodies in thermal 

 equilibrium, N will be different near different bodies on 

 account of the contact difference of potential. The con- 

 siderations just brought forward show that the occurrence 

 of reflexion of the electrons does not affect the conclusions as 

 to the nature of the ensuing equilibrium which were drawn 

 in my previous paper. The effect of electromagnetic radia- 

 tion and photoelectric action will be considered in a later 

 section. 



