﻿of the Electron Theory of Matter. 597 



Lorentz, we assume that the presence of an electric current 

 or a temperature gradient in the metal only causes a small 

 variation from the normal Maxwell distribution, and try the 

 solution 



when xi r ) is a function of r alone. The reason for trying 

 this particular form of solution is that f %(r) contributes 

 nothing to the integrals which express the number per unit 

 volume and mean kinetic energy of the electrons, which are 

 therefore correctly given by 



N = A Vp and * mv2 = w 



Neglecting the % term on the right-hand side of (3) as a 

 small correction, we have 



„ PFyV-^r) f " f"(F-f)«<k df 



\m/ Jo Jo 



= n (^)"~ 1 r'^ i x( r ) \ -k*Z sin 2 a da 

 \w Jo 



\ dx dec/ 



(2hAX-^+r*Af)e-^ 

 , > ___V dx dx) 



47rn \W ^ * J sin 2 6 cc da 

 = ^\2hAK^ + r^)e-^. f4 , 



jfe- 1 = 4ww ^^ j sin 2 0a^a (5) 



Thus 



wher< 



The definite integral in (5) is a function of s only and may 

 be evaluated graphically when s is known. Thus x( r ) does 

 not involve a nor yfr, and only involves £, 77, f in the combina- 

 tion r. It is therefore the solution which we have been 



seeking. 



