460 The Theory of Aether and Electrons in the 



number added to the group by collisions in the same interval is 

 b dx du dv dw dt. Then w^e have 



f (u, v, w, x) + (b a) dt = f (u + eE dt/m, v, w, x + u dt), 

 .and therefore 



7JT ^\ J? r\ J? 



i &fi of oT 



b - a = + u 



m du dx 



Now, the law of distribution of velocities which Maxwell 

 postulated for the molecules of a perfect gas at rest is expressed 

 by the equation 



r z 

 /= TT~^ a' 3 Ne"*, 



where N denotes the number of moving corpuscles in unit 

 volume, r denotes the resultant velocity of a corpuscle (so that 

 r 2 = u* + v~ + w*), and a denotes a constant which specifies the 

 -average intensity of agitation, and consequently the temperature. 

 It is assumed that the law of distribution of velocities 

 among the electrons in a metal is nearly of this form; but a 

 term must be added in order to represent the general drifting of 

 the electrons parallel to the axis of x. The simplest assumption 

 that can be made regarding this term is that it is of the form 



u x a function of r only ; 

 we shall, therefore, write 



a 



/ = NTT~* a' 3 e 2 + u^ (r). 

 The value of ^ (r) may now be determined from the equation 



eE'df df 

 b - a = ~- + u -; 

 m du dx 



for on the left-hand side^ the Maxwellian term 



would give a zero result, since b is equal to a in Maxwell's 

 .system ; thus b - a must depend solely on the term u-% (r) ; and 



