﻿660 Mr. G-. H. Livens on the Electron 



presumed to be polarized parallel to the a?-axis of coordinates, 

 depends on the coordinates of time and space by the ex- 



ponential factor e so that 



E=En* 



K'-f) 



If we now confine our attention to all the electrons which 

 at time t lie in or at least infinitely near the plane z = z (say 

 between z = z and z = z + dz), then we shall have for any one 

 of them which has been moving for a time t since its last 

 collision previous to the instant t 



4>- v 





wherein (f, 77, f) are used as usual to denote the velocity 

 components of the electron at time t. 



Thus the distribution of velocities among these electrons 

 near the plane z = z is such that there is at the instant £, the 

 number 



per unit volume with their velocity components between 

 (?, V , and (f+i£ v + d v , £+<*£). " This gives 



V 7r° L m[l + */>(l — W?)T n JJ 



which determines completely the velocity distribution among 

 the electrons in and near the plane z = z. This is the result 

 which will be of greatest use to us for our future work : it 

 might easily have been obtained directly from the previous 

 result for stationary waves by a simple application of 

 Doppler's principle. 



It must be insisted that the various formulae here obtained 

 are of very general application, in no way less general than 

 Maxwell's law itself. The final results involve no assumptions 

 as to the rapidity or otherwise of the variation in the field E, 

 and will in fact be generally applicable for the most rapidly 

 alternating fields. It is interesting, however, to notice that 

 for these very rapid alternations the velocity distribution is 



