436 Mr. G. H. Livens on the Electron 



In any case it would appear quite hopeless under present 

 circumstances to attempt to obtain the great generality 

 which McLaren claims for his theory, because it' we are 

 prepared to disregard the restriction as to smallness of 

 velocity of the electron we must equally disregard altogether 

 'the whole concept of the electron as a definite entity, and 

 -we must then include in its specification not only the position 

 <of its nucleus but also a definition of the condition of the 

 whole of the surrounding sethereal strain field, which but 

 loosely follows the nucleus in its motion, unless that motion 

 is comparatively small or at least of the quasi-stationary 

 type. 



No advantage can therefore be gained by attempting such 

 generality of procedure, and no excuse is therefore required 

 for offering the analysis for the more special case, which is, 

 .after all, sufficiently appropriate for our purposes. 



2. The Basis of the Theory. 



The whole theory turns on the evaluation of a function / 

 which determines the statistical distribution of: the motions 

 among the electrons at any point in the metal. This function 

 is such that, at any point in the metal whose coordinates 

 referred to a definitely chosen system of rectangular axes are 

 (#, y, z), the number of electrons per unit volume with their 

 velocity components (f, v n £) in the limits between (£, 77, f) 

 and (f + df, Tj + drj, £-\-d£) is 



fd£dyd£ 



and it is, of course, a function of (£, n, f) (a, y, z) and t, the 

 time. If the electrons in the metal are subject to action by 

 external fields, the results of which may be specified by the 

 acceleration (X, Y, Z) which they impose on the typical 

 electron, then the function / is shown to satisfy the dif- 

 ferential equation 



where (b — a)d^dy d£dt denotes the increase of the specified 

 group of electrons during the next succeeding small interval 

 dt, owing to the collisions taking place in this interval. 



The present writer has shown in another place that under 

 the assumption that the dynamical character of the collision 

 between an electron and an atom is similar to that between 

 :a fixed centre of force, repelling the particle in such a way 



