﻿664 Mr. Gr. H. Livens on the Electron 



from which all the circumstances of the problem can be 

 deduced, even though it is impossible to evaluate the last 

 integral except perhaps approximately. We notice, however, 

 that if the velocity u for the majority of the electrons is 



c 

 considerably less than - the velocity of radiation in the 



metal, which condition is, I presume, nearly always fulfilled 

 at all attainable temperatures, this formula reduces as a first 

 approximation to that given above for stationary waves. 

 The theory for stationary wave-radiation is therefore of 

 rather a surprisingly wide generality, in spite of its more 

 apparent restrictions. It will not, therefore, be necessary 

 for us to examine the present case in any further detail, even 

 if that were possible. 



5. On the fundamental differential equation of the Jeans- 

 Wilson theory. — Jeans, and Wilson following him. adopt 

 rather a different mode of attack, based on a calculation of 

 the rule of increase in the momentum of certain specified 

 groups of electrons. Wilson's analysis is slightly the more 

 general and detailed of the two, and I shall therefore confine 

 my attention to his equations alone. 



Wilson assumes that the number rfN of free electrons per 

 unit volume with their resultant velocities between u and u + die 

 remains practically constant, although particular electrons 

 are continuallv entering and leaving the group. He there- 

 fore attributes to each such group a definite permanent 

 existence whose average motion under the action of an 

 electric force may be specified by a certain differential 

 equation which he finds to be of the form 



j t (mwdN)=Eed^-/3wdN, 



wherein w is used to denote the average velocity of the 

 group in the direction of the applied electric force E and 

 /8 is some function of u, m, and e. On integration of this 

 expression over all the groups and using 



I = e§wdN, 



Jeans' equation for the electric current density I is obtained 

 in the form 



dl Ne* T 



-T = E— ryl. 



dt m '■ ' 



In the theories of Jeans and Wilson this differential 



