838 Prof. H. A. Wilson on the Electron Theory 



The gain of ,v momentum due to the electric force is 

 X# dN dt, so that we have 



d / ,xts x- 7at umYdN. ,- N 



-r(mu(n$) = Xe(fl$ j . • . (1) 



at l m 



Let now a denote the mean value of f for all the N 

 electrons so that Ni/ = fwrfN; then, if we find u by means 

 of equation (1), we can get u by putting the value of u in 



iJ 



We also have from (1) 



Comparing this with Jeans' equation we get 





lm J 



7 = 



§udN 



If we take all the electrons to have the same velocity V 

 we get 7 = mV/L Jeans' results consequently agree with 

 mine only if all the electrons are taken to be moving with 

 the same velocity. 



If X is constant then after a sufficient interval du\dt will 

 be zero, so that w = X^m|mV, and 



1 CXel m 



If we assume dN to be given by Maxwell's law this gives 



}< 2 XeL 



"o 



m \7I7 J \7T/ 



where q=3j2Y • 



Suppose now that X = a cos pt, then (1) gives 



^a cos (»£ — S) 



where tan B=pl m jY. 



Hence again assuming Maxwell's law 



Mo 



/? \Wea f " cos (jpf-8) 6-g y2 V 2 ^V 



