﻿662 Mr. G. H. Livens on the Electron 



and we thus get 



dm V nr* J 

 and using v = qu 2 this reduces to 



x 6mq V 7r ° J ' 



which is Lorentz's result for steady currents. 



(ii.) Again in the case or! stationary waves of period p and 

 comparatively long wave-length, we may use 









E=E / i * 



» 







then 



we 



deduce as 



above 











i*= 



_ SirNe^qk 

 3 m 



VWf 



u z e 

 1 + 



£ W 2 ' 



du 

 ipki 



which agrees with the results of my former paper. 



(in.) If, however, we use the real case of progressive 

 simple harmonic waves we must, as above, put 



E=E , ^ c, : 



and then we find firstly that 



X *~ m ~V 58 1 r / nf\ "I M * 



J_„ J-oo*/-oo 1+2/) II -JT m 



Or again by a spherical polar transformation in which 



%=UQOS0, f = U COS 6 COS <£j 



the triple integral reduces to 



f" e'^u^du f ""cos** sinfltffl f^ . 7 , ^ 7 . 



