﻿684 Dr. G. H. Henderson on the Decrease of 



Summing this expression for all the types of electrons 

 n l5 w 2 , etc., we have 



AT An v ™«„ / Qf +1> l 

 Thus the complete expression for the loss of energy is 



Putlog&=log2m~S s ^logQ s + S s ^^|l--^|. (3) 



Then ^ = ^log^V 2 . 



Ax Y 2 6 



Replacing T by ^MY 2 we have in the limit 



-MY^ = ^log£Y 2 , 

 dx V 2 fe 



the negative sign entering because AT is a loss of energy. 



TVi , MYW 

 lhus dx — - - — = r^- 



MbV 2 d(bV 2 ) 

 ~ 2Anb 2 \ogbY 2 



= — A 79 , where y=—2 log 6V 2 . 



2An6 2 y * 6 



Let the velocity of the a, particle initially be Y and the 

 velocity of the a particle after doing a distance x be V, then 



M C Y e~ydy 



X ~~ 2Anb 2 ) y ' 



To 



where Y = - 2 log b V 2 = - log b 2 Y 4 , 



Y = -log& 2 Y 4 . 



Hence , B =^ [Bi(-Y )-E.'(-Y)]. . . . (4) 



~Eii(x) is the exponential integral, defined by 



— X 



oo 



numerical values of which have been tabulated by various 

 writers. 



