Theory of Ionization by Collision. 



131 



due to the first group of electrons, we shall oall N (.r) .dx, 

 where the suffix denotes that the electrons come directly 

 from A without intermediate collisions. 



Fi«\ 2. 



nr 



lliiiiniiiiiill 



X 



We have then 



for x < /o = N («) = 0, 



and for x > / : N (a?) = ^ . e~L. 



(See fig. 2, L). (5) 



We shall then proceed to the determination of the first 

 ionizations which are due to group 2. 



In the element of space (y, y + dy), where y in the same 

 way as x signifies the distance from A and where 0<y<! , 

 the number of collisions per second between electrons and 



no 



molecules is y . dy, but none of these collisions give rise to 

 ionization. The next collision where these T ° . dy electrons 



take part will in the element of space (x, %+dx) give 

 N y (#). dxdy ionizations where 



for .'.'<// + 1 : 

 and for .'■>// + / : 





• } 



.,. € 



s • 



K 2 



(6) 



