600 Prof. J. S. Townsend on the Genesis of Tons 



produced b}^ the impact of a neoative ion. In applying the 

 theory, therefore, it is only necessary to consider one kind 

 of positive ion and one kind of negative ion *. 



Let ??o be the number of ions starting from the negative 

 plate, and let n be the total number arriving at the positive 

 plate. Of the number n — ng of each kind generated in the 

 gas let p be produced in the layer of gas between the 

 negative plate and a parallel plane at a distance ^, and let g 

 be produced in the layer between the plane and the positive 

 electrode. 



Then n = nQ-\-p-{-g. 



Let a be the number of ions of each kind produced bv a 

 negative ion in moving through a centimetre of the gas. 



Let /3 be the corresponding number for a positive ion. 



Considering the number of ions dp generated between the 

 two planes at distances .v and x + dx from the negative 

 electrode, we have 



a 



I 



1^ 



oL[n^+p)dx new ions of each kind produced by the n^+p 

 negative ions moving through the distance d,i\ and (3 g dx 

 produced by the g positive ions moving in the opposite 

 direction. 



Hence dp = a (?? o -^p) ^^^^ + jSgd.v, 



or ■£={a-^)(no-{-p)+n^. 



Hence P= [^ + ^^] (e^^-^^^-l), 



and since p^=n— ?7o, when ^ = a we have 



The quantities a, and 13 depend on the electric force and 

 the pressure, so that if a number of experiments be made 



* [It is evident from the previous researches which Mr. Kirkhy and I 

 have'^made that the negative ion set free fi'om a metal plate by ultra- 

 violet light, or generated in a gas by RoDtgen rays, is the same as the 

 negative ion separated from a molecnle of any gas by collision. The 

 positive ions only can be different in different gases.J 



