Electricity through Gases by Charged Ions. 263 



The distance between the plates in which the electric 

 intensity is constant and equal to X is I— {\ t +\), where / is 

 the distance between the plates. Since \ l + \ 2 = i/qe tne ^ a ^ 

 of potential in this distance is equal to 



hence if V is the potential-difference between the plates 



and 



X = ^V l 



^° \q) efa + ki)' 



so that 



\q/ cft + y I v k Y + k 2 qe JV k x -+k 2 qe qe J 



This gives the relation between the current and the poten- 

 tial-difference between the plates. It is of the form 



y = A* 2 +B t . 



In a paper by Mr. Eutherford and myself in the Phil. 

 Mag. for Oct. 1896, a relation between V and i was given on 

 the assumption that the electric intensity was constant between 

 the plates ; in this investigation I have tried to allow for the 

 variation in the electric intensity. The above investigation 

 ceases to be an approximation to the truth when the two 

 layers touch each other. In this case the current has its 

 limiting value Iqe, and there is no loss of ions by recom- 

 bination ; we may therefore neglect the recombination and 

 proceed as follows. 



Equations (5) become in this case 



^ (k 1 n 1 X) = q, 



^(k 2 n 2 X)=-q. 



If q is constant, the solutions of these equations are 



Ar 1 w 1 X = g-a?, (9) 



k 2 n 2 X=zq{l-x), (10) 



where x is the distance measured from the positive plate and 

 I the distance between the plates, for these solutions satisfy 



