260 Prof. J. J. Thomson on the Theory of Conduction of 



are satisfied by 



7i l = n 2 = {q/a}i y 



k 2 n 2 ~K.i 



h 



©' 



^l + A-2 ' 



e{k x + kc. 



where c is the current through the gas. In this case the 

 amounts of the current carried by the positive and negative 

 ions respectively are proportional to the velocities of those 

 ions. When, however, the current passes between two 

 parallel plates, this solution cannot hold right up to the plates, 

 For, consider the condition of things at a point P, between 

 the plates AB and CD, of which AB is the positive and CD 

 the negative plate. Then across unit area at P 



k, i 



k,+ko e 



positive ions pass in unit time, and these must come from the 

 region between P and AB ; this region can, however, not 

 furnish more than q\, and only as much as this if there are 

 no recombinations ; hence the preceding solution cannot hold 

 when the distance from the positive plate is less than 



k x + k 2 qe ' 



similarly it cannot hold nearer the negative plate than the 

 distance 



k 2 i 

 k x + k 2 qe 



We shall assume that the solution given above does hold in the 

 parts of the field which are further away from the plates than 

 these distances ; and further, that in the layers in which this 

 solution does not hold, there is no recombination of the ions. 

 Let us now consider the condition of things near the positive 

 plate between 



x = and x — , — ^ = X say. 



k x + k 2 qe 



Then, since in this region there is no recombination, our 



