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



giving the connexion between the electric intensity and the 

 distance between the plates are found by experiment to be 

 somewhat as represented in fig. 1. The variation in X (fig. 1) 



Fisr. 1. 



occurs only in two layers near the plates and X is approximately 

 constant in the rest of the field. As the current through the 

 gas increases the layers of inconstant X expand until they 

 touch, and then there is no longer a region in which X is 

 constant. We can easily find an inferior limit to the value 

 of X the thickness of one of these layers when we are given 

 the value of the current. For suppose P (fig. 1) is at the 

 boundary of the layer next the positive electrode, then at P, 

 since X becomes constant, half the current must be carried 

 by the positive and half by the negative ions; if i is the 

 current and e the charge carried by an ion, then ij'le positive 

 ions must cross unit area of a plane through P in unit time, 

 so that at least that number must be produced in unit time in 

 the region between P and the positive plate. Now if X is 

 the thickness of the layer, qX is the number of positive ions 

 produced in unit time; the number that cross the plane in 

 unit time cannot then be greater than qX, and will only be as 

 great as this if no recombination of the ions takes place ; 

 hence 



or 



X> 



2e : 



2qe 



Thus t/2eq is an inferior limit to X. It will not, however, I 

 think be very far from the true value, for we can show that 

 but little recombination will take place in the time taken by 

 the positive ions to traverse a layer of this thickness. For 

 the rate of combination of the positive ions is given by 



dn x 



= — an l ?i 2 . 



