972 Mr. S. Smith on Initial 



terms of y-, values of a may be deduced by substituting 



these values of fju in equation (4). It is interesting to notice 

 that making e 2a =l in evaluating the ratio /j, involves the 

 assumption that the numbers of negative ions produced by 

 collisions in spaces S l5 S 2 , and S 3 are proportional to the 

 numbers of the original ions, liberated from electrode 2, 

 present in these spaces at any moment of time after the 

 steady state has been reached. Let N 1? N 2 , and N 3 be these 

 numbers. 

 Then 



_ rc 2 N 9 



Lb 



ni + nj + n, Nj + N 2 + N, 



(5) 



The values of /j, corresponding to a given value of y may 

 be found as follows : ' c 



By giving £ the values —'2, — % 0, '1, and '2 successively 

 the integrals are found to involve only 



C a i 2 Z t r 



I dx I z~^ e~ "° k * 



Jo Jo 



C^ , C 2 , -10-25? . x ~ 

 dx\ z~*e * zdz, 







where a has the values '4, '3, *2, and *1. 



If now z is given definite values, e. g. '1, *5, 1, 1*5, and 2, 

 the integrals involved are 



I e-^drj and 1 



Jo Jo 



d v , 



where b has certain numerical values. 



These integrals can therefore be evaluated by the use of 

 tables. The values of the original integrals after the £ and 

 z substitutions were plotted against ~, and the values of the 

 integrals, found by a calculation of areas, were plotted 

 against the corresponding values of £. The ratio of the 

 new areas gave the value of //,. 



When the values of /j, found from the curve in fig. 5, and 

 the values of p taken from the curves in fig. 4, were 

 substituted in equation (4), the following results were 

 obtained. 



