Cathode Rays and certain Chemical Effects. 225 



In the special case that follows on the hypothesis that the 

 only source o£ loss of ions is recombination, the total number 

 of ions is * 



21 Vn\a, 



where I is the diameter of the chamber, n is the number of 

 ions produced per c.c. per second, and a is the coefficient 

 of recombination. 



In the special case that follows on the hypothesis that the 

 loss is entirely due to diffusion, the total number of ions is f 



3D ' 



where D is the coefficient of diffusion. 



9 n . . 



Hence, if ivy^ 3 is small compared with 21 s]n\a, the loss 



of ions from diffusion becomes large in comparison with the 

 loss due to recombination, and the latter justifiably negligible. 

 For pressures of the order of those involved in the present 

 work this condition becomes 



9?i<3xl0 3 s/n, 



or n < 10 5 , 



and is amply satisfied. 



While cathode rays cross the ionization-chamber, 



up ions are made per second, 



where a is a constant. 



6 

 There is a loss — N due to diffusion to the walls of the 



P. 

 chamber ; where (3 is a constant and N is the finite number 



of ions in the interior of the chamber. 



When the steady state is attained, we have 



ap = £- N, 

 P 

 or 



N, then, the equilibrium ionization, is proportional to p 2 

 when diffusion through ions to the walls of the ionization- 

 •chamber is considered. 



If, however, the radius of the chamber is comparable with 



* J. J. Thomson, * Conduction of Electricity through Gases,' p. 16 

 ^second edit.). 

 t Ibid. p. 31. 



