Electrodes, one of which is covered luith Radioactive Matter 257 



Hence conditions (1), (2), (3) are identical and determine B. 

 Condition (4) supplies a relation between G and A, 



A^K{G-IR^). 

 Hence 



X' = K 



^x~ log h f 



h 



Rx + BR' 



X' = K 



CO R. 



X ft-l ~f~ rCo 



0<x<R, where BR- = C, 



The constant B can be determined when the potential differ- 

 ence between the electrodes is given*. 



The general character of these results can be shown by numerical 

 calculation for the cases k, = L, l-25k,=k^, A;i = 1-25 A-., (corresponding 

 to the case in which the positive ion moves more slowly, as usual, 

 than the negative ion, and the radioactive matter is spread on the 

 negative plate), and for distances R, 2R, SR between the electrodes, 

 and for B = O'l, 0-5, I'O. In order that the current may be the satu- 

 ration current it is necessary in practice that B should exceed 

 a certain limit. This limit is dependent on the particular conditions 

 of any given experiment. 



The distribution of the electric force X is shown on the graph 

 below. The curves marked (1), (2), (3) are for the cases 

 kj = 1-25 k.2, ki = ^'2, A.-2 = 1-25 k^, respectively. 



The potential difference V between the electrodes is given in 

 the following table, d being the distance between the plates. 



V 

 RKK^' 



These forms of X are not strictly valid in the immediate neighbourhood of the 

 electrodes, as the natural agitation of the ions has been neglected in this theory 

 Vide Pidduck, Treatise on Electricity, 1916, p. 505. 



18—2 



