at the Electrodes in a Solution. 



53 



shall convert it into a definite integral and make I infinite by 

 the substitutions : 



- ± 



I 



d(f it dq' 



dq being the differential of the variable q which assumes 



successively the values dq, 2dq q oo, and k an 



arbitrary positive constant. We thus obtain : 



F , 4F p _ k ( . (2q \ 



The value of k being arbitrary, we can make : 



4q*Kt\ 



e~ * 2 ). 



4K* 



= 1 



1. e. 



*=2^Kt. 



and we find 



F 



2F 



c^^ + Co-^v'KJ 



f?c- 



xq 



COS — -l_g-? 



VKt 



)■ 



This expression is further simplified in the following manner: 

 we differentiate twice according to x and obtain 



-tfc_ 2F 



•dx* ~ TrKjKt 



I dq cos — ^=e 



VKi 



The value of the integral occurring here being known to be 



s/ir _^i 



— ^- e 4 Kf ? we have : 



-dx 2 



K vVK* 



e 4Kf, 



and making use successively of equations (3) and (2) we 

 find 



F f* 



V7rKJo 



dt _± 



r e 4Kt; 



s/t 



(6) 



an equation from which it is not difficult to obtain numerical 

 values for c by one of the approximation methods. For the 

 ■concentration at the electrode for which x=0, this equation 

 assumes the extremely simple form 



=^2F V /.^=o„-l-1284E V /| 



(?) 



