at the Electrodes in a Solution. 51 



a cylindrical vessel bounded at both ends by its electrodes. 

 Let F g.-equivalents o£ salt be uniformly and constantly 

 removed at one end, per unit of surface and time, and let the 

 distance from the electrode forming the other end be so great 

 that changes of concentration occurring there do not affect 

 the concentration at the electrode under consideration. 

 Further, let the initial concentration be uniform and equal to 

 Cq g.-equivalents per unit of volume. Find the concentration 

 in the interior of the liquid and at the electrode at any given 

 time t under the suppositions, that changes of concentration 

 are neutralized by diffusion only, that this takes place 

 according to Fick's law, and that it is not affected by the 

 passage of the current through the liquid *. 



As the concentration at any point of the liquid cannot be 

 influenced by the nature of the cause producing the removal 

 of the salt, it will be the same as that in a similar liquid in 

 which a flow F was produced by a suitable gradient of con- 

 centration being artificially kept up immediately behiud the 

 electrode. In such a solution, and therefore also in the one 

 under consideration, we have for the determination of the 

 state of the liquid the first equation : 



F = K S> (1) 



for x = 0, 



if concentrations at any point are indicated by c, distances 

 from the electrode by #, and the diffusion-coefficient of the 

 salt by K. 



The uniformity of the concentration at the beginning of 

 the experiment affords us the second equation : 



c = Co, (2) 



between a?=0 and x = l for £ = 0, 

 and the general expression of Fick's law gives us the third : 



J 6 =Kp (3) 



^t ox- v ' 



Equations 1 and 3 are satisfied by the following general 

 solution : 



F *=°° fnir \ -^Kt 



C= K^ ^ C0S VT / 6 ;• • • W 



* Note. — The equations given here as far as No. 5 have already been given 

 by H. F. Weber in the elaboration of his beautifully conceived method 

 for the determination of the diffusion-coefficient of ZnSO t (Wied. Ann. 

 vii.p.539). Concentrations in a solution subjected to alternating currents 

 have been recently examined by Warburg (AVied. Ann. lxvii. p. 4951. 



E 2 



