50 Ml!, s. AV. .1. SMITH ON THE NATURE OF ELECTROCAPILLARY PHENOMENA. 



The, First Hypothesis of the Lippmann-Hdmholtz Theory. 



The first hypothesis would apply to any electrolytic cell consisting of two polariz- 

 able electrodes placed in a conducting solution. When an E.M.F. (of which the value 

 is kept within certain limits depending on the nature of the electrodes and of the 

 solution) is applied to such a cell there may be a considerable current for a very short 

 time ; but the system almost at once assumes a practically steady state in which there 

 is only a very feeble continuous current through the cell. The value of this current 

 can in general be neglected in comparison with the current value found by dividing 

 the E.M.F. applied by the calculable resistance of the electrolyte. It is therefore 

 considered that the potential fall within the liquid can be neglected in comparison 

 with the sum of the potential changes in the neighbourhood of the electrodes, and 

 that this sum is equal in value to the applied E.M.F. The system is, in fact, 

 considered equivalent to a pair of condensers (supposed existent at the surfaces of 

 separation between electrode and solution) connected in series by a resistance (repre- 

 sented by the resistance of the electrolyte). For electrodes of the same nature in the 

 same solution the respective capacities are taken to be proportional to the areas of the 

 surfaces in contact with the solution. In the capillary electrometer, therefore, the 

 capacity of one electrode would in general be indefinitely small compared with that of 

 the other. 



Let AA' and BB' represent condensers (of capacities C, and C 2 ) of which the plates 



A' and B' are connected by a resistance R, and of which the " external " plates A 

 and B are at first also connected. 



Supjx)se the condensers are charged, and let A and B be at zero potential while 

 A' and B' are at the potential TT B . Let now an E.M.F. ir t be introduced in the 

 external circuit connecting A and B, and let the resistance of this circuit be R'. Let 

 TT, IT' and TT" be the final potentials of A, A' and B' respectively, B being supposed 

 kept at zero potential. Then it is easy to show that 





