380 Conduction in Solutions and Gases , 



which a jet of mercury, falling from a reservoir into an electro- 

 lytic solution, is so adjusted that it breaks into drops when 

 the jet touches the solution. According to Helmholtz's 

 conclusion there is no difference of potential between the 

 drops and the electrolyte ; and therefore the difference of 

 potential between the electrolyte and a layer of mercury 

 underlying it in the same vessel is equal to the difference of 

 potential between this layer of mercury and the mercury 

 in the upper reservoir, which difference is a measurable 

 quantity. 



It will be seen that according to the theories both of Gibbs 

 and of Helmholtz, and indeed according to all other theories on 

 the subject,* d^ldV is zero for an electrode whose surface is 



* E.g., that of Warburg, Ann. d. Phys. xli (1890), p. 1. In this it is assumed 

 that the electrolytic solution near the electrodes originally contains a salt of 

 mercury in solution. When the external electromotive force is applied, a conduc- 

 tion-current passes through the electrolyte, which in the hody of the electrolyte 

 is carried by the acid and hydrogen ions. Warburg supposed that at the 

 cathode the hydrogen ions react with the salt of mercury, reducing it to metallic 

 mercury, which is deposited on the electrode. Thus a considerable change in 

 concentration of the salt of mercury is caused at the cathode. At the anode, the 

 acid ions carrying the current attack the mercury of the electrode, and thus 

 increase the local concentration of the mercuric salt ; but on account of the size of 

 the anode this increase is trivial and may be neglected. 



Warburg thus supposed that the electromotive force of the polarized cell is 

 really that of a concentration cell, depending on the different concentrations of 

 mercuric salt at the electrodes. He found dy/dV to be equal to the amount of 

 mercuric salt at the cathode per unit area of cathode, divided by the electro- 

 chemical equivalent of mercury. The equation previously obtained is thus 

 presented in a new physical interpretation. 



Warburg connected the increase of the surface-tension with the fact that the 

 surface-tension between mercury and a solution always increases when the con- 

 centration of the solution is diminished. His theory, of course, leads to no 

 conclusion regarding the absolute potential difference between the mercury and the 

 solution, as Helmholtz' does. 



Alan electrode whose surface is rapidly increasing e.g., a dropping electrode 

 Warburg supposed that the surface-density of mercuric salt tends to zero, so 

 dyldV is zero. 



The explanation of dropping electrodes favoured by Nernst, Beilage zu den 

 Ann. d. Phys. Iviii (1896), is that the difference of potential corresponding to the 

 equilibrium between the mercury and the electrolyte is instantaneously 

 established ; but that ions are withdrawn from the solution in order to form the 

 double layer necessary for this, and that these ions are carried down with the drops 



