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380

Conduction in Solutions and Gases,

which a jet of mercury, falling from a reservoir into an electrolytic 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,^[1] $dγ / dV$ 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 conduction-current passes through the electrolyte, which in the body 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 $dγ / dV$ 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 concentration 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 $dγ / dV$ is zero.
The explanation of dropping electrodes favoured by Nernst, Beilage zu den Ann. d. Phys. lviii (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

[p380-1] 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 conduction-current passes through the electrolyte, which in the body 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 $dγ / dV$ 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 concentration 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 $dγ / dV$ is zero.
The explanation of dropping electrodes favoured by Nernst, Beilage zu den Ann. d. Phys. lviii (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

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