SURFACES OF DISCONTINUITY 701 



which is, of course, the expression Gibbs uses just before [689]. 

 But in reahty we can show just as readily that 



d(T = - T]sdt - Vi dNi - Vi dNi - . . . , 



where A^i, A^2, etc. , are any quantities differing from Mi, M^, etc. , 

 by amounts proportional to the various chemo-electrical equiva- 

 lents. This is in fact one aspect of the statement made above 

 concerning a system which has the electric potentials of all 

 its phases raised or lowered by the same amount. 



So far we have considered solutions. If a metal, such as 

 mercury, is one of the phases, then we regard it as a phase with 

 two components, electrons and mercury ions Now the present 

 theory of metals considers the electric charge of a piece of metal 

 to be measured by the excess of the electrons in it above the 

 positive metallic ions, or the deficiency under; and quite simply 

 the "chemical potential" of the electron is just fi^V, where /S^ is 

 the chemo-electrical equivalent of an electron, viz., the 

 negative quotient of the electron-charge number by the mass 

 of the electron, i.e., —1.77 X 10*. In consequence, if the elec- 

 trical potential of mercury changes by 5F the chemical potential 

 of an electron changes by /S^SF or BM^ = ^JV. The region of 

 discontinuity between the mercury and the electrolyte is now 

 treated in the usual way. We must, of course, define the 

 position of the ideal dividing surface in order to give a definite 

 meaning to surface excess of any component. Various defining 

 conditions have been employed by different authors. For our 

 purpose the one used by Butler seems to be the simplest; this 

 places the surface so that the excess of mercury ions on the 

 mercury side of the surface is zero, i.e., so that the excess or 

 deficiency of electrons in the mercury measures the electric 

 charge on it ; in other words, if T^ is the excess of electrons per 

 unit area, q, the electric charge per unit surface, is equal to 

 fiiTf* There may of course be an excess concentration of 

 mercury ions on the electrolyte side of the surface, measured, as 

 usual, by the amount of these ions in excess of the amount that 

 would be in the electrolyte if the concentration of them were the 



Note that /3e is an essentially negative number. 



