SURFACES OF DISCONTINUITY 691 



there is a positive charge on the mercury cathode surface. At 

 the point of maximum a, where da/dV vanishes, q is zero, and 

 on further increase in E, q becomes negative. If we write 

 Lippmann's result in the form 



one sees that it is equivalent to Gibbs' equation [690], although 

 at the first glance it would seem as if there were a difference of 

 sign between the two results; for V" — V is the applied electro- 

 motive force and so [690] becomes 



da^ ly, 



dE ~ Oa 



Since Tif/aa is the excess ionic charge at the surface, a contra- 

 diction apparently arises. This disappears, however, on a 

 little thought; one must bear in mind that Gibbs considered the 

 transport of electricity in terms of ions, e.g., hydrogen ions; 

 these only travel from one discontinuous layer to the other; 

 Fa' represents the excess of (hydrogen) ions in the layer of the 

 electrolyte adjacent to the mercury represented by the singly 

 accented symbols, i.e., the cathode. Thus, as Gibbs points out, 

 there will be a defect of hydrogen ions in this layer in the natural 

 state, since by his equation Tj is negative if da' /BE is positive. 

 This involves a negative charge in this layer which is the 

 counterpart of the positive charge on the mercury surface; 

 for of course the region of discontinuity is uncharged as a whole. 



66. The Double-Layer Hypothesis of Helmholtz 



It was in fact this phenomenon of the double layer of charge 

 which Helmholtz emphasized. Holding as he did decided views 

 in favor of Volta's hypothesis of contact potentials, he pointed 

 out that a discontinuity of potential could only exist between 

 metal and electrolyte for the same reason as between two metals 

 in contact, viz., by a condenser-like action arising from equal 

 and opposite charges segregated in adjacent layers of the two 



