506 J. W. Gihbs — Equilibrium of Heterogeneous Stihstances. 



may take place before the deposit will have the properties of matter 

 in mass. Even when the ion appears in mass, or is absorbed by the 

 electrode or electrolytic fluid, the non-homogeneous film between the 

 electrolytic fluid and the electrode may contain an additional portion 

 of it. Whether the ion is confined to the surface of the electrode 

 or not, we may regard this as one of the cases in which we have to 

 recognize a certain superficial density of substances at surfaces of 

 discontinuity, the general theory of which we have already considered. 

 The deposit of the ion will affect the superficial tension of the 

 electrode if it is liquid, or the closely related quantity which we have 

 denoted by the same symbol o' (see pages 482-500) if the electrode 

 is solid. The effect can of course be best observed in the case of a 

 liquid electrode. But whether the electrodes are liquid or solid, if 

 the external electromotive force V — V" applied to an electrolytic 

 combination is varied, when it is too weak to produce a lasting current, 

 and the electrodes are thereby brought into a new state of polariza- 

 tion, in which they make equilibrium with the altered value of the 

 electromotive force, without change in the nature of the electrodes or 

 of the electrolytic fluid, then by (508) or (675) 



dff' = - r; djjj, 

 da" = - rj' dpi:' ; 

 and by (687), 



' d{ V - V") = - a', {df.i: - dpi:'). 

 Hence 



d{ V— V") = ^dff'- ^, dff". (689) 



If we suppose that the state of polarization of only one of the elec- 

 trodes is affected (as will be the case when its surface is very small 

 compared with that of the other), we have 



dff'=^d(V'—V"). (690) 



«'a 



The superficial tension of one of the electrodes is then a function of 

 the electromotive force. 



This principle has been applied by M. Lijipmann to the construc- 

 tion of the electrometer which bears his name.* In applying equa- 

 tions (689) and (690) to dilute sulphuric acid between electrodes of 

 mercury, as in a Lippmann's electrometer, we may suppose that the 



* See his memoir : " Relations entre les phunomenes electriques et capillaires," 

 Annales de Chimieetde Physique, 5e serle, t. v, p. 494. 



