J. W. Gibhs — Equilibrmm of Heterogeneous Substances. 507 



suffix refers to hydrogen. It will be most convenient to suppose the 

 dividing surface to be so placed as to make the surface-density of 

 mercury zero. (See page 397.) The matter which exists in excess or 

 deficiency at the surface may then be expressed by the surface-densi- 

 ties of sulphuric acid, of water, and of hydrogen. The value of the 

 last may be determined from equation (690). According to M. Lipp- 

 mann's determinations, it is negative when the surface is in its natural 

 state (i. e., the state to which it tends when no external electromo- 

 tive force is applied), since & increases with V" — V. When 

 V" — V is equal to nine-tenths of the electromotive force of a Dan- 

 iell's cell, the electrode to which V" relates remaining in its, natural 

 state, the tension a' of the surface of the other electrode has a maxi- 

 mum value, and there is no excess or deficiency of hydrogen at that 

 surface. This is the condition toward which a surface tends when it 

 is extended while no flux of electricity takes place. The flux of elec- 

 tricity per unit of new surface formed, which wnll maintain a surface 



in a constant condition while it is extended, is represented by — 



in numerical value, and its direction, when F^' is negative, is from 

 the mercury into the acid. 



We have so far supposed, in the main, that there are no passive 

 resistances to change, except such as vanish with the rapidity of the 

 processes which they resist. The actual condition of things with 

 respect to passive resistances appears to be nearly as follows. There 

 does not appear to be any passive resistance to the electix)lytic pro- 

 cess by Avhich an ion is transferred from one electrode to another, 

 except such as vanishes with the rapidity of the process. For, in any 

 case of equilibrium, the smallest variation of the externally applied 

 electromotive force appears to be suflicient to cause a (temporaiy) 

 electrolytic current. But the case is not the same with respect to 

 the molecular changes by which the ion passes into new combinations 

 or relations, as when it enters into the mass of the electrodes, or sep- 

 arates itself in mass, or is dissolved (no longer with the properties of 

 an ion) in the electrolytic fluid. In virtue of the passive resistance to 

 these processes, the external electromotive force may often vary 

 within wide limits, without creating any current by which the ion is 

 transferred from one of the masses considered to the other. In other 

 words, the value of V — V" may often difier greatly from that 

 obtained from (08*7) or (688) when we determine the values of the 

 potentials for the ion as in cases I, II, and III. We may, however, 

 regard these equations as entirely valid, when the potentials for the 



