J. W. Gibbs — Equilibrium of Heterogeneous Substances. 195 



addition to the mass in question of a substance not before contained 

 in it, does any reason appear for supposing that this differential coeffi- 

 cient has generally the value zero. To fix our ideas, let us suppose 

 that S^ denotes water, and 8^ a salt (either anhydrous or any partic-. 

 ular hydrate). The addition of the salt to water, previously in a 

 state capable of equilibrium with vapor or with ice, will destroy the 

 possibility of such equilibrium at the same temperature and pressure. 

 The liquid will dissolve the ice, or condense the vapor, which is 

 brought in contact with it under such circumstances, which shows 

 that //j (the potential for water in the liquid mass) is diminished by 

 the addition of the salt, when the temperature and pressure are main- 

 tained constant. Now there seems to be no a priori reason for 

 supposing that the ratio of this diminution of the potential for water 

 to the quantity of the salt which is added vanishes with this quantity. 

 We should rather expect that, for small quantities of the salt, an 

 effect of this kind would be proportional to its cause, i. e., that the 

 differential coefficient in (211) would have a finite negative value for 

 an infinitesimal value of m^. That this is the case with respect to 

 numerous watery solutions of salts is distinctly indicated by the 

 experiments of Wtillner* on the tension of the vapor yielded by such 

 solutions, and of Rtldorfff on the temperature at which ice is formed 

 in them ; and unless we have experimental evidence that cases are 

 numerous in which the contrary is true, it seems not unreasonable 

 to assume, as a general law, that when tn^ has the value zero and is 

 incapable of negative values, the differential coefficient in (211) will 

 have a finite negative value, and that equation (212) will therefore 

 hold true. But this case must be carefully distinguished from that 

 in which m^ is capable of negative values, which also may be illus- 

 trated by a solution of a salt in water. For tliis purpose let S^ 

 denote a hydrate of the salt which can be ciystallized, and let S.-, 

 denote water, and let us consider a liquid consisting entirely of 8^ 

 and of such temperature and pressure as to be in equilibrium with 

 crystals of S^. In such a liquid, an increase or a diminution of the 

 quantity of water would alike cause crystals of 8^ to dissolve, which 

 requires that the differential coefficient in (211) shall vanish at the 

 particular phase of the liquid for which m, = 0. 



Let us return to the case in which m.^\^ incapable of negative values, 

 and examine, without other restriction in regard to the substances 



* Fogg. Ann., vol. ciii. (1858), p. 529 ; vol. cv. (1858), p. 85; vol. ex. (1860), p. 564. 

 \ Pogg. Ann., vol. cxiv. (1861), p. 63. 



