136 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



ideas, let us suppose that S l denotes water, and 8 2 a salt (either 

 anhydrous or any particular 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 fa (the potential for water 

 in the liquid mass) is diminished by the addition of the salt, when 

 the temperature and pressure are maintained 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 2 . That this is the case with respect to numerous watery solutions 

 of salts is distinctly indicated by the experiments of Wiillner * on the 

 tension of the vapor yielded by such solutions, and of Riidorff t 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 m 2 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 2 is capable of negative 

 values, which also may be illustrated by a solution of a salt in water. 

 For this purpose let S l denote a hydrate of the salt which 'can be 

 crystallized, and let $ 2 denote water, and let us consider a liquid con- 

 sisting entirely of S t and of such temperature and pressure as to be in 

 equilibrium with crystals of S r In such a liquid, an increase or a 

 diminution of the quantity of water would alike cause crystals of S 1 

 to dissolve, which requires that the differential coefficient in (211) 

 shall vanish at the particular phase of the liquid for which m 2 = 0. 



Let us return to the case in which m 2 is incapable of negative 

 values, and examine, without other restriction in regard to the sub- 



Tfi 



stances denoted by 8 l and $ 2 , the relation between /z 2 and - for any 



ii 6-1 



constant temperature and pressure and for such small values of 



l/C'i 



that the differential coefficient in (211) may be regarded as having the 

 same constant value as when m 2 = 0, the values of t, p, and m^ being 

 unchanged. If we denote this value of the differential coefficient by 



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

 i-Pogg. Ann., vol. cxiv. (1861), p. 63. 



