J. W. Gibbs — Equilibrium of Heterogeneous Substances. Il7 



tials c?mj, dm^., . . . dm^ shall be indeiDendent, and shall express 

 every possible variation in the composition of the homogeneous mass 

 considered, including those produced by the absorption of substances 

 different from any initially pi-esent. It may therefore be necessary 

 to have terms in the equation relating to component substances 

 which do not initially occur in the homogeneous mass considered, 

 provided, of course, that these substances, or their components, are 

 to be found in some part of the whole given mass. 



If the conditions mentioned are satisfied, the choice of the sub- 

 stances which we are to i-egard as the components of the mass con- 

 sidered, may be determined entirely by convenience, and independently 

 of any theory in regard to the internal constitution of the mass. The 

 number of components will sometimes be greater, and sometimes 

 less, than the number of chemical elements present. For example, 

 in considering the equilibrium in a vessel containing water and free 

 hydrogen and oxygen, we should be obliged to recognize three com- 

 ponents in the gaseous part. But in considering the equilibrium of 

 dihite sulphuric acid with the vapor which it yields, we shoiild have 

 only two components to consider in the liquid mass, sulphuric acid 

 (anhydrous, or of any particular degree of concentration) and (addi- 

 tional) water. If, however, we are considering sulphuric acid in a 

 state of maximum concentration in connection with substances which 

 might possibly afford water to the acid, it must be noticed that the 

 condition of the independence of the differentials will require that we 

 consider the acid in the state of maximum concentration as one of 

 the components. The quantity of this component will then be capa- 

 ble of variation both in the positive and in the negative sense, while 

 the quantity of the other component can increase but cannot decrease 

 below the value 0. 



For brevity's sake, we may call a substance S^ an actual component 

 of any homogeneous mass, to denote that the quantity ra^ of that 

 substance in the given mass may be either increased or diminished 

 (although we may have so chosen the other component substances 

 that m^ =. 0) ; and we may call a substance S^ a possible component 

 to denote that it may be combined with, but cannot be substracted 

 from the homogeneous mass in question. In this case, as we have 

 seen in the above example, we must so choose the component sub- 

 stances that Wj rz 0. 



The units by which we measure the substances of which we regard 

 the given mass as composed may each be chosen independently. To 

 fix our ideas for the purpose of a general discussion, we may suppose 



