J. W. Gibbs — Eqidlihriut)i of Heterogeneous Sultstuitces. 225 



to a mixture of hydrogen and air, or to any ternary gas-mixture in 

 wliich the proportion of two of the components is fixed. In fact, tlie 

 form of equation (279) which applies to a gas-mixture of any pai'ticu- 

 lar number of components may easily be reduced, when the propor 

 tions of some of these components are fixed, to the form whicli ai)plies 

 to a gas-mixture of a smaller niunber of components. The necessary 

 substitutions will be analogous to those given on page 217. But the 

 components must be entirely different from one another with respect 

 to the gases of which they are formed by mixture. We cannot, for 

 example, apply equation (279) to a gas-mixture in which the com- 

 ponents are oxygen and air. It would indeed be easy to form a 

 fundamental equation for such a gas-mixture with reference to the 

 designated gases as components. Such an equation might be derived 

 from (279) by the proper substitutions. But the result would be an 

 equation of more complexity than (279). A chenncal compound, 

 however, with respect to Dalton's law, and with respect to all the 

 equations which have been given, is to be regarded as entirely differ- 

 ent from its components. Thus, a mixture of hydrogen, oxygen, and 

 vapor of water is to be regarded as a ternary gas-mixture, having the 

 three components mentioned. This is certainly true when the quanti- 

 ties of the compound gas and of its components are all independently 

 variable in the gas-mixture, without change of temperature or pres- 

 sure. Cases in which these quantities are not thus independently 

 variable will be considered hereafter. 



Inferences in regard to Potentials iti Liquids and Solids. 



Such equations as (264), (268), (276), by which the values of 

 potentials in pure or inixed gases may be derived from quantities 

 capable of direct measurement, have an interest which is not confined 

 to the theory of gases. For as the potentials of the independently 

 variable components which are common to coexistent liquid and gas- 

 eous masses have the same values in each, these expressions will 

 generally afford the means of determining for liquids, at least ap- 

 proximately, the potential for any independently variable compon- 

 ent Avhich is capable of existing in the gaseous state. For although 

 every state of a liquid is not such as can exist in contact with a 

 gaseous mass, it will always be possil)le, when any of the components 

 of the liquid are volatile, to bring it by a change of pressure 

 alone, its temperature and composition remaining unchanged, to 

 a state for which there is a coexistent phase of vapor, in which 



Trans. Conn. Acad., Vol. III. 29 May, KSTfi. 



