142 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



its temperature and pressure and the quantities of its ultimate 

 components, while the various transitory states through which the 

 mass passes (which are evidently not completely defined by the 

 quantities just mentioned) may be completely defined by the quantities 

 of certain proximate components with the temperature and pressure, 

 and the matter of the mass may be brought by processes approxi- 

 mately reversible from permanent states to these various transitory 

 states. In such cases, we may form a fundamental equation with 

 reference to all possible phases, whether transitory or permanent; 

 and we may also form a fundamental equation of different import 

 and containing a smaller number of independent variables, which 

 has reference solely to the final phases of equilibrium. The latter 

 are the phases of dissipated energy (with reference to molecular 

 changes), and when the more general form of the fundamental 

 equation is known, it will be easy to derive from it the fundamental 

 equation for these permanent phases alone. 



Now, as these relations, theoretically considered, are independent 

 of the rapidity of the molecular changes, the question naturally arises, 

 whether in cases in which we are not able to distinguish such 

 transitory phases, they may not still have a theoretical significance. 

 If so, the consideration of the subject from this point of view, may 

 assist us, in such cases, in discovering the form of the fundamental 

 equation with reference to the ultimate components, which is the 

 only equation required to express all the properties of the bodies 

 which are capable of experimental demonstration. Thus, when the 

 phase of a body is completely determined by the quantities 4 of n 

 independently variable components, with the temperature and pres- 

 sure, and we have reason to suppose that the body is composed of 

 a greater number n' of proximate components, which are therefore 

 not independently variable (while the temperature and pressure 

 remain constant), it seems quite possible that the fundamental 

 equation of the body may be of the same form as the equation for 

 the phases of dissipated energy of analogous compounds of n f proxi- 

 mate and n ultimate components, in which the proximate components 

 are capable of independent variation (without variation of temperature 

 or pressure). And if such is found to be the case, the fact will be 

 of interest as affording an indication concerning the proximate con- 

 stitution of the body. 



Such considerations seem to be especially applicable to the very 

 common case in which at certain temperatures and pressures, regarded 

 as constant, the quantities of certain proximate components of a 

 mass are capable of independent variations, and all the phases pro- 

 duced by these variations are permanent in their nature, while at 

 other temperatures and pressures, likewise regarded as constant, the 



