EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 139 



example given above, the temperature must not be raised beyond 

 a certain limit, or molecules of hydrogen and of oxygen may be 

 transformed into molecules of water. 



The differences in bodies resulting from such differences in the 

 constitution of their molecules are capable of continuous variation, 

 in bodies containing the same matter and in the same thermodynamic 

 state as determined, for example, by pressure and temperature, as the 

 numbers of the molecules of the different sorts are varied. These 

 differences are thus distinguished from those which depend upon the 

 manner in which the molecules are combined to form sensible masses. 

 The latter do not cause an increase in the number of variables in the 

 fundamental equation ; but they may be the cause of different values 

 of which the function is sometimes capable for one set of values of 

 the independent variables, as, for example, when we have several 

 different values of f for the same values of t, p, m v m 2 , ... m n , one 

 perhaps being for a gaseous body, one for a liquid, one for an amor- 

 phous solid, and others for different kinds of crystals, and all being 

 invariable for constant values of the above mentioned independent 

 variables. 



But it must be observed that when the differences in the constitu- 

 tion of the molecules are entirely determined by the quantities of 

 the different kinds of matter in a body with the two variables which 

 express its thermodynamic state, these differences will not involve 

 any increase in the number of variables in the fundamental equation. 

 For example, if we should raise the temperature of the mixture of 

 vapor of water and free hydrogen and oxygen, which we have just 

 considered, to a point at which the numbers of the different sorts of 

 molecules are entirely determined by the temperature and pressure 

 and the total quantities of hydrogen and of oxygen which are present, 

 the fundamental equation of such a mass would involve but four 

 independent variables, which might be the four quantities just 

 mentioned. The fact of a certain part of the matter present existing 

 in the form of vapor of water would, of course, be one of the facts 

 which determine the nature of the relation between f and the 

 independent variables, which is expressed by the fundamental 

 equation. 



But in the case first considered, in which the quantities of the 

 different sorts of molecules are not determined by the temperature 

 and pressure and the quantities of the different kinds of matter in the 

 body as determined by its ultimate analysis, the components of which 

 the quantities or the potentials appear in the fundamental equation 

 must be those which are determined by the proximate analysis of the 

 body, so that the variations in their quantities, with two variations 

 relating to the thermodynamic state of the body, shall include all 



