198 J. W. Gibhs — Equilibrium of Heterogeneous Substances. 



these may be more complicated. Other cases are explained by mole- 

 cules which differ in the quantity of matter which they contain, but 

 not in the kind of matter, nor in the proportion of the different kinds. 

 In still other cases, there appear to be different sorts of molecules, 

 which differ neither in the kind nor in the quantity of matter which 

 they contain, but only in the manner in which they are constituted. 

 What is essential in the cases referred to is that a certain number of 

 some sort or sorts of molecules shall be equivalent to a certain number 

 of some other sort or sorts in respect to the kinds and quantities of 

 matter which they collectively contain, and yet the former shall never 

 be transformed into the latter within the body considered, nor the 

 latter into the former, however the proportion of the numbers of the 

 different sorts of molecules may be varied, or the composition of the 

 body in other respects, or its thermodynamic state as represented by 

 temperature and pressure or any other two suitable variables, pro- 

 vided, it may be, that these variations do not exceed certain limits. 

 Thus, in the 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 con- 

 stitution 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 pressui-e 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 t, for the same values of ^, jo, m^, ni^, . . . m„, 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 



