J. W. Gihhs — EquUibriiim of Heterogeneous Substances. 197 



Hence, if the independently variable components of any body are 

 aS„, . . . Sg, and S/,, . . . /iS'^., the quantities of the latter being very small 

 as compared with the quantities of the former, and are incapable of 

 negative values, we may express approximately the values of the 

 ])otentials for S,„ . . . /Si. by equations (subject of coui-se to the uncer- 

 tainties of the assumptions which have been made) of the form 



M,.= A,\og^'f^; (217) 



//,=A•log-^^ (218) 



V 



in which A,^, C\, . . . A^., C^. denote functions of the temperature, the 

 pressure, and the ratios of the quantities ni„, . . . rn^. 



We shall see hereafter, when we come to consider the properties of 

 gases, that these equations may be verified experimentally in a very 

 large class of cases, so that we have considerable reason for believing 

 that they express a general law in regard to the limiting values of 

 potentials.* 



ON CERTAIN POINTS KELATING TO THE MOLECULAR CONSTITUTION OF 



BODIES. 



It not unfrequently occurs that the number of proximate compo- 

 nents which it is necessary to recognize as independently variable in 

 a body exceeds the number of components which would be sufficient 

 to express its ultimate composition. Such is the case, for example, as 

 has been remarked on page 117, in regard to a mixture at ordinary 

 temperatures of vapor of water and free hydrogen and oxygen. 

 This case is explained by the existence of three sorts of molecules in 

 the gaseous mass, viz., molecules of hydrogen, of oxygen, and of 

 hydrogen and oxygen combined. In other cases, which are essentially 

 the same in principle, we suppose a greater number of different sorts 

 of molecules, which differ in composition, and the relations between 



* The reader will not fail to remark that, if we could assume the universality of this 

 law, the statement of the conditions necessary for equilibrium between different 

 masses in contact would be much simplified. For, as the potential for a substance 

 which is only & possible component (see page 117) would always have the value — oo^ 

 the case could not 6ccur that the potential for any substance should have a greater 

 vakie in a mass in which that substance is only a possible component, than in another 

 mass in which it is an actual component; and the conditions (22) and (51) might be 

 expressed with the sign of equality without exception for the case of possible 

 components. 



