96 



BUTLER 



ART. D 



In this case, Gibbs therefore writes the conditions of equilib- 

 rium (70) in the following way: 



" Ml = Ml 



for all parts of which Si is an actual component, and 



Ml ^ Ml 



for all parts of which Si is a possible (but not actual) 

 component, 



M2 = M2 !► (72) [22] 



for all parts of which S2 is an actual component, and 



M2 ^ M2 



for all parts of which >S'2 is a possible (but not actual) 

 component, 



etc.. 



Ml, M2, etc., denoting constants, the value of which is only 

 determined by these equations." 



When a component is neither an actual nor a possible com- 

 ponent of some part of the system, the terms /idm and 8m, 

 which refer to this component in that part of the system of which 

 it is neither an actual nor a possible component are absent from 

 (64), and from the equations of condition (67). The condi- 

 tions of equilibrium are otherwise unaffected. "Whenever, 

 therefore, each of the different homogeneous parts of the given 

 mass may be regarded as composed of some or of all of the same 

 set of substances, no one of which can be formed out of the 

 others, the condition which (with equality of temperature and 

 pressure) is necessary and sufficient for equilibrium between the 

 different parts of the given mass may be expressed as follows : — 



The potential for each of the component substances must have a 

 constant value in all parts of the given mass of which that substance 

 is an actual component, and have a value not less than this in all 

 parts of which it is a possible component.'' 



11. Conditions of Equilibrium When Some Components Can 



