EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 105 



of any other phase of the same components which has the same 

 temperature and the same values of the potentials for its actual 

 components, the fluid is stable without coexistent phases; if its 

 pressure is not as great as that of some other such phase, it will 

 be unstable; if its pressure is as great as that of any other such 

 phase, but not greater than that of every other, the fluid will 

 certainly not be unstable, and in all probability it will be stable 

 (when enclosed in a rigid envelop which is impermeable to heat 

 and to all kinds of matter), but it will be one of a set of coexistent 

 phases of which the others are the phases which have the same 

 pressure. 



The considerations of the last two pages, by which the tests relating 

 to the stability of a fluid are simplified, apply to such bodies as 

 actually exist. But if we should form arbitrarily any equation as a 

 fundamental equation, and ask whether a fluid of which the pro- 

 perties were given by that equation would be stable, the tests of 

 stability last given would be insufficient, as some of our assumptions 

 might not be fulfilled by the equation. The test, however, as first 

 given (pages 100-102) would in all cases be sufficient. 



Stability in respect to Continuous Changes of Phase. 



In considering the changes which may take place in any mass, we 

 have already had occasion to distinguish between infinitesimal changes 

 in existing phases, and the formation of entirely new phases. A 

 phase of a fluid may be stable in regard to the former kind of change, 

 and unstable in regard to the latter. In this case it may be capable 

 of continued existence in virtue of properties which prevent the com- 

 mencement of discontinuous changes. But a phase which is unstable 

 in regard to continuous changes is evidently incapable of permanent 

 existence on a large scale except in consequence of passive resistances 

 to change. We will now consider the conditions of stability in respect 

 to continuous changes of phase, or, as it may also be called, stability 

 in respect to adjacent phases. We may use the same general test as 

 before, except that the expression (133) is to be applied only to phases 

 which differ infinitely little from the phase of which the stability is 

 in question. In this case the component substances to be considered 

 will be limited to the independently variable components of the fluid, 

 and the constants M v M z , etc., must have the values of the potentials 

 for these components in the given fluid. The constants in (133) are 

 thus entirely determined and the value of the expression for the 

 given phase is necessarily zero. If for any infinitely small variation 

 of the phase the value of (133) can become negative, the fluid will 

 be unstable ; but if for every infinitely small variation of the phase 

 the value of (133) becomes positive, the fluid will be stable. The only 



