162 J. W. G-ibhs — EquUibriam of Heterogeneous Substances. 



ties 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 156-159) would in all eases 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 gen- 

 eral test as before, except that the expression (133) is to be applied 

 only to phases which difier 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 com- 

 ponents of the fluid, and the constants M^, M^., 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 infi- 

 nitely 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 remaining case, in which the phase can be 

 varied without altering the value of (133) can hardly be expected to 

 occur. The phase concerned woiild in such a case have coexistent 

 adjacent phases. It will be sufficient to discuss the condition of sta- 

 bility (in respect to continuous changes) without coexistent adjacent 

 phases. 



This condition, which for brevity's sake we Avill call the condition 

 of stability, may be written in the form 



f " _ t' rf -^p'v" - fA^' m , " . . . - /V ni^' > 0, (142) 



in which the quantities relating to the phase of which the stability is 

 in question are distinguished by single accents, and those relating to 



