SURFACES OF DISCONTINUITY 625 



Of course this test is not conclusive on the matter; it gives 

 strong presumptive evidence that the system is not stable, but 

 as it is not absolutely necessary for stability the matter has 

 to be cjinched by the necessary test which is actually applied in 

 the text. This goes beyond the purely mechanical considera- 

 tions, and uses the fact that p', p" and a do not change if there 

 is a large enough external mass to draw on to maintain con- 

 stancy of composition in the phases. Hence if p' — p" = 2cr/r 

 then p' — p" > 2(r/r' if r' > r, and so the internal sphere ex- 

 pands encroaching on the outer phase ; whereas p' — p" < 2a I r' 

 ii r' < r and the internal sphere gradually disappears as the 

 outer phase encroaches on it. 



The treatment of stability on pages 285-287 will now be 

 easily followed. Certain obvious generalizations to be intro- 

 duced when gravity is taken into account are given there, the 

 result in [625] being, for instance, a wider statement of the result 

 [549] on page 252. 



XV. The Formation of a Dififerent Phase within a Homogeneous 

 Fluid or between Two Homogeneous Fluids 



4-6. A Study of the Conditions in a Surface of Discontinuity 

 Somewhat Qualifies an Earlier Conclusion of Gibbs Con- 

 cerning the Stable Coexistence of Different Phases 



The possibility of the stable coexistence of different phases has 

 been treated earlier in Gibbs' treatise without reference to the 

 special nature of the surfaces of discontinuity separating them. 

 (See pages 100-115 of Gibbs.) There it is shown that if the 

 pressure of a fluid is greater than that of any other phase of 

 its independently variable components which has the same tem- 

 perature and potentials, the fluid is stable with respect to the 

 formation of any other phase of these components; but if the 

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

 practically unstable. ''The study of surfaces of discontinuity 

 throws considerable light upon the subject of the stability of 

 such homogeneous fluid masses as have a less pressure than 

 others formed of the same components . . . and having the same 

 temperature and the same potentials. ..." Suppose for in- 



