416 <■/. Wl Gihbs — Equitihrium of Heterogeneous ISuhstances. 



sions are constant. This condition is of interest, because it is always 

 sufficient for stability with reference to motion of surfaces of discon- 

 tinuity. For any system may be reduced to the kind described by 

 putting certain parts of the system in communication (by means of 

 tine tubes if necessary) with large masses of the proper temperatures 

 and potentials. This may be done without introducing any new 

 movable surfaces of discontiniiity. The condition (549) when 

 applied to the altered system is therefore the same as when applied 

 to the original system. But it is sufficient for the stability of the 

 altered system, and therefore sufficient for its stability if we diminish 

 its freedom by breaking the connection between the original system 

 and the additional parts, and therefore sufficient for the stability of 

 the original system. 



On the Possibility of the Formation of a Fluid of different Phase 

 within any Homogetieous Fluid. 



The study of surfaces of discontinuity throws considerable light 

 upon the subject of the stability of s\;ch homogeneous fluid masses 

 as have a less pressure than others formed of the same components 

 (or some of them) and having the same temperature and the same 

 potentials for their actual components.* 



In considering this subject, we must first of all inquire how far our 

 method of treating surfaces of discontinuity is applicable to cases in 

 which the radii of curvature of the surfaces are of insensible magni- 

 tude. That it should not be applied to such cases without limitation 

 is evident from the consideration that we have neglected the term 

 \(C^ — G^6{c.^ — C2) ill equation (494) on account of the magnitude 

 of the radii of curvature compared with the thickness of the non- 

 homogeneous film. (See page 390). Vv'hen, however, only spherical 

 masses are considered, this term will always disappear, since (7, and 

 C2 will necessarily be equal. 



Ao-ain, the surfaces of discontinuity have been regarded as separat- 

 ino- homogeneous masses. But we may easily conceive that a globu- 

 lar mass (surrounded by a large homogeneous mass of different 

 nature) may be so small that no part of it will be homogeneous, and 

 that even at its center the matter cannot be regarded as having any 

 phase of matter in mass. This, however, will cause no difficulty, if 

 we regard the phase of the interior mass as determined by the same 



* See page 161, where the term stable is used (as indicated on page 159) in a less 

 strict sense than in the discussion which here follows. 



