252 EQUILIBRIUM OF HETEROGENEOUS SUBSTANCES. 



infinitesimals of the higher orders. By substitution of these values, 

 the condition of stability will reduce to the form 



or 2(p Av) - 2 (<r As) < 0. (549) 



That is, the sum of the products of the volumes of the masses by 

 their pressures, diminished by the sum of the products of the areas of 

 the surfaces of discontinuity by their tensions, must be a maximum. 

 This is a purely geometrical condition, since the pressures and tensions 

 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 

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

 and potentials. This may be done without introducing any new 

 movable surfaces of discontinuity. 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 Homogeneous Fluid. 



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 

 (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 

 magnitude. That it should not be applied to such cases without 

 limitation is evident from the consideration that we have neglected 

 the term ^(O l C^)8(c l c^) in equation (494) on account of the 

 magnitude of the radii of curvature compared with the thickness 

 of the non-homogeneous film. (See page 228.) When, however, only 

 spherical masses are considered, this term will always disappear, since 

 C 1 and 2 will necessarily be equal. 



*See page 104, where the term stable is used (as indicated on page 103) in a less 

 strict sense than in the discussion which here follows. 



