ABSTRACT BY THE AUTHOR 367 



8 8 S 



where ij a , T lt F 2 , etc. are written for , , , etc., and denote the 



888 



superficial densities of entropy and of the various substances. We 

 may regard a- as a function of t, fi lt fjL 2 , etc., from which if known 

 jy g , I\, F 2 , etc. may be determined in terms of the same variables. 

 An equation between a; t, fJ. lt fa, etc. may therefore be called & funda- 

 mental equation for the surface of discontinuity. The same may be 

 said of an equation between e 8 , q 8 , s, m 8 , raf., etc. 



It is necessary for the stability of a surface of discontinuity that 

 its tension shall be as small as that of any other surface which can 

 exist between the same homogeneous masses with the same tempera- 

 ture and potentials. Besides this condition, which relates to the nature 

 of the surface of discontinuity, there are other conditions of stability, 

 which relate to the possible motion of such surfaces. One of these is 

 that the tension shall be positive. The others are of a less simple 

 nature, depending upon the extent and form of the surface of dis- 

 continuity, and in general upon the whole system of which it is a 

 part. The most simple case of a system with a surface of discon- 

 tinuity is that of two coexistent phases separated by a spherical 

 surface, the outer mass being of indefinite extent. When the interior 

 mass and the surface of discontinuity are formed entirely of sub- 

 stances which are components of the surrounding mass, the equilibrium 

 is always unstable; in other cases, the equilibrium may be stable. 

 Thus, the equilibrium of a drop of water in an atmosphere of vapor 

 is unstable, but may be made stable by the addition of a little salt. 

 The analytical conditions which determine the stability or instability 

 of the system are easily found, when the temperature and potentials 

 of the system are regarded as known, as well as the fundamental 

 equations for the interior mass and the surface of discontinuity. 



The study of surfaces of discontinuity throws considerable light 

 upon the subject of the stability of such phases of fluids as have a 

 less pressure than other phases of the same components with the same 

 temperature and potentials. Let the pressure of the phase of which 

 the stability is in question be denoted by p', and that of the other 

 phase of the same temperature and potentials by p". A spherical 

 mass of the second phase and of a radius determined by the equation 



2<r = Q9"-/)r, (27) 



would be in equilibrium with a surrounding mass of the first phase. 

 This equilibrium, as we have just seen, is unstable, when the surround- 

 ing mass is indefinitely extended. A spherical mass a little larger 

 would tend to increase indefinitely. The work required to form such 

 a spherical mass, by a reversible process, in the interior of an infinite 

 mass of the other phase, is given by the equation 



W = <rs-(p"-p')v". (28) 



