HETEROGENEOUS SUBSTANCES. 147 



tendency of the body to expand, the temperature is the intensity of its 

 tendency to part with heat ; and the potential of any component sub- 

 stance is the intensity with which it tends to expel that substance from 

 its mass. 



We may therefore distinguish these two classes of variables by 

 calling the volume the entropy, and the component masses the magni- 

 tudes, and the pressure, the temperature, and the potentials the in- 

 tensities of the system. 



The problem before us may be stated thus : Given a homogeneous 

 mass in a certain phase, will it remain in that phase, or will the whole 

 or part of it pass into some other phase ? 



The criterion of stability may be expressed thus in Professor Gibbs's 

 words " For the equilibrium of any isolated system it is necessary 

 and sufficient that in all possible variations of the state of the system 

 which do not alter its energy, the variation of its entropy shall either 

 vanish or be negative. 



" The condition may also be expressed by saying that for all possible 

 variations of the state of the system which do not alter its entropy, the 

 variation of its energy shall either vanish or be negative." 



Professor Gibbs has made a most important contribution to science 

 by giving us a mathematical expression for the stability of any given 

 phase (A) of matter with respect to any other phase (B). 



If this expression for the stability (which we may denote by the letter 

 K) is positive, the phase A will not of itself pass into the phase B, but 

 if it is negative the phase A will of itself pass into the phase B, unless 

 prevented by passive resistances. 



The stability (K) of any given phase (A) with respect to any other 

 phase (B), is expressed in the following form : 



K = e - v p + rj t m, \L, c. ;;z n ^ 



where e is the energy, v the volume, 77 the entropy, and m u m 2 , c. the 

 components corresponding to the second phase (B), while p is the 

 pressure, t the temperature, and /z 1? /u 2 , &c. the potentials corresponding 

 to the given phase (A). The intensities therefore are those belonging 

 to the given phase (A), while the magnitudes are those corresponding 

 to the other phase (B). 



We may interpret this expression for the stability by saying that it is 



