SURFACES OF DISCONTINUITY 629 



and since 



r(p' - v") = 2cr, 



and 



47rr^ 

 s = 47rr2, v' = -y-, 



it follows easily that 



W{t, m) = \ Sa(t, m) = hv'lp'it, m) - P"a, m)}, 



and so 



3 W(t, m) 



^ p W{t, m) T 



1_ 47r(r(f, m) J 



[556] 



The reader can now follow the course of the reasoning on 

 pages 256-257. If, for given values of temperature and poten- 

 tials, there are two phases possible with different pressures such 

 that equilibrium is possible with an inner /iowogre/ieows sphere of 

 the higher pressure phase, an exterior phase of lower pressure 

 and a surface of discontinuity, we see that since r in [556] is then 

 a real positive quantity and p' — p" is positive, W{t, n) 

 is positive for these values of t, mi, M2, • • • In other words, this 

 system has actually greater energy than the system made up 

 of the lower pressure phase alone, and so there would be no 

 tendency for the latter system to transform naturally into the 

 first. If however, by any external agency, the spherical mass 

 of this size and constitution were formed, then it would be 

 unstable, as we have seen, at least if the external mass is 

 indefinitely extended, which means in practice that if any 

 disturbance caused a small increase in the size of the sphere, it 

 would tend to increase still further up to a limit set by the 

 extent of the exterior phase. Now if, by alteration of the tem- 

 perature and potentials of the system, we find values ^o, Mio, 

 JL120, ... for which 



p'(to, juo) = p"(fo, Mo), 



