HETEROGENEOUS EQUILIBRIUM 283 



when the denominator is positive; (tj' — rj') is of necessity- 

 positive, hence the equilibrium, ice + Hquid, is stable with 

 increasing pressure from the invariant point; on decreasing the 

 pressure we pass on to the metastable portion of the curve, into 

 a region where vapor is stable. 



By solving for dp in the above equations of the type of (1) [97] 

 referring to the solid and liquid phases, v/e get a similar in- 

 equality, 



Jjl _ J^,» 



>o, 



which gives the condition for stability with change in tem- 

 perature. It will be observed that the condition for tempera- 

 ture stability differs from the condition for pressure stability in 

 having dt in place of dp in the numerator, and in having 

 (v^ — V) in place of (r?' — rj*) in the denominator. Since the 

 coefficient in the numerator is unchanged, it is always positive ; 

 the equilibrium, solid -\- liquid, is stable with increasing tempera- 

 ture when the denominator is positive, and is stable with de- 

 creasing temperature when the denominator is negative. In 

 the exceptional case of H2O, this volume change is negative, 

 hence the equilibrium, ice + liquid, is stable with decreasing 

 temperature from the triple point; on increasing the temperature 

 we pass on to the metastable portion of the curve, into a region 

 in which vapor is stable. 



SI. Generalized Theorem Concerning the Order of p-t Curves 

 around an Invariant Point. The above reasoning may be 

 generalized as follows. At an invariant point, if the differentials 

 satisfy the (n + 1) equations of the type of (1) [97] for the 

 univariant equilibrium, P' + P'" -\- P^^ ... + P"+i + 

 pn+2 (jjj which phase P" is missing), we will move along the 

 p-t curve of this equilibrium. In one direction from the in- 

 variant point the missing phase P" will be stable, in the other 

 direction phase P" will be unstable. In the first case, we will 

 be on the metastable prolongation of the p-t curve, in the 

 second case, we will be on the stable portion of the p-t curve. 

 The condition that a given phase in a one-component system is 

 unstable was found to be that its chemical potential is greater 



