282 MOREY ART. G 



Substituting in the equation referring to the Uquid phase, we get 



[v'- — v'~\ 



Similarly, the value of d^y in the stable direction of the curve, 

 is given by 



r v^-v'l 



dp. 



Now since, by hypothesis, we have proceeded in the direction of 

 the stable portion of the curve, ice + Hquid, 



(Zm" > dyiK 

 Hence 



which reduces to 



dp [{V - v^)W - V') - (v^ - v')(v'' - v^)] 



7}^ — t]' 



>0, 



one form of the condition for stability of the equilibrium solid + 

 liquid. 



When we consider the actual magnitude of the various terms 

 in this equation we see that the coefficient of dp in the numer- 

 ator is necessarily positive. All the individual terms {v" — v^), 

 W ~ v'), iff — V^) a-iid (^' ~ V') are of necessity positive except 

 the last one, the volume change of melting of ice, which is 

 negative. But the last term is affected by the negative sign, 

 hence the term as a whole is positive, and the coefficient of 

 dp has a positive sign.* The equilibrium in question will then 

 be stable as the pressure is increased from the invariant point 



* The case that (v^ — v') is negative is, of course, exceptional. But 

 in any case, the coefficient of dp is positive, since the two entropy 

 changes are of the same order of magnitude, while the volume change on 

 evaporation is many times larger than the volume change on melting. 



