34 - LOTIC\. 



Let the system be stable towards He both when x is held constant 

 and also when a* is at the equilibrium value Xi defined by 



^ = / (:r„ G) = (57) 



This means that all the curves "of constant composition " 



<p (a-, G,H)=0 } (58) 



X = constant J 



and also the curve "of equilibrium composition " 



^ (xi, G,H) = (59) 



slope from left to right downwards. 



Now consider two neighboring curves of type (58) (curves of con- 

 stant composition), which we will suppose solved for H and write 



//«=^„(6', .Ta) (60) 



Ih=^,{G,xt) (61) 



Suppose we start with the system in the state represented by the 

 point Q, in internal equilibrium and also in equilibrium with an ex- 

 ternal parameter He (see Fig. 2). 



Let X be changed at constant G, so as to increase // according to 

 (55) until X = Xb, so that the representative point strikes the second 

 curve of constant composition at R. 



Since at the start of this operation 



// = Ha= He (62) 



(63) 



therefore the system is not in equilibrium with the external pressure 

 He in the state represented by the point R, but equilibrium (for 

 X = Xb) occurs at some other point T which must lie to the right of R 

 along the curve of constant composition RT, since, whenever 



H >He 



G increases, in accordance with (56). 



Furthermore, drawing a horizontal QS, T must lie below <S, since the 

 line of equilibrium composition QT must slope from right to left 

 downwards. 



