34 LOTK.^^. 



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

 and also when a- is at the equilibrium value a-i defined by 



J^=f (^-1, 0) = (57) 



This means that all the curves " of constant composition " 



if {x, G, H) =0 j (58) 



X = constant j 



and also the curve " of equilibrium composition " 



cp (xi, G, II) = (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 



7/„=^a(6'. a-„) (60) 



H,==-^b{G,x,) (61) 



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

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

 ternal parameter He (see Fig. 2). 



Let x be changed at constant G, so as to increase H 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 



// = //^= //^ (62) 



and at the end 



H = Hbi 

 > 



H, \ f63) 



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 



// >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. 



