( 195 ) 



pliase has got quite detached fVoiii the curve for the equilibria inter 

 se of the fluid phases. 



In the two previous communications on this subject 1. c. I discussed 



the values of — and iCgf, and I reter to them for more particulars 

 d.v^pT 



on the course of the (T,.i%-cui'ves. 



I will only discuss here one more particular point occurring in 

 these curves for the case that the two surfaces of equilibrium, viz. 

 that for a solid phase with a fluid phase and that for the lluid 

 equilibria inter se, get detached at a value of T and j) below that 

 of the plaitpoints. 



The figures 4, 5, 6 and 7 refer to this. In this case the two intersections 

 of the curve of equilibrium between the solid and the fluid phase with 

 the region of the fluid phases will meet at a certain pressure in a point 

 of the spinodal curve on the liquid side, and then concur to one 

 single curve. In this case the meeting point becomes a double point, 

 and at still higher values of j) ^ P'^^i't is detached, as it is drawn in 

 fig. 6, and at still higher value of p it has contracted to a single 

 point lying on the spinodal curve on the vapour side. 



It has further been assumed in these diagrams that the two 

 branches of the spinodal curve, also if we have to do wi(li a (^;,.i', 7')- 

 surface, lie inside the surface. At high temperatures and in the neigh- 

 bourhood of a plaitpoint this is, of course, the case. At lower tem- 

 peratures, however, the branch of the spinodal curve, which lies on 

 the liquid side in a (z',,r,7')-surface, moves to the vapour side in a 

 (p,^, J')-surface, and gets even far outside the surface. In the same 

 way the branch of the spinodal cur\'e, which lies on the vapour side 

 in a (v,x,T)-iigure, moves to the liquid side in a (^;,,r,7')-surface, 

 and at low temperatures it has even got outside. 



This is the consequence of the fact, that the value of x and T 

 determines a phase indubitabl}^ only when moreover the value of v 

 is given. If the value of p is given, then three different phases may 

 be indicated by tliis value. I shall, however, not enter more closely 

 into the treatment of the complications which are the consecpence 

 of this, here. I shall only just mention that the point where the hidden 

 equilibria disappear in fig. 7, can lie in quite another place than is 

 the case in fig. 7. 



