( 179 )! 

 If we bear in mind that u'sf . vi(j^ toitj . Vs/-, and that 



{.Vs X,,) Vlg y>{Xl— Xg) Vsf 



we come to the conclusion that : 



T—^ = pos. 

 dT 



If we now proceed to greater vahies of ,r, the situation of tlie 

 two PT-hnes changes in this way that the points of intersection on 

 the liquid and the vapour branch of the border line shift to higher 

 temperature and higher pressure, at least when we are on the 

 ascending part of the three-phase region, whereas the said points move 

 to lower pressure at higher temperature, when the PT^-section passes 

 through the descending part of the three-phase region. 



If the three-phase region ap[)roaches the plaitpoint curve till it 

 finally meets it, this means for the (P J').r-sections this that the second 

 point of intersection changes its place in such a way that it finally 

 coincides with the critical point K. The vapour coexisting with the 

 liquid phase and the solid substance has then become a critical 

 phase or in other words the concentration corresponding with this 

 section is that of a critical end-point. 



If we now suppose that the concentration approaches that of the 

 critical end-point, we shall have to take the fact into account that 

 the locus for i?.<; =: enters the stable region so that for a certain 

 concentration y.,/ is equal to zero exactly on the \apoui- branch 

 of the connodal line. 



Then the line for solid-tluid just possesses a vertical tangent in 

 the second point of intersection, while this is not yet the case for 

 the vapour-branch of the border-line liquid-vapour. 



At this moment the first term of the numerator and the last of 

 the denominator becomes zero, but as the sign was already before- 

 hand determined by the other terms, this does not bring about any 



dXq 



change in the sign of T — '- , which remains positive accordingly. 



dT 



If we advance still further in the direction of the concentration 



of the critical end-point, ^;.,ƒ is already positive^) in the vapour point 



G, as Fig. 3 indicates, and so we get the following value: 



- + - - 



«7(7 Vsf «V . Vlrj 



{Xs—X.j) Vl(j {X I Xr,) Us/- 



+ - + ■ -f 



(5) 



V Fig. 3 points to a double retrograde phenomenon, whicli has really been 

 observed for the system ether -anthraquinone. 



