( 388 ) 



same and the conclusions to be derived from these must hold good 

 in general. 



For the sake of clearness we Avill considei a special case, viz. 

 that in which the licjnid curve falls outside the vapour curve and 

 the contact takes place in the critical point of the former. As the 

 saturation cur\'es contract on heating, the two curves will in this 

 case separate ^vhen the temperature is raised above the critical 

 temperature ; on the other hand the liquid curve begins to intersect 

 the vapoiu' curA-e Avhen the temperature is lowered. The relative 

 position of the curves here assumed is very common: it was discovered 

 for the tirst time bv van der Lee for mixtures of phenol and water ^). 



When the liquid curve intersects the vapour-liquid curve an equili- 

 brium between a vapour phase and two liquid phases is possible, 

 but VAN DER Waals ■) has shovvn how this equilibrium mav be 

 ignored and a continuous vapour-liquid curve traced out through 

 the metastable and unstable parts of the diagram : along this curve 

 the liquid phase passes twice through the spinodal curve of the 

 two-liquid curve and at the same moments the vapour branch of 

 the curve forms cusps; the vai)our pressure considered as a function 

 of the composition of the liquid passes at the same time through a 

 maximum or minimum ; the thermodynamicxil condition in these 



points is I — I = 0, where ^ is the tiiermodynamical potential. 



In many cases the further complication arises that there is a 

 condition, where the compositions of the liquid and the vapour, 

 .I'l and .Tj, are the same and where therefore the pressure is again 

 a maximum or minimum : if this poiiit falls, as it often does, between 



the two points where —— = 0, it can onlv be a minimum and botli 

 ^ o.r- 



the other points are then maxima; the composition of the vapour 



in the three-phase equilibriuui then lies between the compositions 



of the liquids and the three-phase pressure is higher than the pressure 



of neighbouring mixtures on both sides. This is the case Avliich was 



assumed by van der Lee in drawing his diagrams for phenol and 



water, but from subsequent measurements by Schreinemakers ^) it 



appears that for these mixtures the maximum where d\ =: .v.^ lies 



outside the three-phase triangle in the v — iv diagram. 



As the temperature approaches the critical point, where the two 



1) Van der Lee, Dissertatie, Amsterdam 1898. Zeitschr. Physik. Chemie 33 p. 622. 



2) Van der Waals, Goutinuitat II, p. 18, fig. 3. 



=5) Schreinemakers, Zeitschr. Physik. Chemie, 35, p. 461. 



