( 4S8 



with the liquid mixtures, foi- wliicli the hue (Ip represent-s the 

 molecular volumes. 



The point b indicates the mol. vol. of the vapour saturated with 

 B and e the mol. vol. of the liquid saturated with B. aJxid is the 

 region of the phase-complexes L -\- G\ the nodal lines drawn in it 

 connect coexisting [)liases. 



The mol. vols, of the vapoui-s coexisting with solid B lie on the 

 curve be, and the triangle bcf is the region for the phase-complexes 

 SB-]r G. 



The coexisting phases lie in this case on lines traced from ƒ to 

 the curve be. The triangle bfe is the three-phase-triangle and there- 

 fore the region for Sb -\- L -\- G. 



The line eh, which divides the space under def into two parts, 

 represents the mol. vols, of the liquids coexisting with solid B. For 

 smaller volumes this line runs to the left, because in normal cases 

 the solubilitj of B in A diminishes with decrease of volume. 



The quadrangle efhl is the region of the phase-complexes Sn + />, 

 the coexisting phases are indicated by the small lines drawn in the 

 figure. Inside delui we have only one phase, viz. liquid, and above 

 ahe only gas. 



The lines eb and eJi are two portions of a continuous curve with 

 an intermediate ])ortion, which will have two vertical tangents in 

 normal cases. It is easy to prove this with the aid of the theory 

 of VAN DEK Waals, and this can be done in a way analogous to 

 that, in which van dkk Waals *) has proved the existence of two 

 vertical tangents to the p.i'-cwvye. for solid-liijuid. 



We start then from the dilferential ecpiatitm of /' when ,r and 7 

 vary. (Cout., II i)ag. J 04). 



Let us denote the concejitration and the mol. vol. of the solid 

 phase by Xs and r., aiul that of the coexisting gas phase and liquid 

 phase by Xf and Vf, the equation is theji : 



{V-Vf) 





d.i 



i'Vs-iVf) 





7' 



ilT—i). 



If T is kept constant, the last term of the first member becomes 

 zero and we get after an iininq)ortant transposition : 





or 



)Vf' 



(»\ -»;/)(•'■.-.''/) 



Wj 



Ó., 



'\rJ vT J 



Ovf.OXf o.cf' 



Ov .(iiCf f'-'Y _ 



dx 



<IXf. 



^) loc. cit. 



