753 



point F [curve F.s- fig. 1], the required so nlionpath is, therefore, i^^,. 

 If we require a solutionpalli, whose r,i curve has a liorizontal 

 tangent in F, we must, as follows from 34) put DM — BN ^ 0. 

 From this now follows : 



tgcf=- ^'' ^ -, ^- .... (37) 



From this it follows, in connection with (30) that in F the 

 solutionpath must touch the boilingpointcurve going through the point 

 F [curve Fh in fig. 1]; the wanted solutionpath is, therefore, FZ^. 



Now it follows from the previous considerations: in the P,7\lia- 

 graiTi' (fig. 2), none of the ternary solutionpaths touches the meltingline 

 Fd in F\ the solutionpath, touching in F in the concentration- 

 diagram (fig. 1) the saturationcurve under its own vapour-pressure 

 going through F, has in the P, 7'diagram a vertical tangent in F\ 

 the .solutionpath, in the concentrationdiagram touching the boiling- 

 pointcurve going through F, has a horizontal tangent in F in the 

 P,T diagram. 



It is evident that the above-mentioned rules apply quite generally 

 no matter whether the. relations of fig. 5 (XI) or 6 (XI) occur or 

 the curves in F are concave or convex towards H. 



In fig. 1 Fl represents the liquidcurve of a region LG, now we 



imagine a solutionpath, touching curve Fl in F. The direction of 



dP 

 this solutionpath is, therefore, fixed by (29). In order to find — 



in the point F of this path, we must, therefore, substitute the second 

 term of (29) in (35) for tgi^. We then find an infinitely great value 

 for (35). From (34) now follows : 



.P B ^.-^+(^-..)J 



-T—c- —é ^''^ 



The latter part of (38) indicates the direction of the PjP-curve 

 of the evaporationline of the liquid F. This line is traced, when 

 we melt the substance F and when we regulate after that the 

 temperature and the pressure in such a way that the liquid remains 

 in equilibrium with an infinitely small quantity of vapour. Therefore 

 the liquid retains the composition F during tiiis. This curve is 

 represented in fig. 3 (III) by Fe, the pressure and the temperalure 

 increase from F along this curve. 



Consequently we find : the solutioiipath, touching in F in the 



