605 



Tn order to find the satiiratioiicur\e under its own vaponrpressure 

 we put in (8) and (9) (II) a = 0. We obtain : 



[.,, f (,/ _.^j),] ,/,,,. _^ |.,, _^ (,, _^^)^] (/^^ ^ ^4,^p ... (6) 



[(■'•i-.^')'' + {y—M d.v 4- [(.f,-.r> + (i/, - y)q dy = CdP^ . (7) 

 In the terminating point of this curve on the side BC (therefore 

 in the points It and n of figs. 2, 3, and 4), x = 0. We find from 

 (6) and (7): 



In order to find the boih'ngpointcurve we must substitute in (6) 

 and (7) AdF by — BdT and CdP by — DdT. We then find : 



JL r^ y^-y-iy-^(^-l^ 



RT - yd,vJ, = o {y,-m+{y~y,)n-\-{i3-y)R,' ' ^^ 



From (8) it follows that in a terminatingpoint of the saturation- 

 curve under its own vaponrpressure on one of the sides (points h 



and n of fig. 2, 3, and 4) — has a definite xalue different from zero 



dx 



so that the pressure is in the terminatingpoint neither a maximum 



nor a minimum. The same follows from (9) for the temperature in 



the terminatingpoint of a boilingpointcurve. 



In the binarj' system BC the relation between a change of P 



and T in the equilibrium F -\- L -\- G is fixed by: 



dF\ ^ {y-m + {y-y^>i + {?-y)H, 



dTj.^o {y,-^)V^{y-y,)v-\-{^^y)V/ ' ' ^ ^ 

 From (8),, (9), and (10) it now follows that: 



dP\ /dT\ _ rdP\ 



'v dxjx = V ^'^' Jx = \d 1 y 3. — 



In order to see the meaning of this we imagine a grapiiical 

 representation of P and T of the binary equilibrium F -\- L -{- G. 

 We will call that part of the P, 7^-curv^e on which the pressure 

 increases when raising the temperature, the ascending branch, the 

 part on which the pressure decreases when lowering the temperature 



dP 

 the descending branch. In the ascending branch — is positive, in 



dT 



the descending branch it is negative; from (11) it follows, that 



dP . dl' 



— and — have in the ascending branch the opposite sign and in 



d.v dx 



the descending branch the same sign. We find therefore: 



39 



Proceedings Royal Acad,. Amsterdam. Vol. XVI, 



( 



