1143 



It follows from (he vjilues of T,., Ti.x, //,. and //]., [(18)— (21)] 

 that we may also write for (30) and (31) : 



{l3-y)Hu.-{i3-y,)H, ...... (32) 



and 



ii3—y) Vu — {^-y^) V, (33) 



(30) and therefore also (32) rej3resent the increase of entroj)}', 

 when at the reaction between L,,, G^, and F in all /i — // quantities 

 of vapour are formed; (31) and (33) represent the change of volume 

 at this reaction. From this it follows: when between the phases X^, 

 Gg, and F a reaction takes place, so that one quantity of vapour 

 is formed, the increase of entropy is : 



Hi..-^~-^H, (34) 



consequently the heat which is to be added : 



Wi,,-^-f^W,. ....... (35) 



and the increase of volume : 



Vi,-^P^ V, (36) 



^-y 



Let us now imagine in a P, 7^-diagram the. quadruplepoint F -\- 

 -\- F' -{- Lg-\- Ga and the binary solutioncurve of F under its own 

 vapourpressure, pr'oceeding from this point, therefore, the curve 

 F -\- Lg~\- (jt-g, its direction' in the quadruplepoint is fixed by 



Wi a,. — ^^^ W, 



T^.^ ^ (37) 



dJ 8 — y, 



iS — 1/ 

 We imagine also in this F, Y-diagram to be drawn the curve of 

 the ternary equilibrium F -\- F' -{- L -{- G proceeding from this 

 quadruplepoint F -\- P^' -\- L,, -\- G^,. Its direction is fixed in this 

 point by (25) and (26). When accidentally : 



'-■) = — (38) 



both the curves will touch one another in the quadruplepoint. 



The meaning of (38) is the following. We imagine in the con- 

 centration-diagram on the side 7iC the liquid of the quadruplepoint </. 

 Through this point </ runs a saturationcurve under its own vapour- 

 pressure and a boilingjwintcurve of F. The meaning of (38) is that 

 the point of maximum or minimum pressure or temperature falls 

 exactly in (/. 



