1142 



mation and Via- 'lie increase of volume at tlio (congruent or in- 

 congruent) sublimation of F-{-F\ II^i, and Ti , are both positive. 

 Therefore, the equilibrium F -]- F' -\- L ^ G proceeds from the 

 quadruplepoint immediately towards lower temperatures and pressures. 

 Let us imagine a 7^,r-diagram with the qnadruplepoint F -\- F' -\- 

 _[_ y^^ -j_ (^' ; Four triplecurves proceed from this point viz. the 

 (congruent or incongruent) binary meltingcurve F -\- F' -{- L^, the 

 (congruent or incongruent) binary sublimationcurve F-\-F'-\-G^ 

 and further the two binary solutioiicurves under their own vaponr- 

 pressure, viz. the curves F -{- L, + G„ and F' + L, + G,. When 

 we draw in this 7-*, T-diagram also the curve for the ternary 

 equilibrium F + F' + /. + 6r, this touches, according to (27) the 

 binary sublimationcurve 7^' + 7^^' + 6^o i" tl»e quadruplepoint. 



An example of this case will be found when we add a third 

 substance, which is not volatile, to the e(piilibrium -. ICl -\- ICl^-\- 

 + Lo + G, occurring at. T, = 22,7° and under 7^o = 42 m.m., in 

 which G^ contains the two components 7, and CI.,. The same shall 

 also be the case when we add a substance, which is not volatile, 

 e.g. NaCl or NaNO, to the equilibrium Na^SO, . 10H,0-\-Na,SO,^ 

 _|_/,^_|_C;^ wherein G^ consists only of water- vapour. 



Let us now consider the case that ( — ) is very large ; as limit- 



case we shall assume ( - j infinitely large. From (25) iind (26) then 

 follows : 



T— =— ^ (28) 



dT V, 



As W^ represents the heat, required for the congruent or incon- 

 gAient melting of F -\- F' , and Vx the increase of volume at this 

 reaction, Wjc is positive, while I" may be as well positive as 

 negative. Imagining in a P,7'-diagram the quadruplepoint 7''-l-7^' + 

 -{- L^-\-G, and the binary (congruent or incongruent) meltingcurve 

 p j^ P' J^ L^, proceeding from this point the curve of the ternary 

 equilibrium 7^ -f 7^' + 7v -j- 6^ will touch this binary meltingcurve 

 in the quadruplepoint. 



In the quadruplepoint F ^ F' ^ L,^ G, always between the 

 phases L, , 6^„ and F the reaction : 



{y, -^) quant, of 7.„ ^- {^—y) quant, of G, + {y-y,) quant, of F = (29) 



may occur. The changes of entropy and of volume at this reaction are: 



{y-?)H-\-{^-y)H,^-{y-y,)n (30) 



{y-?)V+{^-y)V,+{:y-y,)v (31) 



