( 1S7 ) 



reacheil, at which p — p' has descended again to 0, reversing its 

 sign when the volume is still more diminished. The same holds 

 true for Ap ^). 



In order to show this, the approximative value of equation (5) 

 does not suffice. A more accurate value of Ap is: 



A on ^(; /I I ^n /^ ("-/) (1 + «0 «.W 



A;, == 2ir ( 1 — .r) &, „ ( 1 -{- C7 j:) ( 1 — Z.^) 



r ("-M L^-h (1-^)] i«-f>:^^) «' 



if we represent by ƒ the quantity 



[hx — h(l—x)y 

 (b, + b,) . (1 -.r) + "-^ -^ ^ • 



If we calculate /? — p', we find 



{]+a)(l— &)&(! + «0 « 



P — P=- 



V {v — b) 



If a > (I + a) (1 — '')^'(1 + «0, ;' — ;>' is negative, when the 

 volume is large, but positive when 



«< 



l--(l+«)(l-i)(l-«0 



Z\^ has, it is true, a more intricate form than p — p\ But this 

 is more in appearance than in reality. 



If «-,„ > Z-ij (1 + «x) (I — M (1 +«<), Ap is negative, when the 

 volume is large, but positive when v does not differ much from b^. 

 It has in reality no significance that the sign would be again re- 

 versed for other values of v also, e.g. between bx and i, (I — ip) , 

 because in a volume smaller than i.t the mixture could not take place. 



A series of values for Ap, which Mr. Kuenen gives from his 

 observations on mixtures of C0„ and CH3 CI and which we repro- 

 duce here, may be used to test the properties of Ap pointed out here. 



') These results have already been deduced by Margules from the observations 

 of Andrews. Wien Sitz. Ber. 1889, Band XCVIII, Seite 885. See also B. Gautzine. 

 Wied. Ann. Band XLI. 



