( 642 ) 



1 — x v 



holds, or for the limit, where- = 1. 



1—xi 



x f f \ dT k 1 db 

 log.— = [ï-—l) -H (2) 



x v \m ) T k dx b dx 



It is clear that everything will depend on the first term here, 

 because the second would not amount to more than — 1 in the 

 utmost case, i.e. when the b of the other component would be zero. 

 Moreover it might even be possible that the second term was positive, 

 it would hence decrease the value of the second member. 



The greatest difficulty for our calculation lies now in our igno- 

 rance of with the variability of 1\ with ,x, or more strictly in 

 this that for this variability not one fixed rule is to be given, because 

 in every special case it will depend on the special properties of the 

 mixture in question, viz. on the quantity a 19 , a quantity which does 

 not admit of being expressed *) in the characteristic quantities of the 

 components, at least for the present. Tt is, therefore, certainly not 

 permissible to try and derive results for all kinds of systems. But 

 it is only our purpose to determine the course of T k for those cases, 

 in which the components differ exceedingly much in volatility, and 

 for those cases it is perhaps not too inaccurate a supposition to assume 

 for the present that the line which represents T k as function of x, 

 does not deviate too much from a straight one. 2 ) On this supposi- 



T h —T k . 1 dT k f 



tion then we may write — — for —-7—. As now — = 14, as 



l kx Ik dx m 



Tki — T k 

 we already supposed, must not descend considerably below 



1 ) The equation of Galitzine-Berthelot a li = a l a i , which I rejected as general 

 rule already on a former occasion on account of the properties of the mixture 

 ether-choroform (These Proc. IV, p. 159), can certainly not he accepted as such. 

 Not only is it easy to mention other examples which are incompatible with this 

 rule (see e.g. Quint, Thesis for the doctorate p. 44 : Gerrits, Thesis for the 

 doctorate, p. 68) ; but besides, — and perhaps this must be considered as a still more 

 serious objection — by assuming this equation we wilfully break up the unity of 

 the isopiestic figure (v. d. Waals, Proc. of this meeting p. 627) by pronouncing its 

 middle region on the left of the asymptote to be impossible, whereas the left and right 

 regions are considered as real. For if a 12 = Va^a^ it is never possible that da/dx = 

 for whatever system ; and this takes exactly place in the middle region. 1 had 

 overlooked this in the paper mentioned; Prof, van der Waals has since 

 drawn my attention to it. The already mentioned system of Quint gives an 



da 



example of the occurrence of 'this case— =0; a 12 is there smaller than even the 



smallest of the two a's. 



2 ) Cf. van der Waals, These Proc. VIII, p. 272. 



