( 831 ) 



molecules of the same size (— being always though! equal J will 



not so readily mix as those for which the size of one kind greatly 



exceeds the size of the other kind, a properly to which we might 



have concluded without calculations. But in the second place the 



d*a 

 quantity — = 2 (a l -\- a, — 2« la ) has great influence on the height of 

 da* 



d*a 



this temperature, and indeed, -in so high a degree that if — should 



da* 



t/ 2 if' 

 be = 0, the locus - - = would already have disappeared at the 

 da* 



absolute zero point. Indeed, we might have seen from the very 



d/'a 



beginning that this locus could never exist for — negative. Every- 



CLttj 



thing, on the other hand that diminishes « 13 , makes T g rise, and so 

 furthers non-mixing. In some limiting cases we may compare I lie 

 value of Tg with that of 1\, 1 st in the case that into a given sub- 

 stance we should press a gas as 2 nd component following the laws 

 of Boyle and Gay-Lussac perfectly. For such a gas we should have 

 to put b 1 and a, equal to zero, and so probably also « 12 . The value 



of x of the formula for T g is then equal to — . The a for the mixtures 



o 



d*a 



containing only one term then, and being equal to a r c*, — = 2a 2 . 



tl.r* 



The value of b x for the mixture is then equal to b a sc. On these 



suppositions MR r T g = — — , and so T 9 is equal to the critical tem- 



27 6 a 



perature of the 2 nd component. The value of 1\- for every mixture 



taken as homogeneous, is then equal to x(Tk) t . Consequently 



T 9 == 3 (7a-).. For a value of T somewhat below (7a), the locus 



d> 



= is restricted to a very narrow region on the side of the 



dv* 



<*> 

 2 nd component, while — - = still exists, and may be compared to 



a small circular figure whose centre is a point with the coordinates 

 #=Yj and v = b r The spinodal curve has then an equation which 

 may be written as follows : 



MRT 2a. 



e--)' ©' 



57 

 Proceedings Royal Acad. Amsterdam. Vol. IX. 



