( 452 ) 



component promotes tlioieforc in the long rnn tlio relations of case 

 4, large volume of the molecules of the admixture promotes those 

 of case 1. 



Jl. We niay conclude this descriptive part with mentioning some 

 formulae which we have obtained in the course of our investigation, 

 and which will be deriAed in the second part. We do not, however, 

 give them as new, as they must essentially agree with similar 

 equations obtained by Keksom^) and Vkrschaffelt^), if the simplifying 

 hypotheses are introduced on which the original equation of the 

 i|7-surface, used by us, rests. Nor does the way in which they are 

 derived, in which the method of the systematic development into 

 series is followed, differ considerably fi-om that of Vkkschaffklt. 



In these formulae we have i-estricted the nund)cr of notations as 

 much as possible. They only hold at approximation in the neigh- 

 bourhood of point K and of the critical temperature Ti- of the 

 principal component. 



We shall first give expressions for the radii of curvature /^'.,/;. and 

 R'conn. of the projections on the (r, ,7')-surface of the spinodal and 

 connodal cui-ves in the plaitpoint ; from which appears that the radius 

 of curvature of the coujiodal curve in the neighbourhood of the point 

 K is at first approximation three times as great as that of the spinodal. 



7^V = 2^^M(2r'-3x')'-8(y'-x')] (10) 



li'coun. = 2 ^i' [(2y'-3xr-8(r'- x')]=37?V . . (11) 



These radii of curvature are here considered as being positive 

 when both curves turn their convex sides to the r-axis as in the 

 cases 1 — 4 of fig. 1 and negative in the cases 5 — 7. 



We may shortly point out here that the corresponding radii of 

 curvature on the i|?-surfacc itself, on account of the strong inclination 

 of the tangential plane in the neighbourhood of the t'-axis, are quite 

 different and much smaller, though the relation 1 : 3, of course 



^) W. H. Keesom. '"Contiibulions to the knowledge of van der VVaals's i-surface. 

 V. The dependence of the plaitpoint constants on the composition in binary mixtures 

 Avith small proportions of one of the components". Proc. Royal Acad. IV. p. 203 — 307. 

 Leiden, Comm. pliys. Lab. N". 75. 



2) J. E. Verschaffelt. '■Contributions to tlie knowledge of van der Waals, -i-surface. 

 VIL The equation of state and tlie r'-surface in tiie immediate neighbourbood of 

 the critical state for binary mixtures with a small proportion of one of the com- 

 ponents". Proc. Royal Acad. V, p. 321—350, Leiden, Comm. Pbys. Lab. N". 81. 



