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Physics. — "Contribution to the theory of binary mixtures" By 

 Prof. J. D. van der Waals. 



The theory of binary mixtures, as developed in the "Theorie 

 moleculaire", has given rise to numerous experimental and theoretical 



investigations, which have undoubtedly greatly contributed to obtain 

 a clearer insight into the phenomena which present themselves for 

 the mixtures. Still, many questions have remained unanswered, and 

 among them very important ones. Among these still unanswered 

 questions I count that bearing on a classification of the different 

 groups of ty-surfaces. For some binary systems the plait of the 

 ty-surface has a simple shape. For others it is complex, or there 

 exists a second plait. And nobody has as yet succeeded in pointing- 

 out the cause for those different forms, not even in bringing them in 

 connection with other properties of the special groups of mixtures. 

 It is true that in theory the equation of the spinodal curve which 

 bounds the plait, has been given, and when this is known with perfect 

 accuracy, it must be possible to analysis to make the classification. 

 But the equation appears to be very complicated, and it is, especially 

 for small volumes, only correct by approximation, on account of 

 our imperfect knowledge of the equation of state. Led by this consi- 

 deration I have tried to find a method of treatment of the theory 

 which is easier to follow than the analytical one, and which, as the 

 result proved, enables us to point out a cause for the different shape 

 of the plaits, and which in general throws new light upon other 

 already more or less known phenomena. 



Theory teaches that for coexisting phases at given temperature 



fdip\ fdtp\ fdip\ fdtu\ 



three quantities viz. — I — ) , — J and if' — v ( — — x\ — 



\dvJxT \d'Vj rT \dvJ xT \dxJ v T 



must be equal. The first of these quantities is the pressure, which 

 we represent by p; the second is the difference of the molecular 

 potentials or M 2 n 2 — M a (i 1 , which we shall by analogy represent 

 by q. The third of these quantities is the molecular potential of the 

 first component, which we shall represent by M^. Now the points 

 for equal value of p lie on a curve which is continuously trans- 

 formed with change of the value of /;, so that, if we think all the 

 p-curves to be drawn, the whole v,#-diagram is taken up by them. 

 In the same way the points for given value of q lie on a curve 

 which continuously changes its shape with change of the value of (/; 

 and again when all the ^-lines have been drawn, the whole /,./- 

 diagram is taken up. Both the p-lines and the ^-lines have the 

 property, that through a given point only one p-line, or only one 



