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Physics. — u Contributions to the knowledge of fht' ty-surfaee of 

 van der Waals. XV. The case thai one component is a gas 

 without cohesion with molecules that have extension. Limited 

 miscïbüity of tiro gases." By Prof. H. Kamerlingh ONNEsand 

 Dr. W. H. Keesom. Supplement N°. 15 to the communications 

 from the Physical Laboratory at Leiden. 



(Communicated in the meeting of Februari 23, 1907). 



§ 1. Introduction. In the Proceedings of Dec. '06, p. 502. 

 (Comm. N°. 96è) it was mentioned that the investigation of the 

 ^//-surface of binary mixtures in which the molecules of one compo- 

 nent have extension but do not exert any attraction, would be taken 

 in hand as a simpler case for a comparison with what the observations 

 yield concerning mixtures of He, whose molecules are almost without 

 cohesion. Before long we hope to give a fuller discussion of such a 

 «//-surface x ). In the meantime some results have already been obtained 

 in this investigation, which we shall give here. 



Thus it has appeared, that at suitable temperatures, at least if the 

 suppositions concerning the applicability of van der Waals' equation 

 of state with a and h not depending on v and T for constant x, 

 mentioned in § 2 hold for these mixtures, 2 ) tmn different phases 

 mui/ be in equilibrium which must be both considered as gasphases. 

 Then the two substances which are the components of these mixtures, 

 are not miscible in all proportions even in tin' gas state. And if 

 certain conditions are fulfilled this may continue to be the case when 

 the one component is not perfectly without cohesion, but possesses 

 still some degree of cohesion, which, however, must be very slight. 



From the considerations of van der Waals, Contin. II p. 41 et sqq. 

 and p. 104, follows that the mixing of two substances in the fluid 

 state is brought about in consequence of the molecular motion 

 depending on the temperature T, and promoted by the mutual 

 attraction of the molecules of the two components determined by 

 the quantity a ls , whereas the attractions of the molecules of each 

 component inter se determined by r/ n and a^_, oppose the mixing. 



i) Van Laar, These Proc. May "03. p. 38, cf. p. 39 footnote i, treated the 

 projection of the plaitpoint curve on the v, x-plane for such a mixture, without, 

 however, further investigating the shape of the spinodal curve and of the plait. 



2) The possibility of the occurrence of a longitudinal plait at temperatures above 

 the critical ones of both components was supposed by van der Waals in his 

 treatment of the influence of the longitudinal plait on critical phenomena. (Zittings- 

 versl. Kon. Akad. v. Wetensch. Amst. Nov. 1891, p. 133'. [Added in the English 

 translation!. 



