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Physics. - "Contributions to the Jmoioledge of the ty-surface of 

 van der Waals. XIII. On the conditions for the sinking and 

 again rising of the gas phase in the liquid phase for binary 

 mixtures," by Dr. W. II. Keesom. Communication N°. 96c from 



the Physical Laboratory at Leiden. (Communicated by Prof. 

 H. Kamerlingh Onnes). 



§ I. Introduction. As has been observed in Communication N°. 96fi 

 (See the preceding paper) (cf. Comm. N°. 96^, Nov. '06, p, 459, 

 note 1) it lies to hand, to take as point of issue the ifj-surface for 

 the unity of mass of (he mixture considered, in the investigation 

 according to van der Waals' theory of binary mixtures, of the sinking 

 and subsequent rising of the gas phase in the liquid phase, i.e. the 

 barotropic phenomenon. Two coexisting phases of equal density are 

 joined on this ifj-surface by a tangent-chord whose projection on the 

 ./.', r-plane l ) is parallel to the .'-axis, li has already been observed 

 in Comm. N°. 966, that with decrease of temperature starting from 

 the critical temperature of the first (least volatile) component such 

 a barotropic tangent-chord may make its appearance in two ways: 



</. by the angle of inclination of the tangent to the plait in the 



plaitpoint, p i, reaching the value of; ai a certain temperature I i, r i 



and by i t s exceeding tins value at lower temperature. 



b. by 6 showing a maximum and a minimum on the plait at a 

 certain temperature, and by this maximum reaching or exceeding 



31 



the value of — . Also in this latter case one of the two barotropic 



tangents-chords which then appear, might reach the plaitpoint at 



n 

 lower temperature, and thus become & r i = — . 



In both cases in which a^i = — at a certain temperature it should 



u 



be expected apart from complications as e. g. a longitudinal plait 

 etc. (cf. Comm. N°. 96A, p. 502), the description of which will be 



given later on, that & p i becomes again = — for mixtures of the same 



substances at a lower temperature. 



In the first part of this paper the conditions are discussed on which 



n 

 a plaitpoint with d p i — — , barotropic plaitpoint, occurs on the if'-sur- 



l ) Cf. for the meaning of x and v Comm. N'. 96&. 



