( 501 ) 



logram y^<KklO x or the product o! the two cylindres in which points 

 of velocity were found before impact. The product of the cylindres, 

 in which points of velocity are found after impact is equal to the 

 producl of dOdO } and the area of the rectangle with sides parallel 

 to the axes 06* and o'd\ described round the parallellogram under 

 investigation. In this rectangle lie a number of points which have 

 no corresponding points in the first rectangle. Only when m = m 

 rectangle and paralellogram coincide. 



Collisions of opposite kind, now, are such for which the combina- 

 tions of velocity before impact arc represented by points of the 

 paralellogram in the plane d'Od\ and after impact by points of the 

 rectangle in the plane dOd 1 . 



Physics. — "Contribution* to the knowledge of the ^-surface of 

 van der Waals. XII. On the gas phase sinking in t/w liquid 

 pha.se for binary mixtures." By Prof. II. Kamerlingh Onnes 

 and Dr. W. H. Keesom. Communication N°. 96'' from the 

 Physical Laboratory at Leiden. 



§ 1. Introduction. In what follows we have examined tlie etj ui- 

 librium of the gas phase with the liquid phase for binary system-, 

 with which the sinking of the gas phase in the liquid phase may 

 occur. 



It lies to hand to treat this problem by the aid of if; (free 

 energy)-surfaces for the unity of mass of the mixture (van der Waals. 

 Continuitat II p. 27) for different temperatures construed on the 

 coordinates v (volume of the unity of mass of the mixture) and x 

 (quantity of mass of Ihe second component contained in the unity 

 of mass of the mixture). 



As van der Waals (loc. cit.) has already observed, the laws refer- 

 ring to the stability and the coexistence of the phases are the same 

 for these ^-surfaces as for the more generally used ^-surfaces for 

 the molecular quantity : in particular also the coexisting phases are 

 indicated by the points of contact of the i|'-surface with a plane 

 which rolls with double contact over the plait in the if?-surfaee. In 

 what follows we have chiefly to consider the projections of the con- 

 nodal curve and of the connodal tangent-chords on the rr-plane. 



More particular cases as the occurrence of minimum or maximum 

 critical temperature or minimum or maximum pressure of coexistence 

 we shall leave out of account ; we shall further contine ourselves 

 to the case that retrograde condensation of the first kind occurs. 

 Moreover we shall restrict ourselves to temperatures, at which the 



