( 504 ) 



Physics. — "Contribution to the tJieory of the binary ntii'ture^ XVI." 

 By Prof. J. D. van der Waals. 



In the Proceedings of Oct. 1911, p. 421 Prof Kuenen says that 

 he cannot agree with the \'ie\v that in the point in which a plait 



splits oiF from the transverse plait, the value of — should be 



equal to 0. 



fd-v\ f(rv\ , 

 The enualitv -—,=:-— he admits as valid, bnt he objects 

 ^ \dxyuu \d.v^J,, 



to the assumption that the double point at the same time would be 



a point of inflection of an isobar. Now in the double point the equality, 



which he wants to maintain, has strictly speaking ceased to exist. 



fd-v\ 

 In such a double point ( — I is infinitely great, because there the 



\dx''Jyjin 



binodal curve consists of two line elements, which enclose an acute 



or an obtuse angle. But leaving this aside as self-evident, it seems 



d'''v 

 of importance to examine whether his opposition to — ; = is 



dx-f, 



well-founded. This equation has namely enabled me to indicate the 

 place where such a splitting up is possible — and it has even been 

 one of the reasons which led me to examine where points of inflec- 

 tion can occur in the isobars and to occupy myself with the locus 

 of these points of inflection ^). 



Kuenen thinks he can justify his objection to the theorem that in 



the said double point — ; = by the observation that this splitting 



dx'-f, 



up is assumed to take place inside the binodal curve. And this 



observation is by no means conclusive. Inside the binodal cnr\e the 



surface is only partly unstable — there is also a stable part, in 



which the surface seen from below, is convex-convex. And for the 



circumstance that the splitting up be such that in the double point 



— - =0, it is now only required that it lie (to express it briefly) 

 dx'jj 



on the convex-convex part of the surface — or expressed more 

 sharply, that a moment after the splitting up there exist a convex- 

 convex part between. The very consideration that properties of the 



3) If the four branches of the binodal curve in the double point are reduced 



to two branches, ( — ^- ) :^ ( — ) can be maintained also in the double point 



\dxyiin \dx-Jp 

 and wc are naturally led to the insight that the value is there =0. 



