( 317 ) 



Physics. — "Contribution to the theory of binary mixtures". X. Ry 

 Prof. .1. D. van der Waals. 



d 9 ip d'ifc 



THK INTERSECTION Of? THE CURVES =0 AM) - = 0. 



(f.lf (fv" 



The points in which the two curves =0 and intersect, 



d,r'- ilr' 1 



lie of course in the unstable region. For il is required for the points 



d*ip 

 ot the spinodal line, the limit of (he unstable region, that ^> <> 



das 1 



•lh]< </></•-' if /d'ibY 



and ^> 0, and the product — = . Hence the use of 



i/r' 3 dx ilr- \dxdvj 



the study of the way in which these two curves intersect, must not 

 be looked for exclusively, nor even chiefly, in an indication for the 

 course of the spinodal curve. It is, indeed, clear and has heen repeat- 

 edly set forth in the previous papers that only iu the cases in which 



there is intersection between the two curves, or when = lies 



dx % 



outside the curve =0, the spinodal line deviates greatly from 



dry d*ty d s tl> 



— = 0; whereas, when =0 lies entirely within - = 0, the 



dv* d,V' ' dv* 



course of the spinodal line deviates little from the course of =0. 

 1 dv* 



But above all the knowledge of the relative position of =0 



1 dx % 



d*ty 

 compared with - = seems of importance to me for the question 



whether for a given binary mixture three-phase-pressure is to be 

 expected or not. And everything thai can contribute to elucidate a 

 matter of such practical importance, must necessarily be considered 

 important. We shall again put b = f> l (\ — ,,) _|_ /,.,,,■ also in this inves- 

 tigation, and so again disregard the influence of v on the value of 

 h. So from a quantitative point of view our results may lie very 

 deficient. But on the other hand it has sufficiently appeared in our 

 former investigation, iu which the same approximation was used that 

 the indication of the course of the phenomena obtained in such a way, 

 is correct in the main. 

 So let us put : 



/ db V d'a 



d ^-MRT\ ! \&l\ -^ = 



dx* ( ,/■( — x) ' ('•—/<) 



v 



21* 



