( 389 ) 



saturation ciu'\'es separate, tlie tw o li(|iiid [)hases approach each other 

 and finally coincide in the critical point : what becomes of the 

 minimum {.i\ == a\) during this change, if we suppose such a point 

 to lie inside the three-j)ha8c triangle? The simplest supposition which 

 we can make is that up to the last moment the minimum remains 

 between the two maxima and thus a fortiori between the coexiiSting 

 liquids; on that supposition the various points would all coincide 

 in the critical point and unile into one maximum ; in llie critical 

 point we should then iiave the condition d\ = ,r.^, i. e. the li(piid in 

 the critical point would have the same composition as llie vapour 

 with which it is in equilibrium. This assumption was made as ahnost 

 self-evident bv myself^) as well as by van dkk Lke^), Init on fuller 

 consideration it now appears to me to l)e incorrect; VxVxN der Lee') 

 tried to prove its correctness by the aid of the thermodynamical 

 relations for binaiy mixtures, but we shall show that the proof was 

 not valid. 



The equation to be used is the following : 



introducing into this the condition ^ — ^ = 0, which defines the spino- 



dal curve and thus holds a fortiori in the critical point, we obtain 



df) 

 the equation -— = : but it does not follow from this that the vapour 



pressure has a maximum value ; for it may be proAed that not only 



diy d^p 



the first ditferential coefficient —- , but also the second - — ~ disappears. 



d^p dp 



Calculating the value of —^ from — we find : 



but in the point of contact of the two curves we have not only 



^- 1=0, but at the same time ——-^ = 0, because the spinodal 

 dx.^J^ dx d./'j' ^ 



curve of the two-liquid curve touches the connodal curve of the 



vapour-liquid curve in the critical point of contact ; thus as none of 



1) KuENEN en RoBsoN, Phil. Mag. (5) 48 p. 184, fig. 2. 

 ") Van der Lee, 1. c. p. 69. 

 3) Van der Lee, 1. c. p. 74. 



