f 508 ) 



phases of tlie three phase equilibrium ; it will certainly not have its 



highest point in C. Mj attention was drawn to this circumstance by 



KoHNSTAMM immediately after the appearance of contribution XV. 



And this same error is expressed in words on p. 900, where it says 



that the point C lies on the binodal curve of the equilibrium liquid- 



dp d'p 



vapour, and that — and — are equal to zero in the point 6. So 

 dx dx^ 



these two sentences ought to be omitted, and wdien Kuene?^ does not 

 mean anything by his remark but this, I entirely agree with him. 

 But I read more in liis remark, and this is the reason why I think 

 I should make these observations. It namely seems to me that 

 KuENEN I.e. means that the double point of the spinodal curve 

 (which is naturally always also a double point of the binodal 

 curve) would always ha\'e to lie outside the binodal curve of the 

 transverse plait. This will, indeed, be probably possible; then the 

 point where the i)laitpoint line ECDFK intersects the line of the 

 three phase equilibria, must lie between C and D of the fig. 47 of 

 contribution XV. Only by way of exception it could have risen as 

 high as the point D. Compare also these Proc. VIII p. 184, 

 where 1 slill harboured some doubt, but finally arrived at the con- 

 clusion Ihal I had to locate (he intei'seclion of the plaitpoint line 

 with the binodal line before 1). 



But at least as often, if not oftener, the case will occur that the 

 double point lies inside the binodal curve of the transverse plait; in 

 this case the endpoint of the three-phase pressure lies on the bi'anch 

 CE of the plaitpoint line. The foregoing remarli may also be expressed 

 thus. Korteweg's theorem that the coincidence of two heterogeneous 

 plaitpoints must always take place inside the binodal curve, is inter- 

 preted by KuENEN thus, as it seems to me: "The coincidence of two 

 homogeneous plaitpoints must not take place inside the binodal curve." 

 This would mean in fig. 47 : "As the point where the plaitpoint 

 line enters the binodal curve, cannot lie on the right of D, it cannot 

 lie on the left of C either". This would have certainly called for a 

 proof, for these two theorems are certainly not identical. 



Or if I had to comprise my defense against the objection in one 

 phrase, it would run : When a theorem is "true, it does not follow 

 that the reverse of this theorem is true. Korteweg's theorem is true 

 and can be considered as self-evident, namely if we understand by 

 binodal line a line which can bo realized. But it does not follow 

 from this that every double plaitpoint inside the binodal curve is a 

 heterogeneous double plaitpoint. 



Besides 1 have nowhere asserted that the binodal curve could be 



