( 186 ) 



case for the point Q vanishing on the ontline. Jnst as experiment 

 yields the \aliies of Te and T„, it also gives us the values of x^ 

 and ,/'„ at which the tops P and Q will disappear. For temperatures 

 higher than Tc and lower than 7« the (/;, -i')?- -curves have lost 

 the complications which they had for values of T between Tc and 

 Ta- Ojily at temperatures which lie little above Te or little below 

 Ta, there is still a deviation to be found from the well-known 

 looplike shape of these figures, as there are inflection jioints to be 

 found. So at Tc and 7\ the complications which I shall call exter- 

 nally visible complications, ha\'e disappeared. But before we can 

 say we know all the particularities of the whole {p, T, .i;)-surface, 

 among which I also reckon the hidden complications, the question 

 is to be settled whether the disappearance of the external complica- 

 tions involves the disappearance of the hidden complications, whether 

 perhaps the hidden complications may continue to exist long after 

 the external complications have disappeared. Figures (1) and (2) 

 make clear bet\veen which two alternatives a choice must be made. 

 According to fig. (1) the disappearance of the external complications 

 would involve the disappearance of the hidden ones. According to 

 fig. (2) the hidden ones continue to exist when the external ones 

 have disappeared. And even wdien T rises above 7e, they are still 

 there. At higher values of T the hidden complication gets detached 



from the outline. The spinodal curve retains its maximum 



and minimum, and there are still two plaitpoints, viz. at this maxi- 

 mum and mininnim. And only at a certain value of T lying above 

 Tc that maximum and minimum have coincided to a double point 

 and the hidden complication is about to disappear. 



For the point ^ a similar question occurs. Have all the complications 

 disappeared at T„, or is it required that T descends below Ta before 

 the hidden complications have also disappeared on this side? 



I must own that I have long been in doubt on this point, as will 

 appear when Ave compare the answer I shall now give to this 

 question with remarks I made previously on the experiments of 

 KuENEN and Robson. 



According to Korteweg's result a double plaitpoint will always 

 originate on the spinodal curve. But in itself this does not seem 

 decisive. For according to both figures, to fig. 1 as well as to fig. 2, 

 a double plaitpoint disappears or appears on an existing spinodal 

 curve. But in fig. 1 this takes also place on an existing binodal 

 curve. And now it is Korteaveg's opinion, that such an appearance 

 of a double point, viz. on an existing binodal curve, would be such 

 a special case that we must not conclude to it but in the utmost 



