( 506 ) 



At somewhat liighei' tempemtui'e, so above that of the splitting 

 up, the convex-con\'ex pai-t of the t^-surface has made its appearance 

 in the double point — a separate curve has split off either quite 

 closed or open towards the side of the limiting volumes, concerning 

 which I refer to former observations. And moreover the transverse 

 plait has got a branch plait with a plaitpoint at the side of the 

 small volumes. To close this branch plait a hidden plaitpoint is required 



— also in reference to this I may refer to former communications. 

 At still higher temperature the branch plait has retreated more and 

 more towards the transverse plair ; the plaitpoint reaches the binodal 

 curve of the transverse plait, and then the liquid branch of this 

 binodal no longer runs through an unstable region. 



But, and for this I also refer to former investigations, then too 

 the hidden plaitpoint still exists. And not before the temperature is 

 still higher does the hidden plaitpoint unite with the plaitpoint of 

 the branch plait that existed before. From the temperature at 

 which this plaitpoint lay on the binodal curve there existed inside 

 the binodal curve a pair of heterogeneous plaitpoints. But strictly 

 speaking if we do not confine ourselves to that part of the surface 

 lying inside the transverse plait, there exists such a i)air of hetero- 

 geneous plaitpoints already at Ts,.. And if the longitudinal plait on 

 the side of the small volumes is closed, there exists such a pair of 

 plaitpoints already before the splitting up. Only then at the spitting 

 up all at once substitution of quite another point takes place for 

 one of the points belonging to the pair of plaitpoints, to which subject 

 1 shall return in a following communication. 



This first case for the place which may be possible for the double 

 point, is not known, and is certainly not realized in the mixture 

 -examined by van der Lee. And now it was my puri)ose to explain 

 the 2"^^ case in Contribution XV. 



Not that there is a great difference with what I described above 



— there is only a difference as far as the place of the double 

 point is concerned. 



This double point might happen to lie exactly on the binodal 

 curve of the transverse plait, which I have refeired to above as the 

 third case. This would certainly have to be called a coincidence. 

 As I remarked above the property of the surface which leads to 

 splitting up, and the property on the vapour side of the transverse 

 plait which governs the place of the binodal curve of the transverse 

 plait to a high degree, would have to answer very special demands. 

 I consider the chance that this takes place as about zero. 



Moreover the difference be i ween this particular case and the 2"^^ 



