( 505 ) 



surface at that place must decide about the possibility of the existence 

 of the assumed splitting up, whereas the position of the binodal 

 curve is also determined by properties of the surface in sometimes 

 very remote parts, makes us see that the circumstance whether a 

 point lies inside or outside the binodal line, cannot be decisive. 



The first, and I think I may say the well-known case of such a 

 splitting up of a plait, occurs for mixtures with a minimum value of Tk 

 (for mixtures taken as homogeneous). In tliis case also the binodal 

 curve of this transverse plait splits up, and both parts of these binodal 

 lines can be realised. But it is by no means an absurdity to suppose 

 that in consequence of properties of the surface in parts lying very 

 far to the left this double point was covered, and unrealisablc. 

 Then the binodal curves at the temperature at which the splilliiig up 

 takes place would be quite difierent ones and the already existing 

 one would also have remained covered for a great part. 



That at this well-known splitting up — =: in the double point, 



is, I think, also accepted by Kuenen, — and the admission that after 

 the splitting up the plaitpoints lie in such a wav that for one 



d-v\ 



—— is positive and for the second negative, leads to the conclu- 



"'^' / bin 



d'V 



sion that in the double point — must necessarily lie equal to 0. Such 



dx"^ 



a splitting up of a transverse plait into a righthand side and a left- 

 hand side exists and can be demonstrated experimentally for a number 

 of mixtures. Now for an explanation of other phenomena I was 

 confronted by the cpiestion whether a plait could also split up in 

 such a way that after the splitting up there can be question of an 

 upper and a lower part — or rather in a part with greater and in 

 one with smaller volumes. That in this respect experimental investi- 

 gation is still very incomplete, is readily admitted. 



Now with regard to the place of the double point three diiferent 

 suppositions can be made; 1. outside the binodal curve of the trans- 

 verse plait; 2. inside the binodal curve; 3. just on the binodal curve. 

 At the temperature at which the splitting up takes place CJ\,) the 

 transverse plait still extends over the whole breadth. 



In the first case the splitting up can be observed experimentally. 

 If we inquire into the properties of the binodal curve for the e(|ui- 

 librium liquid-lic|uid and liciuid-vapour, we get 1. in the double point 

 two intersecting curves, 2. the already existing liquid branch of the 

 transverse plait, of course shghtly modified, and running through 

 the unstable part of what I will call longitudinal plait. 



