( 652 ) 



cuts the rim the binodal curve will simply have a tangent parallel to 



the v-axis. 



The shape which the different figures will assume, will now depend 



entirely on the fact whether such points Q and Q' will also exist 



when the solid substance is one of the components and if so, where 



they lie. The best and most general way of solving these questions 



would be a full consideration of the different forms which the (/-lines 



may present. As however the solution of the special question we 



are dealing with does not call for such a discussion, I believed to 



be justified in preferring another briefer mode of reasoning. For this 



purpose 1 point out first of all that it is easy to see. that at least 



in a special case such a point must exist also now. Let us imagine 



a plait, the plait-point of which has shifted so far to the side of the 



small volumes, that the tangent to the plait in the plaitpoint points 



towards the point indicating the solid state 1 ). The plait touching the 



isobar in the plaitpoint, the plaitpoint lies evidently on the line 



D = in this case 2 ). But the plaitpoint lies also on the spinodal line, 



s if? 

 so the point Q lies here in the plaitpoint, as neither ^— - = 0, nor 



— = oo. We may conclude from this that in such like cases, so 



those cases where the plaitpoint has been displaced still somewhat 

 further or somewhat less far to the side of the small volumes, and 

 perhaps in general when the difference in volatility between the two 

 components is great, a branch of i\ r =0 will pass through the figure, 

 and that it will most likely have a point of intersection with the line 

 D — 0. A closer investigation of this supposition can, of course, only 

 be given by the calculation. 



1 ) The above was written before Prof. Onnes' remarkable experiment (These 

 Proc. VIII p 459) had called attention to "barotropic" plaitpoints. Now that the 

 investigations started by this experiment have furnished the proof that plaitpoints 

 can exist, in which the tangent runs // x-axis, the existence of plaitpoints as 

 assumed in the text, in which the slope of the tangent need not even be so very 

 small, has, of course been a fortiori proved. 



2 ) We may cursorily remark that it is therefore not correct to say in general 

 that the line D = runs round the plait in the sense which van der Waals 

 (These Proc. VIII p. 361) evidently attaches to this expression, i. e. that the 

 point of intersection of the line D = with the binodal and spinodal curves would 

 lie on either side of the plaitpoint. For if the plaitpoint should have moved still 

 a little further to the side of the small volumes, the two points of intersection of 

 I) = with binodal and spinodal curves lie evidently on the vapour branch of 

 these lines (the part of these lines between the plaitpoint and the point with the 

 largest volume on the ;r-axis). 



