( 421 ) 



Keeping (his rule in view and considering (lie diagram in the 

 neighbourhood of a critical point for two of the phases, where a 

 plaitpoint makes its appearance (or disappears; we at once arrive 

 at the following important law : 



When a plait touches a second plait in its plaitpoint the curvatures 

 of the tiro are of the same sign. 



An independent proof of this law may be given using the pro- 

 perties of the curves of constant pressure, the isopiëstics. It is well 

 known that the isopiëstic which touches a plait in its plaitpoint is 

 curved iji the same direction as the plait. At the point under con- 

 sideration the three curves (viz. the binodal with the plaitpoint, the 

 second binodal and the isopiëstic) touch each other. But (he isopiëstic 

 cannot touch the second binodal curve simply on the outside, for 

 that would mean, that the point was also one of maximum vapour 

 pressure on the second plait, and it is well known that this is not 

 the case. The isopiëstic and binodal curves must therefore intersect 

 as well as touch, i. e. they have the same curvature, from which it 

 follows that the second binodal is like the isopiëstic curved in the 

 same direction as the plait which it touches. 



Analytically the law is expressed by (he equality ot the two 

 'd^v\ /d'-v' 



expressions — and ( - which may be easily confirmed by 



* \d\rjtin VÖ'^'V/' 



calculation. I find that some time ago a proof of this relation 



was given by van der Waals ^), but 1 must add at once that I 



do not agree with the view expressed by him that the value 



of these coefficients should be zero at the point in question, in 



which case the two curves would have a point of inflexion there. 



d'v , , . 



The condition = holds at a pomt where a plait separates 



d,v^p 



into two parts with a plaitpoint on each. Van der Waals assumes 



a separation of that kind, but it occurs inside the second binodal 



curve, not on it "), and the condition does not hold at the point 



where one binodal curve with a plaitpoint emerges from a second 



binodal curve. If I am right some of the diagrams in van der Waals' 



paper would need modification. 



The literature on the subject shows again a number of diagrams 



which are not in harmony with the law enunciated concerning the 



curvature of the two plaits. The figures in my own treatise on 



1) J. D. VAN DER Waals. Proceedings XI. p. 900, 1909. 



2) Gomp. the paper on plaits by Kortewec (Arch. Need. 24), and e. g. van 

 DER Waals, Proc. X p. 141. 1907. 



