( 422 ) 



mixtures ') will be found to be correct in this respect : in drawing 

 those 1 was guided partly by experimental results partly by another 

 law ') which was deduced from the theory and which comes to this, 

 that the sejiarated two-liquid plait lies outside the vapour-liquid plait, 

 if the tw^o components, as liquids, mix with expansion and vice versa. 

 It stands to reason that this law and the new one must essentially 

 be one and the same. 



As regards the direction of the two hinodals which meet in an 

 angle of the triangle it was mentioned that they always form an 

 angle and naturally such that the curves enter the metastable part 

 of the surface. A proof of this may be given without directly using 

 the theory of plaits by means of van der Waals's formulae. If the 

 two directions coincided at any moment we should have : 



Ov- ö,tOv 





V, V, J Ow 



d.c 



-^ 1 _ '^3-'^ A _M^ 



If the common factors in numerator and denominator are not equal 

 to zero we may divide by them and we obtain the condition for a 

 plaitpoint at 1, a case which we may exclude. If the factors are 

 zero the three phases are in a straight line : this has a practical 

 meaning only, if 2 and 3 coincide and we already know that the 

 two binodals at 1 form one continuous curve in that case. Under 

 other circumstances therefore the curves must meet at angle, q. e. d. 

 For the special case that the point 1 lies at the extreme limit of 

 the plait, in the so-called critical end point, the proposition was 

 proved and used by vax der Waai-s. ') 



In conclusion it may be pointed out that by taking into account 

 the last proposition one may easily deduce from the v — x diagram 



1) J. P. KuENEN. Theorie u. s. w. von Gemischen, Barth. Leipzig p. 153. et seq. 1906. 



3) 1. c. p. 158, 159 



3) J. D. van dee Waals. Proc. XI p. 822. 1909. 



