( 36 ) 



of the different series of' hidden plaitpoints, etc. etc., as has, inter 

 alia, been indicated in Jan. 25, 1 906 (cf. also Teyler II). Dr. Keesom 

 does not mention that in his figure I (loc. cit. p. 794) besides the 

 plaitpoint line from K m to K x drawn there, there always exists 

 also a second branch, which runs along the r-axis in the neighbour- 

 hood of x = 1 from the point where v = h to K, — and which 

 gives rise to a three phase equilibrium at lower temperatures, as this 

 has been explained by me. (also in Jan. 25, 1906 and Teyler II). 

 The fact whether a plait extends in the way mentioned, depends 

 therefore, as we said before, in the first place on the fact whether 

 b„ . a„ / 2'. . p 2 



the values of — and —(so of 6 = — and jt = — 1 are such that 6 



b x «1 V T , pj 



is larger than that value of 6 for which the plaitpoint line has a 

 double point with given value of jr. The knowledge of this double 

 point, being therefore of so great importance for the distinction of the 

 different types, I have carried out in Teyler I the lengthy calculations 

 required for this, and drawn up the results obtained in tables. [See 

 also Teyler II, where fig. 22 (p. 30) represents the results graphs 

 /call i/]. 



Hence not the fact that 7\,„ ^> T^ [with perfect justice Keesom 

 says in a footnote (loc. cit. p. 794) thai 7'/,,,, may also be <[ T^], 

 but only the fact that 6 lies above the double point value, determines 

 the considered course of the plaitpoint line. (See also Oct. 25, 1906, 

 where I summed up most of the results obtained by me). 1 ) 



It is true that Keesom mentions in a note (loc. cit. p. 786) that 

 I have examined the plaitpoint line for the case a, = 0, but this 

 statement is not quite complete, for I have not only examined such 

 a plaitpoint line for tins particular case a, = 0, which I cursorily 

 mentioned in a no'e (June 21 , 1905, p. 39), but for all cases. Quali- 

 tatively the plaitpoint line C„ C, for the case a, = is not distinguished 

 in anything from that for the case a x ^> (provided it remain in 

 the case of type I), hence there was no call for a special investigation 

 of the form of the spinodal line and of the plait for «, = 0, this 

 having already been done for the general case. Moreover Keesom 

 himself considers later on the case a, small, and no longer a x = 0, 

 which of course does not occur in practice. 



Also the equation of the spinodal line (for molecular quantities) : 



RTv* = 2 (1— x) (o [/a, — b, [/a)' 4- 2« (v \/a t — b, ]/a)*, 



i) Prof, van der Waals says (These Proc, March 28, 1907, p. 621), "that as yet no 

 one has succeeded in giving a satisfactory explanation of the different forms (of 

 plaits)." 1 think 1 have done so to a certain degree in my papers of 1005—1906, 



