0,98, and 



46 



For A^ and /^ we then liiul fi-oiii (3) and (4) l^ 

 also I, = 0,98. 



Remark. The values of ).^ and A^ found, change only very little 

 when association or quasi association is assumed. Then the expres- 

 sions for 7' = Vf, : /)!,; RTi, pk tind s, indeed, become more intricate 

 (cf. Van L. I and II), and we shall among others find — according 

 as partial (very slight) association to double molecules is assumed, 

 or association to triple ones — in which the Cjuantity h changes in 

 consequence of this association (loc. cit. I, p. 295 — 297 ; II, p. 428 — 431): 



out the N'alues of Aj and ?..^ remain in the immediate neighbourhood 

 of unity; that of Aj on an average 1,007, and that of X^ on an 

 average 1,013; i.e. they are about 1 7o ^bove unity, whereas when 

 the association is disregarded, they remain about 2 7o beloiv -it. 



For b'k and — viJ)"k lower values, viz. the mean values 0,043 and 

 0,25 are found when association is assumed; whereas 0,094 and 0,40 

 are found, when association is left out of account. 



As appears from the above values of the factor a;, of RTk (resp. 

 = (1 -\- j?A- : 2 or (1 -[- 2,:?a) : 3), the association at the critical point 

 is still exceedingly slight'); the mean value of at being =0,975, 

 on an average only 2V2 7o of the simple molecules have aggregated 

 to multiple ones. 



1) hi their interesting and tliorough paper on the equation of slate in the 

 Encyldopadie der Math. Wiss. (12 Sept. 1912, p 615—945) Kamebltngh Onkes 

 and Keesom make the very true remark on p. 177 (paging of the reprint in the 

 "Gomm."), that it is going too far to ascribe every deviation from the ideal 

 equation of state to association. Also my statement in the TEYLER-paper cited 

 there, is too sweeping in this respect. It appears sufficiently from the above 

 remarks that the simple assumption of the variability of b with r can also satis- 

 factorily account for tliese deviations (see also § 2). It remains of course to be 

 seen to what this variability of b is due: in a quasi or in a real diminution of 

 the volume of the molecules (v. d. waals) — or in a variation of b also in 

 consequence of the association (v. L. I and II). 



On this occasion, in connection with the footnote on p. 178 in the cited paper 

 by Kamerlingh Onnes and Keesom, we may remind of the fact that according 

 to my considerations tliere would indeed be double and triple molecules in the 

 neighbourhood of the critical temperature — but only to an exceedingly slight 

 amount, viz. about S^/^ 0/0 (see above). 



