49 



that equation (7) is accurately satisfied witli these values of .s^and/. 

 With regard to the first equation (6) it should be borne in mind 

 that when association is taken into account, a factor a/^ appears in 

 the second member, (because then ƒ becomes = «/,• /?21- : jyjc {vt — bk). 

 Thus : 



r 8 A^ 



/ = «k s = ak — , 



r — 1 ? — 1 /, 



in which according to the table in § 1 ak has the mean value of 

 0,975. (cf also v. L. A., p. 772). From 



;• and .v may be expressed in /* — 1, and we find then : 



• ' = y|X — ^' • ■ • («) 



two relations also deri\'ed by Van dkr Waals, — but now, the 

 factors Aj and ?.^ having been taken into account, quite accurate. 

 Putting P-i and A, = 1, we find from this approximately, when ƒ =: 7: 



'6 8 



r = -— = 2,12 ; s = — l/2 = 3,77. 

 |/2 3 "^ 



That the factor \/2 pla^s a part, I had already surmised before, 

 without knowing the cause. See inter alia the Yorlesungen fiber 

 theoretische und physik Chemie by Van 't Hoff, 3^^ Heft, p. 14, 

 and the Vorwort p. VI (1900). Besides already in 1905 (Arch. 

 Teyi.er) I expressed some critical quantities in experimentally deter- 

 minable quantities in a perfectly analogous way as later Van der Waals 

 — however with the exclusion of the quantity /, as the possibility that 

 b and particularly a could be functions of the temperature, was not 

 excluded by me. (Cf also v. L. A., p. 773). 



3. Difficulties and objections. 



So far there is not a single objection, and if there were no 

 other characteristic critical quantities than r, s, and ƒ, it would 

 suffice to consider b as function of v, and to seek the cause of this 

 variability. The association (or quasi-association) might then be 

 accepted or left as a gratuitous addition. It would not be necessary. 



But unfortunately, matters are different. There is namely one more 

 characteristic quantity, i.e. the quantity (f, given by 



_ F—l 6 

 '^~ Fk—l dj,' 



4 

 Proceedines Royal Acad. Amsterdam. Vol. XVI. 



