( -^'^1 ) 



i^z=:0,95 into simple molecules (so only 7.^^ part is still complex), 

 while on assumption of an association to double or triple molecules 

 in the neighbourhood of the critical point the value of A6 is found 

 to be such that the limiting volume [b,, = vh., for v = 00) has duly 

 decreased to half its original size {h^ = b^, where h^z='^/.,vh^), when 

 V has become = b. 



To tiiis is added the circumstance that the minimum molecular 

 volume />„ for v = b pi'oves to be the same for every temperature. Kor 

 hovvc\er high or low the temperatui-e may be, /? will always be = 

 in the ex|)ression (1) for (3 (see § 2) for v = b ; hence b„ = b^, in 

 ^vhich b^ is iiie molecular volume of the complex molecules, on 

 account of t!ie above expressions for b and hb. And reversely the 

 value of />„ will again be = b^ for T=zQ for every volume, because 

 also for 7' = () the degree of dissociation /^ will approach to 0. Hence 

 there is not only one limiting volume for great volume and high 

 temperatui-e, but also only one limiting volume for small volume and 

 low temperature; the latter about half the first. 



The ditferences which continue to exist for different substances in 

 the reduced etpiation of state, and which van der Waals p. 1212 

 pointed out, can now also easily be accounted for by a somewhat 

 divergent value of /? (and possibly also of A6). For it is clear that 

 the degree of dissociation of the complex molecules will not be the 

 same for every substance. It will of course entirely depend on the 

 constants of tlie equation of dissociation \1). And thus substances 

 will also be found with abnormally greatlj^ divergent values of /?, the 

 so-called anouia/oiu substances. 



Also the value of i' can be different. It will namely also depend 

 on the constants of the substance, hoio many molecules wil combine 

 to a com[)lex molecule at different temperatures and volumes. I have 

 already pointed out in my last paper on the solid state (p. 98 at the 

 bottom) that also i' will be a function of v and T, and that on an average 

 a greater number of molecules will associate at low temperature and 

 small volume than at high tem})erature and great volume. But in our 

 following considerations we shall for the present neglect tliis depend- 

 ence, because we shall confine ourselves exclusively to the critical 

 quantities. And at this volume and this tenqjerature v will ap[)ear 

 to be about from 2 to 3, i. e. the few molecules which arc still 

 associated then (about Vso) ^'^'ll be on an average associations of 

 double or tiipie molecules. [At 7'^ ao and r^ x the exceedingly few 

 conq)lex molecules, still present then, the number of which approaches 

 to 0, will only be double ones of course]. 



In my last paper I came to the conclusion (p. 100) that v is about 



