( 93 ) 



So liore llio condilions are still irioro favoiiraltlc, as wo jilroadv foiiiid 

 in VI p. 644; These Proc. of Dec. J910. Foi-ri' = 0,07 /Mnust be at 

 least =2 for .?; = 0,5 ; ibr .v — 0,'S at least =5; for .r = 0,1 al 

 least =11; wliieh would again api)roa(di to 14 foi- ,/=:0. 



If we now suppose that in reality ± L h will probably always be 

 <^7j' '"^'I'l i^ we assume e.g. 0,1 as mean value, then from this 

 would follow n = \l, resp. 11 — let us say 14 on an average, a 

 very plausible value, also in connection with v.\n dkr Waals' inves- 

 tigations. 



34. To the foregoing remarks a great deal might be added. In 

 reality the i-elations will probably not be so simple as w^e have 

 thought them in what precedes; particularly in the easily mobile 

 liquid state — where the situation of the compound molecules is 

 not fixed as in the solid state — all possible combinations will be 

 conceivable: double molecides, triple, qnadrnj^le etc. And all this in 

 ratios which depend on the constants of the substance, and moreover 

 on the temperature and pressure. In the solid state, on the other 

 hand, probably one kind of multiple molecules will prevail. But 

 this would simply render the above computations somewhat more 

 complicated, the essential i)art will remain the same. Accordingly I 

 have not entered into the calculation for a special case, e. g. n = 10. 

 The main point is, and remains that on account of association, 

 both in the liquid and in the solid state, the occurrence of this lattei' 

 state follows from this as a necessary consequence for not too low 

 values of Ab. The considerations and calculations of the foregoing 

 papers have taught us this. At certain high pressures the isotherms 

 turn hack once mort, and this is repeated for the second time 

 at low pressures, after which they finally rise to /> =: oc. And we 

 ha\e seen critical points appear both in the case A/6 negative, and 

 in that where A/> is positive (see specially V and VI, which I shall 

 not discuss any further here). 



So the whole dieory of the solid state rests on two suppositions : 

 that of the association and that of the variation of volume {Lb) \\\\\\ 

 the association. The former supposition is now universally accepted, 

 though VAN DER Waals continues to speak of "Quasi" association. 

 Yet he applies the thermo-dynamic conditions of equilibrium to it 

 already in his l**- paper (p. 121 — 123), which strictly speaking only 

 hold for ''real" association. Hence I have never understood quite 

 clearly, why quasi association is spoken of — unless it should be 

 tliat (|uasi association specially appears imder the exclusive influence 

 of the molecular forces and that in the expression for the variation 



