( 282 ) 



8 at the critical point. But this was only an approximative calculation : 

 a more accurate calculation makes ns find a value of 2 a 3 for r. 



But now we proceed to derive tlie critical quantities from the 

 equation of state on the supposition of the variability of Z» exclusively 

 in consequence of the dependence of the degree of dissociation /? on 

 the volume v; while i^Thas to be multiplied by the factor 1 + (»' — l)i^, 

 because in all there are 1 — ,? complex molecules and v^i simple 

 molecules, in which v will denote the number (for the present 

 considered constant by us, see above) of simple molecules which are 

 on an average associated to one complex .molecule. 



Also the quantity a will be assumed to be constant by us (see 

 Solid State VII, p. 94 at the bottom, so that the contraction introduced by 

 VAN DER Waals in the value of a is not introduced in our derivations. 

 The number of molecules associated to one complex molecule (on an 

 average Vj.,) is not great enough for it at the critical temperature, 

 so that no reasou whatever would exist for tiiis contraction, (see 

 also VAN DER Waals, Quasiassociation. These Proc. XIII p. 119 — 

 121). So we consider the formula 



as valid, which passes into a ^ n^ with /ij = l — |?, n^^n^,a^.^ = 



^— , «2 = ^ J ill whicli (and this will henceforth be the case when 



the contrary is not asserted) always r-fold molecular quantities of 

 the substance are considered. 



The formulae following here were ah-eady derived by me in 1908, 

 and published in the Arch. Teyler (2) 11, Troisième Partie : "7%(^(?m 

 de tassociation etc.", where (see p. 25—34) comparatively simple results 

 were obtained. But these formulae only hold for the case r = 2, 

 and we shall, therefore, give the derivation here once more for the 

 perfectly general case that not 2, but v molecules are associated to 

 a complex molecule, in which at the same time some simplications 

 will be applied in the derivation. 



2. The general formula for /? was already derived for the case 

 of Ï' molecules in my Solid Slate VII p. 84 —86. We found there nl. : 



(1-/3) (1 -h (r-l)i5)-^-i (p + "AO-^-' 



If we substitute for /;-|-^'/,.2 the expression which follows for it 

 from the equation of state 



(P -f-A-) (v-h) = (1 + (r-l) i?) RT, 



