57 



again tlie factoi- A*^';^. : pi, {r/. — />/,) z= s yields already ƒ =^ 7, now 



r — 1 ' 



too t'a; must be either (about) 0'), or exceedingly small, so that also 



in this case the formulae (6), (7), and (8) can remain intact. 



And as for t'a; = again formula (9/>) holds, viz. A = — g'V^ : (ƒ— 1), 

 because the coefficients of a- and [3 in (9a) will l)e = (see above 

 at a), we again determine only b"ii. 



We find: 



cVp\ 2R hkr' 2RT (hkx'\' RT bkx" 



dry, {v-bkry Tk {v-hkxY\TkJ {ü-bkxy Tk' 

 hence, when r't = is put : 



„ Tk^fd^p\ RTk „ bk „ 



pk \dlyk pk{vk—hky vk--bk 



taking the value of ƒ into account according to (Qb) — when x'l, 

 is put there = 0. 

 So we find for A: 



^=-7^-^- (9<0 



/— Ir— 1 



d'r 

 in which x" = — for v constant. We draw attention to this, that 



dm' 



X = x"k was found on the assumption of a = akx (formula 96'). 



Nqw ƒ : (ƒ — J) (r — j) =3 7 : 6 X 1,11 = 1,05, SO that we must 

 now get : 



x^= — 6,8 ; 1,05 — — 6,5. 



So whether one takes a as temperature function or b — in both 

 cases one will find t'^:- = 0, and x"k not far from 7, resp. — 7. 



And as to the dependence of the quantity b on v, b'k will be at 

 most 0,1, vkb"k at most — 0,4 (see § 1). 



By the side of "/<- iio function of v can occur which could 

 account at the same time for the course of the quantity (p at 7\; 

 and for the known values of the critical quantities. So not van dek 

 Waals's factor (1 — 72'^')'^ either, in which x is a function of v 

 (see § 3). 



1) It is of course impossible that r't is absolutely = 0, for then the critical 

 temperature would have an exceptional meaning in tlie series of temperatures 

 between r=oc and 2' = 0, to which it cannot lay claim. For quantities which 

 have only significance in the heterogeneous region, wliere liquid and vapour coexist, 

 there can indeed be question of a factor 1 — m in the neighbourhood of Tt, 

 which factor would become = at Tn {m = 1) — but never for quantities as 

 a and b, for which the critical temperature is no more than an ordinary tempe- 

 i'ature. So t'^ can only be exceedingly small. 



