284 
b= xb, +'/,(1—2x)b, — when 6, represents the co-volume of 1 
single molecule and 6, that of 1 double molecule — which quantity 
refers, therefore, to the original single-molecular quantity. But 6’ 
refers to the molecular quantity, which on an average yields 1 
molecule after the association, and which is 2: (1 + 2) times greater 
than the single-molecular quantity. [i.e. at «=O (exclusively double 
molecules) twice greater; at «1 (exclusively single molecules) 
once greater; etc]. For from the original single molecule there have 
been formed '/, (1 + #) new molecules, so that every new molecule 
corresponds averagely to 2: (1 + ) original single molecules]. 
dw 
We can now compute ae As 6 is a function of v (through 6, and 
av 
6,) and of a, and also v a function of « on account of the equation 
of state v= f(p, 7,.x,a, 6), in which also a and 6 are functions of 
a, we have: 
d F et a Ves L Ade /( Ob \ adn 0b L (0b\ dv 00 
=I es je ale (Ge il i se zE), | 
| db 
$ = db dv 
when is written for {= dv, aud because evidently 
v—b v—b 
x=const. x=const. 
Lea ae hr GL 
(5 BE in 8 ence 
d 1 dv 1 /0b 00 
(ew Pr at 6 )= gash ce GE G3) 
00 
For the further calculation of El the quantity @ must be 
known, i.e. 6 in function of v. When we assume for this the 
approximate relation derived by me before *): 
v—b b 
PE 
in which 8 is a coefficient that depends on the nature of the 
substance, then (5) a ek 3) bo, ahah Bu vb) 
easily follows 
dv Ne IE 
from: = BE ae In consequence of this @ becomes: 
= pe ee et 5 See fl eee: + Jen 
Br (v—b,) (Bv + (1—B) b,) Bot (pe, eee 
x—=const 
1) See Recueil des Trav. Chim. N°. 3 and 5 of 1920. 
