11 
Besides, the value of f can be modified, when in the dissociation 
of the double moleeules increase or diminution of volume takes place, 
or when the beat of dissociation differs from 9. This is e.g. very 
apparent in the formula, which | derived before for fp in the most 
general case '). 
ay dd 
For the value or ( — de) = fr we find namely at 7%: 
Pis € 
k 
° d 4 En qk 
== xX (p 1 4——— | 
Jk (7k)o f ( f i) 
in which (f;,), is the value of /;, when the substance were simple, 
i.e. 3 (degree of dissociation of the double molecules) = 0 or 1. 
The factor p is a rather complicated function of 3 (and of the possible 
change of volume Aé for dissociation of '/, double molecule to one 
single molecule), while 2 is also a function of Bp and 4d. The quantity 
q' represents the internal heat of dissociation (absorbed) for the said 
dissociation. When Ab = 0, the value of gp is always <1, both in 
the neighbourhood of 3==0 and in that of 8 = 1. The latter is appa- 
rently in contradiction with what we observed above with regard 
to substances which behave as acetic acid, where for lower tempe- 
ratures f is found greater than normal. But then we should forget 
that in the neighbourhood of 7% the association also of the acetic 
acid vapour — after having passed through a minimum in the 
neighbourhood of 7% — again increases with increase of temperature, 
just as for substances as mercury, water ete. 
[f (fp), lies in the neighbourhood of 7, the factor ¢ (A= 0 
being assumed) is e.g. = 0,84 for @==0,1, and 0,96 for B = 0,9. 
We find a minimum, viz. g = 0,72, for 8 — 0,4. As far as / is con- 
cerned, this coefficient is —0O for 6=0O and 8—1, and reaches a 
maximum value, e.g. 0,22, for @= 0,5. For 3=0,1 2 is = 0,086; 
also for g— 0,9 + is = 0,086. This quantity is namely symmetrical 
with respect to 3. 
If, therefore, also g'=0, then in consequence of the factor ¢ 
the value of fr can be as much as 28°/, smaller than the normal 
value. The value 7 can therefore decrease to 5 (when viz. for 
T the value of 8— 0,4). For substances where 8 = 0,1 at 7%, the 
value 7 would any way have already been reduced to 7 pr Ost = 
5,9. Ete. If therefore we find for 7% a value for f that is greater 
than the normal one — as for acetic acid, methyl alcohol, ete. — 
then it is certain that g' differs from 0. (the value of Ab has but 
little influence). This is in perfect concordance with what we remarked 
') See Archives Teyrer 1908, p. 40—42, and also These Proc. of Nov. 7, 1914, p. 606. 
