617 
validity of (2°), and it shows that practically the possible objections 
to the validity of the second method are unfounded. 
4. This objection consists in this that now we do not integrate 
along the states of equilibrium, and that it is therefore questionable 
whether it is allowed to substitute the known expression of the 
mixture 8, as a function of v and 7 for py.,,. 
Dr. Hornren says: strictly speaking it is not allowed, but after 
some extension of the definitions of the thermodynamic functions, it is. 
I will not argue about this, but will only draw attention to what 
follows. 
In my opinion it is namely not of the least importance in the 
calculation of the function yw for a mixture whether the components 
happen to be in equilibrium or not. For what would else be the 
meaning of the statement: In case of equilibrium yw must be a minimum! 
How can a function be a minimum when the values outside the 
minimum, where therefore there is no internal equilibrium, are 
declared invalid? 
Nobody has as yet taken any notice of the said objection, neither 
Gipps in the calculation of the state of dissociation of N,O,, nor 
“VAN DER Waats') in his numerous calculations on these subjects, and 
in my opinion justly. . 
For we write the value of the function yw for an arbitrary mixture 
of the components, even though there should be no internal equili- 
brium, and then determine the special values of 8 for which yw becomes 
Ip ow | . 
minimum, (from (Ge) =0). by which the required concentration 
P Sov 
of equilibrium is obtained. 
It is namely also possible to regard the mixture fictitiously as 
non-reacting (this fiction is realized in many cases of retardation and 
similar ones), and write the expression of yw which the mixture would 
have if the components really did not interact. For another value of 
the ratio of mixing 2 there is another value of y — and for a 
definite value of B (independent of the constants of energy and 
entropy determining the equilibrium) yw will have a smallest value. 
Then there is really equilibrium, and now no change in the condition 
can set in even after ages. 
5. Finally I will just reproduce the calculation of $ 7 of the cited 
paper in the Ch. W. (p. 7—8), in which the identity of the methods, 
represented by the formulae (1°) and (2°), is proved. 
1) Cf also VAN DEK WAALS-KoHNSTAMM, p. 159 et seq. 
