165 
_(Sackur) or (NI)! (Terrropr I) can be forced into the “thermody- 
namic probability W” in order to obtain an admissible value for 
the entropy. The law of dependence on N can only be satisfactorily 
settled by utilizing a process in which N changes reversibly and then 
comparing the ratios of the probability with the corresponding differ- 
ences of entropy. 
If condensation and evaporation (Stern and Terroper II) are not 
to be used, and the whole process is to be carried out with gases, 
it will be necessary to work with a gas-mixture and change the 
mamversvoy;- molecules N,, N,,..... N; of the various gases by dis- 
sociation. 
Remembering the real object of the calculation of the chemical 
constants, viz the deduction of the dissociation-equilibrium, the follow- 
ing formulation of the problem is finally arrived at: Consider 
X, Y,Z,.... atoms of different elements contained in a volume VV 
and possessing an energy /. These atoms can unite to molecules 
of different kinds in a large number of different ways. Determine 
by means of the quantum theory directly, which of the various states 
of dissociation possesses relatively the greatest probability. 
This problem is to be solved by methods belonging to statistical 
mechanics and the quantum-theory which will be set forth in § 2 
and § 4. On comparing the dissociation-equations arrived at in this 
manner with the corresponding thermodynamical equations values 
are obtained for the expressions containing the chemical constants 
which occur in the latter (§ 6). 
Our method: removes, as we hope, any remaining obscurities as 
regards the occurrence of N,! N,!.... This could only be accom- 
plished, as it appeared to us, by not stopping at the numbers of 
the molecules in the combinatory computations, but by going down 
to the atoms. This is the only way of obtaining a solid common 
basis for the computation of the relative probability of different 
states of dissociation (variations of the numbers of molecules N,, 
N,,...N;), viz. the phase-space of 6(X + Y + Z) dimensions (§ 4). 
The introduction into the combinatory calculation of this refinement, 
viz. the consideration of the atoms, confirms a result already attained 
by Terropr (ID): the factor which depends on the permutation of 
the atoms of the same kind 
MIX LZ! 
ING PN las ING ASG, +" Ostia 
(comp. e.g. (18) 
1) Comp. § 9. 
4) Comp. § 8. 
11* 
