HOL 
can take part in the reaction. The r’s are necessarily whole numbers, 
some of them must be negative. 
We will imagine the molecules to be built up of atoms «,...4@;...a, 
in such a way that the chemical formula for the xt? molecule is 
B Yard ander Herpen Ter et VB) 
the numbers 4, being positive whole numbers or zero. 
We will first treat the case that the system has so great a volume 
that the mutual action of the molecules may be neglected in the 
expression of the energy. 
The state of the system can be characterised by the coordinates 
of the centres of gravity of the molecules and the corresponding 
moments of momentum and by a certain number of internal coor- 
dinates and moments of momentum. The expression giving the energy 
of each molecule consists in the kinetical energy of the centrum 
of inertia, a quadratic expression in the moments of momentum of this 
centrum, the coordinates of the centrum of inertia not playing a part. 
Further in the energy corresponding to the internal coordinates, 
which [ shall represent by «, An element of the extension in phase 
corresponding to the internal coordinates of the «th molecules will 
be represented by ds. Be the mass of the molecules m,. 
Be the total number of systems of the ensemble J, the statistical 
free energy W. 
We now want to know the number of systems (2”) in this en- 
semble, for which n,...7,...n; molecules of the different kinds 
are present in the volume V. That is to say those molecules produ- 
ced by a completely specified combination of atoms, for which the 
internal coordinates and moments are situated in completely determined 
elements dÀ,...dà,...dà. As for the situation of the molecules 
within the volume V, and the moments of momentum of the centres 
of gravity, we will not apply any restricting conditions’). We 
find for 2” 
n, -= nN, 
" — Ne aa (2m) e ze TE ERE (3) 
The number of systems in which no restrictions are applied not 
even for the internal coordinates and moments is obtained by inte- 
grating over the d's with respect to all possible values. 
We now put 
tee 
1) Comp. for the case that one should want to specify for these quantities also, 
my diss. p. 39, where the case of non-reacting molecules is treated. 
