168 
X+ Y+Z) atoms, and therefore by a ‘“y-point” in a 6(X+ Y+Z)- 
dimensional “y-space”’. To a given condition of dissociation (N,, N,....Vj) 
of the gas-mixture, owing to the assumptions II ($ 1), a sub-space 
corresponds of 2 # dimensions, where 
ai] 
FE Nifi sve to ow 
1 
fr as before being equal to 3, 5, or 6 according as the index 7 
refers to molecules of one, two or more atoms (comp. eq (7). 
We must now consider more in detail the structure of this 
sub-space. 
Consider an individual “phase” of the system (any point y, of 
the y-space); the X + Y-+ Z atoms, which we shall provisionally 
think of as being individualized by numbers attached to them, are 
associated to MN molecules, which we shall also suppose to be indivi- 
dually numbered. The total energy of the system then also possesses 
a definite value 4. We now apply to the phase of the system 
changes of two types (A) and (4)'), which both leave the dissocia- 
tion (N,, NV,,..., Ns) and the total energy unchanged. 
Changes of type [A]. Starting from the initial phase y, we make 
the molecules independently of each other, pass through the total 
volume V7?) and all possible rotational orientations, and also make 
them assume successively all possible velocities of translation and 
rotation, which are in accordance with the original total energy. 
While in this manner the y-point starting from y, describes a 
region (A,) of the y space, the u-points of the various individual 
molecules — each in its own u-space — describe the regions which 
were discussed in § 2. In the classical theory the “y-volume” is 
obtained in cases of this kind by taking the product of the corre- 
sponding “gp-volumes”’. Analogously we shall here define the y- i: 
fvi4) of the region just mentioned by the relation 
Thee nn 
1 
where for {u;} we have to take the expressions (4), (3), or (2) of 
§ 2 according to whether 7 corresponds to a molecule of one, two 
or more atoms. The limits of the integrations over the momenta 
See Rene in (16) are determined by the fact, that on account of 
I) Comp. the somewhat similar discussion in P. and T. EHRENFEST, Math. Enc. 
Bd. IV. Art.432, § 12 6. 
2) The volume-correction which is due to the finite dimensions of the molecules 
is left out of account. 
a 
