de 
Keer, 
Let us now consider a layer between the spaces Fo fore and 
Ean for e+ de as the values of the energy, and let us divide 
this layer on the following way in elements. If P is a point in the 
space Po, 1 and ZL the path of the system through the point, 
Ra, perpendicular to L, we shall take in the section of 2,1 
and Ro, an element do and draw the trajectories through the 
limits of it, let now further P’ be a point on the path Zand A's, 
a space perpendicular to L, in this space an element do’ is formed 
by the trajectories. Now at the points of do and do’ we construct 
the normals on ZZ», 1, these lines cut /’s,-;, and in this manner 
there are formed (27—1)-dimensional space elements of the volumes 
Ado and A’do’; the distance of the space /o,—; and L’s,—; at the 
points P and /” respectively is designate by 4 and 4’. In the time 
dt all the systems cross the elements which are situated in the volumes 
vdoAdt and v’do’L’dt. But Lrouvitirs’ theorem teaches us that these 
volumes are equal, therefore: 
do Kvz=do Au. 
Taking into account the relation (9) we find: 
And do' de 
do — do' . 
We must now suppose that the space between 4%, and /’s, is 
filled everywhere with a homogeneous density @2,; in this way 
the microcanonical ensemble of Gress is constituted. In an element 
of the layer dofds lie @2,do4ds systems, ds is an element of length 
of the path £. The last expression can be transformed into 
do ds 
Oon de ——_. 
5 
If we let now de approach to O and e@»,de = A remains a finite 
constant, we find in the limit a distribution in the space /,—, with 
the density Q2,—1 
Therefore the energy space-ensemble is the limit of the micro- 
canonical ensemble. 
‘By the probability of a system I understand the number of systems 
in an element of volume that surrounds the point representing the 
system under discussion, divided by the total number of systems 
in the ensemble. 
We shall represent this probability by w, suppose w, and w, to 
