( 814 ) 
If it is natural to use the line-ensemble for the definition of the 
probability of a rea! system, we see by the preceding discussion 
that the energy space-ensembles are also natural for this purpose. 
It may be noticed that in all those ensembles the majority of the 
systems are equivalent for observation. If we take the probability 
equal for all those equivalent systems, we find a large group which 
have a greater probability than all the other systems of the ensemble 
§ 3. Let us consider the velocity in some speeial cases. We have 
found for the velocity 
(py + gy’). 
7 
ee 
l 
Suppose that the kinetic energy gets the form 
m “8 veh : 
Ep = = ms qa 5 PF a . . ° ° : F (13) 
then we have 
oO n / Of 2 
es | 53, 
== Ey Tiel 5 ) . . . . . . (14) 
m 1 Od, 
; hey : 
Let us begin with the case that ~ material points are enclosed 
within a given volume. We assume that the points do not exercise 
any mutual action, that, however, the walls of the vessel repulse 
them with forces which become infinite when a point has penetrated 
a very short distance @ into the wall. Within the vessel up to the 
walls the forces are neglectable. The points will move into the 
walls until their kinetic energy has been exhausted; they then 
possess a finite potential energy. During a collision with the walls 
Dei 
( is very great in comparison to the potential energy. 
ag, 
. "ds ae 
il nisl == cf S= CA 
» 
ee 
the integral taken thus over the path of the system, 7’ is the time which the 
representing point requires to get round the trajectory. 
In the second place the path can be open, the time 7 becomes then infinite; 
we have to restrict ourselves to the formula (10). If, however, the path returns 
to the initial phase in a time 7” without exactly reaching il, it is possible that 
always after the period 7” the same phases are approximately reached. In this 
case w the probability of the phase might be defined by the equaiion : 
or 
