( 861 ) 
and accidental deviations in the several causes not a system of exactly 
the energy «, will be produced, but one of the energy ¢; in general 
(¢, — 8) will be small in comparison to ¢,. Positive as well as negative 
deviations will occur. 
If we now construct a real system by trying to give the energy 
é, to N systems or by choosing N systems of this kind in nature, 
we shall suppose that the probability that a system of the energy 
&, + «’ will be chosen is as great as that for the one with the 
energy ¢,—e’; a hypothesis which will be plausible as long as «’ 
is small. If the hypothesis is right, it may easily be shown that the 
canonical ensemble will play a part in the definition of the proba- 
bility of a system. 
In analogy of other cases (e.g. the law of errors) it seems admis- 
sible to suppose that in a real ensemble the number of systems 
whose energy lays between ¢ and e+ de can be represented by 
Wave CHa de. hy ne) ae, Head LE) 
It is not possible to prove this formula as long as we know nothing 
about the way in which the energy is supplied to the systems, or 
in which the energy «, of the systems chosen from nature is 
determined *). 
If we form hypotheses on this subject we can deduce (15), but 
much importance should not be aseribed to such a deduction. *) 
Proceeding further in the same way as in the case of the micro- 
canonical ensembles we find for systems in the real ensemble which 
are represented in each layer between e and e + de a homogeneous 
distribution. 
1) If we suppose that the ensemble is constructed by choosing the systems from 
nature, the measurement of energy will be subjected to an error, the aualogy with 
the law of errors therefore is still more obvious. Only we have now the difficulty 
that we do not know in what distribution the different systems of a certain energy 
appear in nature. 
2) To give an example take the following case. From a recipient of infinite 
energy, the energy is supplied to N systems. Equal portions z are supplied to a 
total amount of Nx portions to the systems of an inilial energy 0. The supply of 
energy takes place in Nx distributions. In every distribution one system is taken 
from the N systems, the energy « supplied to it, and the system replaced among 
the others. This is Nx times repeated. It is evident that in a definite case not 
each system has obtained the energy z=, but it is possible to indicate the 
number of the systems containing an energy between #'z and (n'—1) z. If the 
mentioned process is repeated several times, one distribution will be the most 
probable or most (frequently occurring) among all the possible distributions and 
this will be that for which (15) expresses the number of systems obtaining an 
energy between e and e+de. If z is infinitely small, we can be sure that the 
real ensemble obtained will be the ensemble characterised by (15). 
