( 863 ) 
ad” ple 5 : 
(=>) does not follow as far as I can see from the physical 
250 
signification of these quantities *). 
8 a faye) y—! 
Graas has proved that the quantity alte has properties corre- 
0 
sponding with those of temperature. The mentioned quantity, however, 
has a definite value for a given value of the energy £,, so the 
modulus of the canonical ensemble used has to be put equal to the 
oye ee E 
value of (55) . The ensemble defined by (15) and the canonical 
ensemble (18) deviate slightly from each other, but these deviations 
are of less significance the greater the number of degrees of freedom 
is. The deviations are most important for those systems of which 
the energy ¢ is such that (e«—e,) is large in comparison to ¢,, but 
suchlike systems are very infrequent in both ensembles. We can 
without fearing errors in our results suppose the real ensemble to 
be a canonical one, and if we further suppose that in the real 
ensemble the distribution in every layer is homogeneous, we find for 
the probability of a system in the real ensemble 
a 
oo DY Bios OG = Teln ar NP Veda ts (19) 
The identity of the real and the canonical ensemble is no more 
fully proved or to be proved completely than that of the micro- 
canonical or energy-space ensemble. It exists in this respect that the 
number of systems in the layer ¢...¢-+-de can be represented by 
J (ede, f(e) being a maximum for «= gs,, as well for the real as for 
the canonical ensembles; in the microcanonical ensembles without it 
F(e&)=9, to a certain degree the latter ensembles have therefore less 
physical sense than the canonical, provided that we do not take as 
startingpoint the single system and with it the time-ensemble, but take 
into account that a given system has a not totally definite energy. 
§ 6. Hertz has developed in the paper mentioned considerations 
about the theorem that two systems of equal temperature produce 
1) Gress has proved (Chap IX (350)) that we have the relation 
é 2) 1 
el =, 
In the real ensemble (15) the mean value (e—<,)? is equal to 2k, therefore in 
the real and the canonica! ensemble the mean value of the squares of deviations are 
equal 
