( 539 ) 
where the numbers n, and n, have the values following from (VI). 
We now have 
dn,” 
Ya, a 
e = (297) (Meese) a n— hs 
e 
and therefore, using (13) and (14), we find for 4” 
U 3 k Ny Ey 
as 7 n Ne ye 
gn =(2%Om)*' "|| ( ) e hittin (XJ) 
n, 
9 
GaBBs showed that the quantity — defined by the equation 
ne XII 
Ne te OS 
a (XL) 
has the proporties of the entropy s. Here the quantity e is the average 
energy in the canonical ensemble; it is equal to the energy of the 
system of maximum frequency *). 
The kinetic energy of this system amounts to 
3 
—n@. 
2 
For the potential energy we have written 
k 
Ny &, 5 
l 
and the value of ¢ is therefore 
k 
= ee 
e=570+) ae ae 
2 
1 
For s we have the equation 
k 
anes 
pat Tog telog (2 a © m) Fn log np as 
3 : i 
= Const + = nlog O + ee ag 
Z 
3 w 
= Const + 5 nlog @ + fn log” de Subst hoot fe a ae ea RE EN 
n 
0 
1) GrBBs showed that the average energy in an ensemble is equal to the 
most common energy in that ensemble. Now not every system with this energy 
is equivalent to the system of maximum frequency, but the most common energy 
is-equal to the energy of the latter system, therefore the same is true for the 
average energy. This result may also be obtained by determining e directly by 
means of (VII). 
