1055 
It would have been better, it seems to me, to divide the ““thermo- 
dynamie probability”, which does not represent the originally meant 
probability at all now, also by V/, as Trrropr did for the denominator, 
by which property (3) is also satisfied. 
Instead of the numerator, Lorentz uses the denominator in his 
above-mentioned article. It may be represented by: 
Sees 
(2x Ein)? „2amovN 
OL dE. 
dV. nae: 
Now 2 represents the function — introduced by Gisps, of which 
: 
the dog forms one of the three functions for the entropy given by 
Gipps (viz. ). If we now still divide by g\, and if we omit the 
terms which do not contain N as a factor, we get again PLanck’s 
formula for S= k log P. 
Terrope makes use of another function introduced by Gusss’). 
This function (V) does not represent the extension of the microcanonic 
ensemble, but the total extension below the / in question. We now find: 
EN 
V (22 Em)? .oN 
) “ren 
while FrrropE now puts: 
S=k log gv. NT 
from which follows: 
S=klog}3 log (2 4 Em) + log v 
> 
3 log (3 N) — log N + & — log g} 
which formula differs from that of PrarcK in the term — log N, 3 
having taken the place of $. Property (3) is now satisfied without 
relor 
a special assumption having to be made about the elementary volume g. 
Now the vindication of the division by g\ and N/ is still to be 
discussed. As far as the former is concerned, that the dimensions 
are not in order is of course no reason to divide particularly by 
gÀ, which causes the result to depend on g, whereas it would 
otherwise be independent of it. 
When it has once been assumed that S— 4 log extension (either 
of the state of equilibrium alone, of all states at definite £ or of 
all states between 0 and £). the division by gqÀ may be justified 
by this that not a purely microcanonic ensemble must be considered, 
but a roughly microcanonic one, in which elements of certain 
1) H. Terrope, “Die chemische Konstante der Gase und das elementare Wirke 
ungsquantum’”’. Ann, der Phys. 38 (1912), 
