1183 
Then © fd; taken over an arbitrary group of elementary regions, 
is the probability that the system lies in one of them; when this 
group is now chosen so that the interval syn corresponding to it 
becomes equal to the M-fold of that of the group of a system of V 
molecules compared with the group, evidently : 
(SA IG) un = (ZVidGi)n 
Le 
As the interval Ae of & may be chosen so small that ae it 
may be put, the argument of the logarithm in (35) may be put 
constant in the summation extended over a group. 
In this way we get: 
Sun = — kE fiuNdG arn log (fiun €Giun ) —klog (MN)! — klog (p UN) = 
iM 
—k& fid: log ae [dG] i) 
—kMNlog M—kMN log N + kMN—kMN log p= — KM fd; log (f;dG;) 
+ (MN log MM). (Efi dG) + ete. = 
(as 2fidGi= 1) 
— AME f; dG; log (f,dG;) — kMN log N + kMN — kMN log p = MSy, 
which we have now derived from an expression depending only on 
the product MN, which expression we had, of course, to treat 
differently, as far as M/ and N are concerned. 
Prof. Lorentz, whose communication ““Opmerkingen over de theorie 
der eenatomige gassen”*) induced me to take up the treated problems, 
points ont to me, among different valuable remarks, for which I 
am greatly indebted to him, that [ have now indeed demonstrated 
that my formulae may be considered as convenient precepts for the 
caleulations for the thermodynamic probability of the gas, but that 
I have not yet explained how through the consideration of the gas 
alone they could be derived, in particular why after all it is in this 
case necessary to divide by N/. This is a difficult question. In some 
connection with it is what follows: 
We have seen that a di-atomic gas, the molecules of which consist 
of perfectly equal atoms, at higher temperatures must have a &: log (2) 
smaller entropy than when the atoms are different. Must not the 
specific heat of the gas then have a different course in the two 
cases at low temperatures, and how could this be accounted for? 
1) H. A. Lorentz, Zittingsversl. Akad. Amsterdam, 23, 515 (1914). Not yet 
translated. 
78 
Proceedings Royal Acad. Amsterdam. Vol. XVII. 
