1107 
For a gas the function / takes the form of the function considered 
above. We will not consider the form more closely now. This being 
observed, it will be easy to point out the changes which (11), the 
formula that gives the number of systems, will undergo. We find 
idd at 
od x 
| 220 
a En eert vom TTS = mn)? 3. BES) 
n, 
id (6) 
Asking again which is the most frequently occurring state, we 
find for the condition of equilibrium 
a 0 log f f : 
= wf -- log n, + 3 log (22 © m,) + log V —log 5, + 5 0e er 0 
Ny 
For the statistical free energy we find 
3 : ‘ 
Si 5 =n, 3 Zn, 
oO C f(Vn, woe My vee hey 0) Vv 1 in 1 
NAE Mee nytt CR 
the numbers 7,..7, relating here to the maximal system. 
alculating the pressure from 4” we find 
RT te Vial he y log f 
ly 
— = Nn, + 
BN RR 
where the terms again are zero on account of the condition of 
equilibrium. Like Prof. H. A. Lorentz in his “Abhandlungen” also 
Dr. Hornen uses the equation of state 
Rt: 
We a 
eee NTA 
(1 put it in molecular form), the term q then denotes the deviation 
from the gas-laws, the g there used therefore agrees with our 
ger 0 log f 
JS => r Aj — 
N ov 
log f may be given the form 
oo 
log f Sth oe eg 
(Te q dv 
ww Be de 
De 
where & is a function of temperature depending on the 7, also. 
Introducing this into (20) then 
3 00 iN ke dg 8 
> Vv, behan ds ie log (2.17@m,)+ log V —logs, + — a ps = | Peel i. 
n / L 1 Ull, 
¥ 
