De 
WY k k 
0 ow) Vann @)\ Ny. 
es I] ( Nx) ) =) (=) 
Introducing the function », we obtain for § 
¥ ; Ser 
EE ve? PA 5 ie ms a, Il (2270 =. i Lal e 
The volume being given, the function wp is a function of the 
densities n,, for 
wy? k 
ore n,.. nz) — log ni} = 
k 
V & {n, log w (n, .. ny. . nj) — log n,} 
1 
3. We shall use the form now given to § to put the question of 
probability of deviations in such a form that the deviations of density 
appear from our formulae. We then have to examine for which 
values of the densities /oy$ will be a maximum. Suppose n,) to 
represent these values and gy. to represent the deviations of densities 
for other systems, then 
l 
DS) Ox = 0. 
1 
For dlog& we have 
1 lk OW) 1! Ow, 
dS log§ = ——| YF — Oy, = pie ee 
oe ak 7 On, *” TZ dnp? a 
Sell if - 91 a The 8 te 
DES Tr 102) 
As conditions of equilibrium we now find 
OP ee igh erotic, be Den KT suka ee 
On, F 
Further 
1 ! fd, d'u» 
ne Ni .2— 402) ot 0 . : 8 
Za ln zen + Òni, na, ~ en | ge ©) 
l 
yy", "hi 5 
ze EE Art LI | —— Hp) el) ie „ra | = Zt epee n 
the quantity v being an additive constant without any physical meaning; =y* , 
however, being connected with the difference of free energy from the zero state 
defined spare! 
