261 
lecules, do not influence terms of the first order of small quantities. 
By treating all the pairs of molecules contained in dv, in the same 
way, and then all the pairs of molecules in dv, ete., we obtain for 
the number of micro-complexions in the group macro-complexion 
4 
aE" 
n! t—=n— 1 3 
w= x" ee TS ENT ii Sat 71 | eg mie 
Rnd teen Riga Lena tl dv, 
jn 
Se aoe Anr dr 2 
: (ES erat MT ak 
Vv, 
5 Dial 
ET (2 N16) } 
Retaining the principal and first order terms in the expression for 
loge W, and abandoning higher orders of small quantities. as well as 
all terms which remain constant under all the considerations involved, 
we obtain the expression 
4 3 
2 3 TT 
loge W==— la loge Nila — nur loge N11b1 «+» -— =) — 
5 dv, 
nlsl ll, chen 
PP ee Bar ioe = ere) 
dv dr 2 dv, 
If the sign of this expression is changed, it becomes a form of the 
Bottzmann H-function for this case. 
The state of equilibrium: 
Let us write — g(r,) for the potential energy as dependent upon 
the mutual forces exerted by a pair of molecules at a distance 7, 
apart, and let us assume that for separating distances greater than 
rt the potential energy of a pair of molecules may be taken to 
be =0; we may then write the energy condition in the form 
eS Sn var} on servi oF, == Comat: Fe vec (BO) 
dv dw r 
(for the significance of w#1 cf. $ 3 
The condition that logeW is a Ae together with this equation 
(28), and the condition » = const, and equations (24) and (25) give 
— RT? 
——— — huty) + loge ce == 0 
dv, 
4 , 1129) 
4nr,*dr, 
+ £ loge nin +4 loge EI Sn 
1 
— loge Nia —N, 
—loge 21141 TU 
1 
—uwl—h {sg(r,)} + loge € = 9 
