270 
(44) and (45) the deduction of the distribution in the state of equi- 
librium and the calculation of the entropy are mutatis mutandis made 
as in § 5. We shall give only the following results : 
The number of pairs of molecules with freedoms dr, d0,, d6,, dp 
is obtained from 
nu 7 sin Ô, sin O,drdd,d,dp 
N41 — nae é En dv, e . 5 (49) 
v 2 
on division by 2. 
From 
hm /2:hBy he Hu) 7 *sin® sind ,drdO dO dp i 
IS ze) aa wil tT" ae ay ae (50) 
it follows that the distribution of the velocities (including qg, and 7;) 
is independent of the position of the molecules relative to each other. 
We also find that 
n (hm 2 hB, n —hu nn 
Mja 1—-. ie dv,dw,dq,,drr,, +» (51) 
Qa) Qn v 
in which 
Tee 
Pe UM es ’ 9? sin 0, sin O,drd0,dO,dp,. . . (52) 
7000 
where the summation with respect to 7, 0,,0,, has been replaced 
by a corresponding integration. 
Macroscopically the distribution throughout space is uniform. 
Elimination of 4 from 
kol Aaen Leip Ze 
= nk v ——nkplnh ‘Phu + —kp —P— kp—.— 
8 nkp ln 5 v 5 eS Er En 
and (53) 
Dn 18de 
dn te 
in which 
<u QT 
1 —huy) NS 
=) e u, r'sin0,sin0,drd0,d0,dp . . . … … (54) 
¢000 
gives the canonical equation of state. 
1 
From (53) we again obtain 7 = -—. 
kph 
The specific heat at constant volume in the AvocGapro state, y-a, 
