269 
3 
—_ NT 
ele aL) EE as was done in $ 5. Doing this in turn for the 
U, 
other pairs of molecules, we finally obtain 
3 
n! t=n,—1 Ee 
een ee | 1, 
Miia! Mii! ++. do c= dv, 
Kata! 
nm! rt sin Ô, sin 0, dr dO, dO, dp\ 2 
en | ee — : (46) 
7,949 "11 2 dv, 
2 101 
pees 
27 (2) 
where JZ indicates that the product must be taken for all freedoms 
7,929 
(elements in a corresponding space) determined by 7, 6,,0, and p 
respectively. The notation of this expression has been simplitied by 
omitting the index which is used to indicate the special freedom 
(dr dô, dO, dp) except in the notation referring to the number of 
molecules. From (46) we obtain (ef. §5 for the omission of terms) 
4 
— rr 
: ned 
loge W = — marys loge Puma — Uun loge n mm +++» — = EE 
dy. 2 dv, 
Ni), my Ni; r° sin Ó, sin O,drd, d.d 
£33 [2 mam EDT 
dv 76,6 2 2 2dv, 
Changing the sign we obtain an expression for the BOLTZMANN 
Ai-function for this system. 
The equilibrium state: 
The energy condition gives 
u= LVL (Mae tM +...) uw + LY LY mn ws = const. (48) 
dv 
dw dv r0,0,p 
where 
Ul = km (8,° + n° + ¢6,’) + 4 Be (qr? + 71’) represents the kinetic 
me? : ; 
and up = — (2 cos 0, cos 0, + sin, sin O,cosp) the potential energy 
pn 
m is the mass of a molecule, B, the moment of inertia around an 
axis perpendicular to the axis of the doublet, and 1, the moment 
of the doublet. From the condition for a maximum value of log, W, 
together with the conditions (48) and n == const. and the equations 
18* 
