255 
8 may be regarded as the mass obtained taking the volume con- 
tained within the inner distance surface as having unit density, 
and adding to it the sum of the volume-elements contained within 
the shell between the two surfaces, each multiplied by its own 
density ¢. 
ee 
dv, 
ways if one takes no account of the complication introduced by the 
approach of three molecules (cf. § 3). Finally we get 
The placing of the third molecule can be done in xuv 
! t= nl 
W = (xuv)” Sed fie, lege 
Nii DO LES 
Omitting constants this gives 
log. WSS SS Sn loden 2 Pare 
d. dw dw, dv 4 dv, 
Subsequent treatment of this problem differs from that given in 
§ 3 only in so far as the energy condition, under the same assump- 
tion as was there made regarding the potential energy, must now 
be written 
>>> ain 2 mn (5.°+-7,°+5,7) a 5 A;p,” ae 5 B, (qr a) en 
de dw dw, 
te 
wo tw 
ed 2 ; 
dv N dv, 
GOOSE Tap te tet Ree 
The result then follows that the specific heat at constant volume 
for these rigid (but not smooth) ellipsoids is 3/7, while as regards 
the thermal equation of state equation (14) gives the value of B if 
we substitute d 
b ant (21 
Wer re et (2) 
As far then as concerns the term with the virial-coefficient B, 
we find the same equation of state as for rigid spheres’), only with 
the ellipsoids, 6, is not such a simple funetion of the volume of 
the molecules as with rigid spheres. 
We shall now introduce the assumption that the ellipsoids are 
perfectly smooth, so that the velocities of rotation around the axis 
of revolution undergo no change on collision. We shall also assume 
that the attractive forces cause no modification in these angular 
speeds. In that case it is not necessary to allow for the value of 
1) This may be regarded as a particular case of the general proposition indicated 
by Botrzmann (Gastheorie IL §61), for molecules which behave as solid bodies 
of shape other than spherical, 
