251 
from which with ae it follows that 
it 
s 3 
SSS — log 2 - > oy eh—— + — —w0*. 
wu ni ene 0de v 4 7 Ode h EN, RE n ei 
Using (12) and the ae ep = ey a se hk is the gas con- 
stant for the quantity under consideration, this equation is trans- 
formed into 
dw. RT 
3 
w= —RT log, v — te er ne en Retire CG 
. Bes 
in which 6, has been written {or = Sa ao’ and a linear function 
nd 
of 7 has been omitted. 
€ 
From this equation one obtains the value = R for the specific 
heat at constant volume, while the thermal equation of state becomes 
dT: Der re 
Ca ee | 
v v 
Hence (cf. § 1) 
eg a ee oe eee 
§ 4. The virial-coefficient B for rigid ellipsoids of revolution subject 
to VAN DER WAALS attractive forces. 
Determination of the macro-complexion. 
We shall first assume that in collision between two ellipsoids the 
speed of rotation around the axis of revolution can also vary. To 
make sure that HAMILTON’s equations are sufficient to determine the 
mutual action of two such ellipsoids (ef. also p. 248 note 3) we 
shall make it essential that the surfaces of the colliding bodies which 
we are considering can never exert other than normal forces upon 
each other at their point of contact. We shall, however, assume that 
it is found on closer investigation that the surfaces of the ellipsoids 
are not perfect surfaces of revolution but show, it may be, a uni- 
versal wave-formation; but in the meantime we shall assume that 
deviations from the true shape of an ellipsoid of revolution are so 
small that they may be altogether neglected except in so far as they 
give rise to a moment around the “axis of revolution” during colli- 
sion. Hence in formulating the condition that the energy has a given 
value, we shall also have to allow for the speed of rotation around the 
axis of revolution. To express that condition, then, it is desirable to 
determine the macro-complexion as was done in § 3 and also 
with respect to the speeds of rotation around the three axes of 
‘ivf 
Proceedings Royal Acad. Amsterdam. Vol. XV. 
