254 
obtained is a possible position for the centre of the second ellipsoid, 
and in any of those positions all orientations of the axis of revo- 
lution of this ellipsoid are possible. Calling v. the volume enclosed 
by the outer distance surface thus obtained, then the above volume- 
=| possibilities. 
dv, 
Along the normal to each point of the ellipsoid mark off a distance 
6 (equal to half the minor axis), we thus obtain a surface within which 
no centre of another molecule can lie. We shall call this the ner 
distance surfuce, and designate by v, the volume which it encloses. 
In the shell enclosed between these two distance surfaces the centre 
of the second ellipsoid can be placed, but then all u orientations do 
are not possible, but only a portion of them, which can be deter- 
mined in the following fashion (Fig. 3). Let A be the first ellipsoid 
which we shall regard as immovable. Let ? be a point of the shell 
determined by the coordinates relative to A: X in the direction of the 
elements give rise to zw {1 - 
Fig. 3. 
axis of revolution, y in the direction perpendicular to it. Now place 
the second ellipsoid with its centre at P, and, keeping its centre 
fixed, allow it to roll on the surface of A; during this rolling the 
point of contact & describes a trace on the surface of A. We can 
write for the solid angle of the cone which is described during the 
rolling by the semi-axis of revolution, PQ, 2 ag if the ellipsoid is 
prolate, 22 (1— y) if oblate, in which g is a function of x and y; 
there are then w(l—g) orientations do possible for the ellipsoid 
jee 
dv, 
B with its centre fixed at P. Altogether we shall have xur 
cases, where 
B= 2; + fede. ENNE fics 
the integration being taken throughout the shell. 
