252 
inertia, pr, qr, Fr, in which p, represents the speed of rotation around 
the axis of revolution. 
The group macro-complexion is now determined by specifying that 
N,,, unspecified molecules are present in dv, dw, dw. 
Nan $5 En 2 er RE EN A EED 
in which dw: represents an element of the space involving the 
coordinates p,,q:, and 7,; these elements are also assumed to be equal. 
Determination of the micro- 
complexion : 
For this it is necessary to spe- 
cify the position of the ellipsoid. 
To do this choose a fixed system 
of axes XYZ, and through the 
“origin draw a line OA parallel 
to the axis of revolution; we shall 
determine the position of the ellip- 
soid by the angles AZX — gp, 
AOZ = 6 and the angle 2 
between the plane AOZ and a 
fixed meridian plane of the ellipsoid (Fig. 1). 
Angular momenta: We may represent the kinetic energy of rota- 
tion, Li, by the formula 
Fig. 1. 
Lp App? Fe Belge + 7e), ee oe 
in which A, == the moment of inertia about the axis of revolution, and 
(in == ef es Dye es fe » an equatorial axis. 
We shall choose the equatorial axis to which q, refers, OB, in 
the plane AOZ, OC perpendicular to OA and OB in such a 
direction that a rotation from A towards B seen from Cis in the 
same direction as a rotation from X towards Y seen from Z. 
It is seen that 
Pr =p cos 0 + ¥ 
gepaint A We EE 
ek 6 
in which the dots represent differentiation with respect to the time. 
If we call the angular momenta with reference to p, 9, x, D, 5, ri 
respectively, we then obtain 
p= A, cos0.p. + By sin @. Qi, 
6=— Br, Sees ME 
= Ar Pros 
in which p,, gr, and r, have the values given in (17). 
Instead of determining the micro-complexion by dp dO dx dy de dy 
we shall introduce a slight modification. From (18) we find 
