4 
ASTRONOMY: G. F. BECKER 
lum then must be possessed of energy and moment of momentum, but 
I shall suppose its axis of rotation to stand at an angle to its greatest 
principal axis of inertia. 
Such a bacular nebula would pass through some of the phases famiHar 
to readers of cosmogony; energy would be dissipated by collisions; a 
part of the material would subside towards a central nucleus or several 
excentric nuclei; excepting for some outlying cometary detritus, the mass 
would tend to flatten in the invariable plane; and finally orbits of great 
eccentricity would or might be reduced by colHsions to an approximately 
circular form, while of course the moment of momentum would remain 
nearly or quite constant. The flattening of such a nebula and its rotation 
about the centre of inertia of the whole system are so nearly independent 
that the principle of superposition is applicable; the mass may be sup- 
posed to subside into its invariable plane without flexure of the axis 
of the baculum, and thereafter to rotate about a line perpendicular to 
this axis. 
The question then arises how the axis of a bacular nebula would be 
distorted compatibly with Kepler's third law if the orbits of the com- 
ponent particles were sensibly circular, or if eccentricities are neglected, 
only a first approximation being sought. 
In its simplest form Kepler's third law expresses the equahty be- 
tween the attraction of a heavy point on a particle moving in a 
circular orbit and the centrifugal force, or normal acceleration, of 
the particle. If co is the angular velocity of the particle, r its dis- 
tance, and M the mass of the heavy point, 
Here M may mean the mass of a system concentrated at its centre of 
inertia and it is easy to see that r may be replaced by the mean distance 
a, of a particle moving in an elliptical orbit. 
The law so expressed would be valid for the solar system, so far as 
two bodies are concerned, were it practicable to take the centre of 
inertia of that system as an origin; most astronomical problems, how- 
ever, involve not absolute but relative motions, and Kepler's law must 
then be modified by substituting If +m for For small planets m 
can be neglected because the sun's centre is then almost exactly at the 
centre of inertia of the system. 
If a system consisted of a single nucleus and a great number of minute 
secondary particles which, at a given epoch, were arranged on an axis, 
