The shape of a mass of rotating liquid 549 
an ideal star, which resembles a real star in the fact that it is formed 
of gravitating and rotating matter, and because its shape results from 
the forces to which it is subject. It is unlike a star in that it possesses 
the attributes of incompressibility and of uniform density. The 
difference between the real and the ideal is doubtless great, yet the 
similarity is great enough to allow us to extend many of the con- 
clusions as to ideal liquid stars to the conditions which must hold 
good in reality. Thus with the object of obtaining some insight into 
actuality, it is justifiable to discuss an avowedly ideal problem at 
some length. 
The attraction of gravity alone tends to make a mass of liquid 
assume the shape of a sphere, and the effects of rotation, summarised 
under the name of centrifugal force, are such that the liquid seeks 
to spread itself outwards from the axis of rotation. It isa singular fact 
that it is unnecessary to take any account of the size of the mass 
of liquid under consideration, because the shape assumed is 
exactly the same whether the mass be small or large, and this 
renders the statement of results much easier than would otherwise 
be the case. 
A mass of liquid at rest will obviously assume the shape of a 
sphere, under the influence of gravitation, and it is a stable form, 
because any oscillation of the liquid which might be started would 
gradually die away under the influence of friction, however small. 
If now we impart to the whole mass of liquid a small speed of rota- 
tion about some axis, which may be called the polar axis, in such 
a way that there are no internal currents and so that it spins in the 
same way as if it were solid, the shape will become slightly flattened 
like an orange. Although the earth and the other planets are not 
homogeneous they behave in the same way, and are flattened at the 
poles and protuberant at the equator. This shape may therefore 
conveniently be described as planetary. 
If the planetary body be slightly deformed the forces of restitution 
are slightly less than they were for the sphere; the shape is stable 
but somewhat less so than the sphere. We have thena planetary 
spheroid, rotating slowly, slightly flattened at the poles, with a high 
degree of stability, and possessing a certain amount of rotational 
momentum. Let us suppose this ideal liquid star to be somewhere 
in stellar space far removed from all other bodies; then it is subject 
to no external forces, and any change which ensues must come from 
inside. Now the amount of rotational momentum existing in a 
system in motion can neither be created nor destroyed by any 
internal causes, and therefore, whatever happens, the amount of 
rotational momentum possessed by the star must remain absolutely 
constant. 
