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 is a 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 then a 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. 



