408 Lord Kelvin on the Formation of 
the planets and satellites; but Sir George Darwin * has given 
the very important suggestion that the separation from a 
planet of material to become a satellite may in some cases 
have been a single portion of the mass, breaking away from 
what was earlier a rotating mass of liquid, in the shape of a 
figure of revolution, contracting by loss of heat, and there- 
fore rotating with greater and greater angular velocity as it 
became denser. 
§ 2-i. Suppose for example the mass which is now Earth and 
Moon to have been at one time a single oblate spheroid of 
revolution. Its figure would then have been exactly elliptic, 
if its rotational angular velocity, and its density, were each 
equal from surface to centre. If it was denser in the central 
regions, its figure would have been an oblate figure of revo- 
lution, but not in general exactly elliptic in its meridional 
sections. "While the spheroid shrinks in cooling it becomes 
more and more oblate, till, all round the equator, gravity is 
exactly balanced by centrifugal force ; or till the spheroid 
becomes lopsided, as suggested in § 25 below. Farther 
continued shrinkage cannot give a stable oblate figure of 
revolution. It might cause an equatorial belt to be detached 
from the main bodv ; or the result might be as suggested in 
§§ 25, 26, below. 
§ 25. Poincaire's ct pear-shaped " figure of equilibrium of 
a rotating liquid suggests the idea that the first instability 
produced by cooling and shrinkage, with constant moment of 
momentum, may possibly give rise to a stable figure with a 
protrusion on one side of the centre of what was the equa- 
torial circle, and a flattening of the surface on the other side 
of the centre of inertia. This idea is to some degree sup- 
ported by the elaborate and powerful mathematical investi- 
gations of Poincare t and Darwin + on <l pear-shaped " figures 
of liquids rotating in stable equilibrium, under the influence 
of gravity and centrifugal force. 
§ 26. Continued cooling and shrinkage would produce more 
and more protrusion on one side of the centre of inertia, 
* Phil. Trans. 1879, p. 447, " On the Precession of a Viscous Liquid 
and on the remote History of the Earth " ; Phil. Trans. 1880, p. 713, " On 
the Secular Changes in the Elements of the Orbit of a Satellite revolving 
about a tidally distorted Planet"; British Association Report, 1905, 
p. 3, Presidential Address. 
t H. Poincare, "Sur la Stabilite de l'Equilibre des Figures Pvri- 
formes," Phil. Trans. 1902. 
% Sir George Darwin, "On the Pear-shaped form of Equilibrium of 
a rotating Mass of Liquid," Phil. Trans. 1902 ; " On the Stability of the 
Pear-shaped figure of Equilibrium of a rotating Mass of Liquid," Phil. 
Trans. 1903; " On the Figure and Stability" of a Liquid Satellite/* 
Phil. Trpns. 1906. 
