550 The Genesis of Double Stars 
A real star radiates heat, and as it cools it shrinks. Let us 
suppose then that our ideal star also radiates and shrinks, but let 
the process proceed so slowly that any internal currents generated 
in the liquid by the cooling are annulled so quickly by fluid friction 
as to be insignificant; further let the liquid always remain at 
any instant incompressible and homogeneous. All that we are con- 
cerned with is that, as time passes, the liquid star shrinks, rotates 
in one piece as if it were solid, and remains incompressible and 
homogeneous. The condition is of course artificial, but it represents 
the actual processes of nature as well as may be, consistently with the 
postulated incompressibility and homogeneity*. 
The shrinkage of a constant mass of matter involves an increase 
of its density, and we have therefore to trace the changes which 
supervene as the star shrinks, and as the liquid of which it is com- 
posed increases in density. The shrinkage will, in ordinary parlance, 
bring the weights nearer to the axis of rotation. Hence in order 
to keep up the rotational momentum, which as we have seen must 
remain constant, the mass must rotate quicker. The greater speed 
of rotation augments the importance of centrifugal force compared 
with that of gravity, and as the flattening of the planetary spheroid 
was due to centrifugal force, that flattening is increased ; in other 
words the ellipticity of the planetary spheroid increases. 
As the shrinkage and corresponding increase of density proceed, 
the planetary spheroid becomes more and more elliptic, and the 
succession of forms constitutes a family classified according to the 
density of the liquid. The specific mark of this family is the flatten- 
ing or ellipticity. 
Now consider the stability of the system. We have seen that 
the spheroid with a slow rotation, which forms our starting-point, 
was slightly less stable than the sphere, and as we proceed through 
the family of ever flatter ellipsoids the stability continues to diminish. 
At length when it has assumed the shape shown in Fig. 2, where 
the equatorial and polar axes are proportional to the numbers 1000 
and 583, the stability has just disappeared. According to the general 
principle explained above this is a form of bifurcation, and corre- 
sponds to the form denoted A. The specific difference a of this 
family must be regarded as the excess of the ellipticity of this figure 
above that of all the earlier ones, beginning with the slightly flattened 
planetary spheroid. Accordingly the specific difference a of the family 
has gradually diminished from the beginning and vanishes at this 
stage. 
1 Mathematicians are accustomed to regard the density as constant and the rotational 
momentum as increasing. But the way of looking at the matter, which I have adopted, 
is easier of comprehension, and it comes to the same in the end. 
