gas may be stable. This furnishes a
reason why it is worth while to consider the unstable forms of rotating
liquid.

There can I think be little doubt but that Jeans is right in looking to
gravitational instability as the primary cause of fission, but when we
consider that a binary system, with a mass larger than the sun's, is
found to rotate in a few hours, there seems reason to look to rotation
as a contributory cause scarcely less important than the primary one.

With the present extent of our knowledge it is only possible to
reconstruct the processes of the evolution of stars by means of
inferences drawn from several sources. We have first to rely on the
general principles of stability, according to which we are to look for a
series of families of forms, each terminating in an unstable form, which
itself becomes the starting-point of the next family of stable forms.
Secondly we have as a guide the analogy of the successive changes in
the evolution of ideal liquid stars; and thirdly we already possess some
slender knowledge as to the equilibrium of gaseous stars.

From these data it is possible to build up in outline the probable
history of binary stars. Originally the star must have been single, it
must have been widely diffused, and must have been endowed with a slow
rotation. In this condition the strata of equal density must have been
of the planetary form. As it cooled and contracted the symmetry round
the axis of rotation must have become unstable, through the effects of
gravitation, assisted perhaps by the increasing speed of rotation. (I
learn from Professor Jeans that he now (December 1908) believes that
he can prove that some small amount of rotation is necessary to induce
instability in the symmetrical arrangement.) The strata of equal
density must then become somewhat pear-shaped, and afterwards like an
hour-glass, with the constriction more pronounced in the internal than
in the external strata. The constrictions of the successive strata then
begin to rupture from the inside progressively outwards, and when at
length all are ruptured we have the twin stars portrayed by Roberts and
by others.

As we have seen, the study of the forms of equilibrium of rotating
liquid is almost complete, and Jeans has made a good beginning in the
investigation of the equilibrium of gaseous stars, but much more remains
to be discovered. The field for the mathematician is a wide one, and in
proportion as the very arduous