computed from the
observations, but it must not be accepted as the calculated form of such
a system. I have moreover proved more recently that such a figure of
homogeneous liquid is unstable. Notwithstanding this instability it does
not necessarily follow that the analogous figure for compressible fluid
is also unstable, as will be pointed out more fully hereafter.

Professor Jeans has discussed in a paper of great ability the difficult
problems offered by the conditions of equilibrium and of stability of a
spherical nebula. ("Phil. Trans. R.S." Vol. CXCIX. A (1902), page 1. See
also A. Roberts, "S. African Assoc. Adv. Sci." Vol. I. (1903), page 6.)
In a later paper ("Astrophysical Journ." Vol. XXII. (1905), page 97.),
in contrasting the conditions which must govern the fission of a star
into two parts when the star is gaseous and compressible with the
corresponding conditions in the case of incompressible liquid, he points
out that for a gaseous star (the agency which effects the separation
will no longer be rotation alone; gravitation also will tend towards
separation... From numerical results obtained in the various papers of
my own,... I have been led to the conclusion that a gravitational
instability of the kind described must be regarded as the primary agent
at work in the actual evolution of the universe, Laplace's rotation
playing only the secondary part of separating the primary and satellite
after the birth of the satellite.)

It is desirable to add a word in explanation of the expression
"gravitational instability" in this passage. It means that when the
concentration of a gaseous nebula (without rotation) has proceeded to
a certain stage, the arrangement in spherical layers of equal density
becomes unstable, and a form of bifurcation has been reached. For
further concentration concentric spherical layers become unstable, and
the new stable form involves a concentration about two centres. The
first sign of this change is that the spherical layers cease to be
quite concentric and then the layers of equal density begin to assume
a somewhat pear-shaped form analogous to that which we found to occur
under rotation for an incompressible liquid. Accordingly it appears that
while a sphere of liquid is stable a sphere of gas may become unstable.
Thus the conditions of stability are different in these two simple
cases, and it is likely that while certain forms of rotating liquid are
unstable the analogous forms for