oses the liquid forming the cylinder to shrink in diameter, just as
we have done, and finds that the speed of rotation must increase so as
to keep up the constancy of the rotational momentum. The circularity of
section is at first stable, but as the shrinkage proceeds the stability
diminishes and at length vanishes. This stage in the process is a form
of bifurcation, and the stability passes over to a new series consisting
of cylinders which are elliptic in section. The circular cylinders are
exactly analogous with our planetary spheroids, and the elliptic ones
with the Jacobian ellipsoids.

With further shrinkage the elliptic cylinders become unstable, a new
form of bifurcation is reached, and the stability passes over to a
series of cylinders whose section is pear-shaped. Thus far the analogy
is complete between our problem and Jeans's, and in consequence of
the greater simplicity of the conditions, he is able to carry his
investigation further. He finds that the stalk end of the pear-like
section continues to protrude more and more, and the flattening between
it and the axis of rotation becomes a constriction. Finally the neck
breaks and a satellite cylinder is born. Jeans's figure for an advanced
stage of development is shown in a figure titled "Section of a rotating
cylinder of liquid" (Fig. 4.), but his calculations do not enable him
actually to draw the state of affairs after the rupture of the neck.

There are certain difficulties in admitting the exact parallelism
between this problem and ours, and thus the final development of our
pear-shaped figure and the end of its stability in a form of bifurcation
remain hidden from our view, but the successive changes as far as they
have been definitely traced are very suggestive in the study of stellar
evolution.

Attempts have been made to attack this problem from the other end. If
we begin with a liquid satellite revolving about a liquid planet and
proceed backwards in time, we must make the two masses expand so that
their density will be diminished. Various figures have been drawn
exhibiting the shapes of two masses until their surfaces approach close
to one another and even until they just coalesce, but the discussion of
their stability is not easy. At present it would seem to be impossible
to reach coalescence by any series of stable transformations, and
if this is so Professor Jeans's investigation has ceased to be truly
analogous to our problem at some undeterm