the sun, would still remain. We might make other
suppositions; for whatever ratio of the distances we assume for the
density of the medium, the periodic times will be compounded of those
distances and the assumed ratio. Seeing, therefore, that the periodic
times of the planets observe the direct ses-plicate ratio of the
distances, and that it is consonant to all analogy to suppose the
contiguous parts of the vortex to have the same ratio, we find that the
density of the ethereal medium in the solar vortex, is directly as the
square roots of the distances from the axis.

Against this view, it may be urged that if the inertia of the medium is
so small, as is supposed, and its elasticity so great, there can be no
condensation by centrifugal force of rotation. It is true that when we
say the ether is condensed by this force, we speak incorrectly. If in an
infinite space of imponderable fluid a vortex is generated, the central
parts are rarefied, and the exterior parts are unchanged. But in all
finite vortices there must be a limit, outside of which the motion is
null, or perhaps contrary. In this case there may be a cylindrical ring,
where the medium will be somewhat denser than outside. Just as in water,
every little vortex is surrounded by a circular wave, visible by
reflection. As the density of the planet Neptune appears, from present
indications, to be a little denser than Uranus, and Uranus is denser
than Saturn, we may conceive that there is such a wave in the solar
vortex, near which rides this last magnificent planet, whose ring would
thus be an appropriate emblem of the peculiar position occupied by
Saturn. This may be the case, although the probability is, that the
density of Saturn is much greater than it appears, as we shall presently
explain.

In order to show that there is nothing extravagant in the supposition of
the density of the ether being directly as the square roots of the
distances from the axis, we will take a fluid whose law of density is
known, and calculate the effect of the centrifugal force, considered as
a compressing power. Let us assume our atmosphere to be 47 miles high,
and the compressing power of the earth's gravity to be 289 times greater
than the centrifugal force of the equator, and the periodic time of
rotation necessary to give a centrifugal force at the equator equal to
the gravitating force to be 83 minutes. Now, considering the gravitating
force to be uniform, from the surface o