es greater at Saturn than at
the earth, or as the square roots of the distances directly.

BODES' LAW OF PLANETARY DISTANCES.

Thus, in the solar vortex, there will be two polar currents meeting at
the sun, and thence being deflected at right angles, in planes parallel
to the central plane of the vortex, and strongest in that central plane.
The velocity of expansion must, therefore, diminish from the divergence
of the radii, as the distances increase; but in advancing along these
planes, the ether of the vortex is continually getting more dense,
which operate by absorption or condensation on the radial stream; so
that the velocity is still more diminished, and this in the ratio of the
square roots of the distances directly. By combining these two ratios,
we find that the velocity of the radial stream will be in the
ses-plicate ratio of the distances inversely. But the force of this
stream is not as the velocity, but as the square of the velocity. The
_force_ of the radial stream is consequently as the cubes of the
distances inversely, from the axis of the vortex, reckoned in the same
plane. If the ether, however, loses in velocity by the increasing
density of the medium, it becomes also more dense; therefore the true
force of the radial stream will be as its density and the square of its
velocity, or directly as the square roots of the distances, and
inversely as the cubes of the distances, or as the 2.5 power of the
distances inversely.

If we consider the central plane of the vortex as coincident with the
plane of the ecliptic, and the planetary orbits, also, in the same
plane; and had the force of the radial stream been inversely as the
square of the distances, there could be no disturbance produced by the
action of the radial stream. It would only counteract the gravitation of
the central body by a certain amount, and would be exactly proportioned
at all distances. As it is, there is an outstanding force as a
disturbing force, which is in the inverse ratio of the square roots of
the distances from the sun; and to this is, no doubt, owing, in part,
the fact, that the planetary distances are arranged in the inverse order
of their densities.

Suppose two planets to have the same diameter to be placed in the same
orbit, they will only be in equilibrium when their densities are equal.
If their densities are unequal, the lighter planet will continually
enlarge its orbit, until the force of the radial stream becomes