he nebulous ring is decidedly quoit-shaped, and therefore
aggregates into a mass whose greatest dimension lies in the plane of
the orbit, both tendencies will conspire to produce rotation in that
plane.

On referring to the facts, we find them, as far as can be judged, in
harmony with this view. Considering the enormous circumference of
Uranus's orbit, and his comparatively small mass, we may conclude that
the ring from which he resulted was a comparatively slender, and
therefore a hoop-shaped one: especially as the nebulous mass must have
been at that time less oblate than afterwards. Hence, a plane of
rotation nearly perpendicular to his orbit, and a direction of rotation
having no reference to his orbital movement. Saturn has a mass seven
times as great, and an orbit of less than half the diameter; whence it
follows that his genetic ring, having less than half the circumference,
and less than half the vertical thickness (the spheroid being then
certainly _as_ oblate, and indeed _more_ oblate), must have had a much
greater width--must have been less hoop-shaped, and more approaching to
the quoit-shaped: notwithstanding difference of density, it must have
been at least two or three times as broad in the line of its plane.
Consequently, Saturn has a rotatory movement in the same direction as
the movement of translation, and in a plane differing from it by thirty
degrees only. In the case of Jupiter, again, whose mass is three and a
half times that of Saturn, and whose orbit is little more than half the
size, the genetic ring must, for the like reasons, have been still
broader--decidedly quoit-shaped, we may say; and there hence resulted a
planet whose plane of rotation differs from that of his orbit by
scarcely more than three degrees. Once more, considering the comparative
insignificance of Mars, Earth, Venus, and Mercury, it follows that, the
diminishing circumferences of the rings not sufficing to account for the
smallness of the resulting masses, the rings must have been slender
ones--must have again approximated to the hoop-shaped; and thus it
happens that the planes of rotation again diverge more or less widely
from those of the orbits. Taking into account the increasing oblateness
of the original spheroid in the successive stages of its concentration,
and the different proportions of the detached rings, it may fairly be
held that the respective rotatory motions are not at variance with the
hypothesis but contrari