, some illustration will be necessary. Suppose we take an orange,
and, assuming the marks of the stalk and the calyx to represent the
poles, cut off round the line of the equator a strip of peel. This strip
of peel, if placed on the table with its ends meeting, will make a ring
shaped like the hoop of a barrel--a ring of which the thickness in the
line of its diameter is very small, but of which the width in a
direction perpendicular to its diameter is considerable. Suppose, now,
that in place of an orange, which is a spheroid of very slight
oblateness, we take a spheroid of very great oblateness, shaped somewhat
like a lens of small convexity. If from the edge or equator of this
lens-shaped spheroid, a ring of moderate size were cut off, it would be
unlike the previous ring in this respect, that its greatest thickness
would be in the line of its diameter, and not in a line at right angles
to its diameter: it would be a ring shaped somewhat like a quoit, only
far more slender. That is to say, according to the oblateness of a
rotating spheroid, the detached ring may be either a hoop-shaped ring or
a quoit-shaped ring.

One further implication must be noted. In a much-flattened or
lens-shaped spheroid, the form of the ring will vary with its bulk. A
very slender ring, taking off just the equatorial surface, will be
hoop-shaped; while a tolerably massive ring, trenching appreciably on
the diameter of the spheroid, will be quoit-shaped. Thus, then,
according to the oblateness of the spheroid and the bulkiness of the
detached ring, will the greatest thickness of that ring be in the
direction of its plane, or in a direction perpendicular to its plane.
But this circumstance must greatly affect the rotation of the resulting
planet. In a decidedly hoop-shaped nebulous ring, the differences of
velocity between the inner and outer surfaces will be small; and such a
ring, aggregating into a mass of which the greatest diameter is at right
angles to the plane of the orbit, will almost certainly give to this
mass a predominant tendency to rotate in a direction at right angles to
the plane of the orbit. Where the ring is but little hoop-shaped, and
the difference between the inner and outer velocities greater, as it
must be, the opposing tendencies--one to produce rotation in the plane
of the orbit, and the other, rotation perpendicular to it--will both be
influential; and an intermediate plane of rotation will be taken up.
While, if t