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Updated: May 27, 2025


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.

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.

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.

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.

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.

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.

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