FORMATION OF NEBULOUS RINGS. 269 



the resulting planet. In a decidedly hoop-shaped nebulous 

 ring, the differences of velocity between the inner and out- 

 er surfaces will be very small ; and such a ring, aggrega- 

 ting into a mass whose 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 ig 

 but little hoop-shaped, and the difference of the inner and 

 outer velocities also 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 rota- 

 tion will be taken up. While, if the nebulous ring is de- 

 cidedly 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 enor- 

 mous circumference of Uranus's orbit, and his compara- 

 tively small mass, we may conclude that the ring from 

 which he resulted was a comparatively slender, and there- 

 fore a hoop-shaped one : especially if the nebulous mass 

 was at that time less oblate than afterwards, which it must 

 have been. Hence, a plane of rotation nearly perpendicu- 

 lar to his orbit, and a direction of rotation having no refer- 

 ence to his orbitual 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 thick- 

 ness (the spheroid being then certainly as oblate, and in- 

 deed more oblate), must have had considerably greater 

 width — must have been less hoop-shaped, and more ap- 

 proaching to the quoit-shaped : notwithstanding difference 

 of density, it must have been at least two or three times as 



