443. That no very irregular figure is found among the planetary bodies, may therefore be considered as a proof of the universality of that system of waste and reconsolidation that we have been endeavouring to trace in the natural history of the earth. A farther proof of the same arises from considering, that for every given mass of matter, having a given period of rotation, there are two different spheroids that answer the conditions of establishing an equilibrium among its parts, the one near to the sphere, and the other very distant from it, and so oblate as to have a lenticular form. Thus the earth, supposing it homogeneous, might either be in equilibrium, by means of the figure which it actually has, or of one in which the polar was to the equatorial diameter as 1 to 768. The same is true of the other planets; and yet we no where find that this highly compressed spheroid is actually employed by nature. The reason, no doubt, is, that in so oblate a spheroid, the equilibrium between the gravitating and the centrifugal force is of the kind that does not re-establish itself when disturbed; so that the parts let loose, and not kept in their place by firm cohesion, would fly off altogether. In such a body, the waste at the surface would lead to an entire change of form, and therefore the constitution here supposed could not be permanent. 444. In the system of Saturn, we have a great deviation from the general order, which, nevertheless, has led to a very unexpected verification of some of the conclusions deduced above. A principle extremely like that which is the basis of all the foregoing reasonings, led one of the greatest philosophers of the present age to discover the revolution of Saturn's ring on its axis, and even to determine the velocity of that revolution, such as it has been since found by observation. LA PLACE, laying it down as a maxim, that nothing in nature can exist, where there are causes of change, not balanced or compensated by other causes,[234] concluded, that the-parts of the ring must be held from falling down to the body of the planet by some other force than their mere cohesion to one another. Were it otherwise, every particle detached from the ring, by any means, must descend in a straight line, almost perpendicular to the surface of Saturn; and the final destruction of the ring must be inevitable. The only force that could balance this effect of gravitation, seemed to be a centrifugal force, arising from the rotation of the ring on an axis passing through its centre, and perpendicular to its plane. La Place proceeded to inquire what celerity of rotation was adequate to this effect, and found that one of ten hours and a quarter would be required, which is almost precisely the time afterwards determined by Dr HERSCHEL from actual observation. If, with this rotation, the ring is a solid annulus generated by the rotation of a very flat ellipsis about a given