IT is from the order of succession in Nature, and not from the everlasting endurance of her works, that we may reasonably expect the reign of perpetual activity in her wide domains. In the animal and the vegetable kingdoms the ravages of decay and death are eternally repaired by the birth of new representatives of life; and the loss which our continents undergo by occasional submergence is compensated by the appearance of new lands above the waters. Even those stupendous catastrophes involving planetary fate do not make an irreparable loss in the vast array of celestial objects. The matter saved from such mighty wrecks will again be available for useful ends; the forces which seem destroyed in the terrific convulsions only assume other forms to participate in new movements and operations, and even the space-pervading medium, while dooming the present worlds to an end in the distant future, yet contributes much to bring others into being, and to perpetuate the events and the wonders of our universe. A clew to the manner in which such important purposes are achieved is to be found on tracing the fate of planets or of satellites introduced into orbits of the smallest size possible; and these inquiries can be conducted with the aid of mathematical principles which are almost wholly unavailable in pursuing the details of the nebular hypothesis.
In treating on the equilibrium figure of the earth supposed to be a homogeneous fluid, Laplace has been much embarrassed on finding that, if the rotation were so rapid as to reduce the length of the day to two hours and twenty-five minutes, stability would cease to be possible, though the equatorial gravity would be only partially neutralized by centrifugal force. In solving analogous problems respecting the form of satellites confined to very small orbits and distorted from a spherical