{9} The orbitual revolutions of the satellites of Uranus have not as yet been clearly scanned. It has been thought that their path is retrograde compared with the rest. Perhaps this may be owing to a _bouleversement_ of the primary, for the inclination of its equator to the ecliptic is admitted to be unusually high; but the subject is altogether so obscure, that nothing can be founded on it. {12} Astronomy, Lardner’s Cyclopædia. {17} M. Compte combined Huygens’s theorems for the measure of centrifugal force with the law of gravitation, and thus formed a simple fundamental equation between the duration of the rotation of what he calls the producing star, and the distance of the star produced. The constants of this equation were the radius of the central star, and the intensity of gravity at its surface, which is a direct consequence of its mass. It leads directly to the third law of Kepler, which thus becomes susceptible of being conceived _à priori_ in a cosmogonical point of view. M. Compte first applied it to the moon, and found, to his great delight, that the periodic time of that satellite agrees within an hour or two with the duration which the revolution of the earth ought to have had at the time when the lunar distance formed the limit of the earth’s atmosphere. He found the coincidence less exact, but still very striking in every other case. In those of the planets he obtained for the duration of the corresponding solar rotations a value always a little less than their actual periodic times. “It is remarkable,” says he, “that this difference, though increasing as the planet is more distant, preserves very nearly the same relation to the corresponding periodic time, of which it commonly forms the forty-fifth part,”—shewing, we may suppose, that only some small elements of the question had been overlooked by the calculator. The defect changes to an excess in the different systems of the satellites, where it is proportionally greater than in the planets, and unequal in the different systems. “From the whole of these comparisons,” says he, “I deduced the following general result:—Supposing the mathematical limit of the solar atmosphere successively extended to the regions where the different planets are now found, the duration of the sun’s rotation was, at each of these epochs, sensibly equal to that of the actual sidereal revolution of the corresponding planet; and the same is true for each planetary atmosphere in relation to the different satellites.”—_Cours de Philosophie Positif_. {42} The researches on this subject were conducted chiefly by the late Baron Fourier, perpetual secretary to the Academy of Sciences of Paris. See his _Théorie Analytique de la Chaleur_. 1822. {52} Delabeche’s Geological Researches.