The theory of vortices has had many staunch supporters amongst those deeply versed in the science of the schools. The Bernoullis proposed several ingenious hypothesis, to free the Cartesian system from the objections urged against it, viz.: that the velocities of the planets, in accordance with the three great laws of Kepler, cannot be made to correspond with the motion of a fluid vortex; but they, and all others, gave the vantage ground to the defenders of the Newtonian philosophy, by seeking to refer the principle of gravitation to conditions dependent on the density and vorticose motion of the ether. When we admit that the ether is imponderable and yet material, and planetary matter subject to the law of gravitation, the objections urged against the theory of vortices become comparatively trivial, and we shall not stop to refute them, but proceed with the investigation, and consider that the ether is the original source of the planetary motions and arrangements. On the supposition that the ether is uniformly dense, we have shown that the periodic times will be directly as the distances from the axis. If the density be inversely as the distances, the periodic times will be equal. If the density be inversely as the square roots of the distances, the times will be directly in the same ratio. The celebrated J. Bernoulli assumed this last ratio; but seeking the source of motion in the rotating central globe, he was led into a hypothesis at variance with analogy. The ellipticity of the orbit, according to this view, was caused by the planet oscillating about a mean position,--sinking first into the dense ether,--then, on account of superior buoyancy, rising into too light a medium. Even if no other objection could be urged to this view, the difficulty of explaining why the ether should be denser near the sun, would still remain. We might make other suppositions; for whatever ratio of the distances we assume for the density of the medium, the periodic times will be compounded of those distances and the assumed ratio. Seeing, therefore, that the periodic times of the planets observe the direct ses-plicate ratio of the distances, and that it is consonant to all analogy to suppose the contiguous parts of the vortex to have the same ratio, we find that the density of the ethereal medium in the solar vortex, is directly as the square roots of the distances from the axis.