Reverting to the dynamical principle, that the product of every particle of matter in a fluid vortex, moving around a given axis, by its distance from the centre and angular velocity, must ever be a constant quantity, it follows that if the ethereal medium be uniformly dense, the periodic times of the parts of the vortex will be directly as the distances from the centre or axis; but the angular velocities being inversely as the times, the absolute velocities will be equal at all distances from the centre. Newton, in examining the doctrine of the Cartesian vortices, supposes the case of a globe in motion, gradually communicating that motion to the surrounding fluid, and finds that the periodic times will be in the duplicate ratio of the distances from the centre of the globe. He and his successors have always assumed that it was impossible for the principle of gravity to be true, and a Cartesian plenum also; consequently, the question has not been fairly treated. It is true that Descartes sought to explain the motions of the planets, by the mechanical action of a fluid vortex _solely_; and to Newton belongs the glorious honor of determining, the existence of a centripetal force, competent to explain these motions mathematically, (but not physically,) and rashly rejected an intelligible principle for a miraculous virtue. If our theory be true, the visible creation depends on the existence of both working together in harmony, and that a physical medium is absolutely necessary to the existence of gravitation.