...Kepler's elliptic orbits and laws of motion were deducible from the simple hypothesis of gravitation, directly as the mass, and inversely as the square of the distance ; and on this principle laid the foundations of physical astronomy, which has been carried to its present...

...operation, from separate marks,) were all marks of moving round a common centre, with a centripetal force varying directly as the mass and inversely as the square of the distance from that centre. This is the greatest example which has yet occurred of the transformation,...

...which sub- ' stances are propelled towards the earth ; it exists in all known forms of matter, and acts directly as the mass, and inversely as the square of the distance : And, when restrained by inertia, it preserves the planetary bodies in their orbits, presides over their...

...that the author has proved what he enunciates, namely, that the attraction upon any particle must vary directly as the mass and inversely as the square of the distance ; and that the repulsion must vary directly as the mass and inversely as the cube of the distance. Suppose...

...repulsion arising from the undulations of an ether within them, and partly by the attraction which is directly as the mass and inversely as the square of the distance. And lastly, these molecules consist of atoms held together by their attractive and repulsive forces, the...

...Solar System, conformed to the law of moving around a common centre, urged by a centripetal force, varying directly as the mass, and inversely as the square of the distance from the centre, he inferred the existence of such a law for all the bodies of the system,...

...been if no disturbance had existed, or generally : — , Two bodies attracting one another with forces varying directly as the mass and inversely as the square of the distance, to determine the orbit of one relatively to the other. Let M, M ' be the masses of the bodies,...

...them. But when Newton showed that Kepler's laws were only partial inferences of a centripetal force, varying directly as the mass, and inversely as the square of the distance from the central power, he linked together a host of particular inferences, and established...

...of which is composed of concentric homogeneous shells, every particle of which attracts with a force varying directly as the mass, and inversely as the square of the distance, then each sphere will attract an external particle with a force which varies directly as...

...of modern physical science, is chiefly due to three or four distinguished philosophers. Tycho Brahc, by his system of accurate measurement of the positions...distance, and thus to reduce celestial phenomena to tho greatest simplicity, by comprehending them under a single law. Without tracing the details of the...