But Newton proved that a sphere of uniform density, or made up of any number of concentric shells of uniform density, attracted a body outside itself, just as if its entire mass was concentrated at its centre. The distance of the stone from the Earth must therefore be measured, not from the Earth's surface, but from its centre; in other words, we must consider the stone as being distant from the Earth, not some 16 feet, but 3963 miles. This is very nearly one-sixtieth of the Moon's distance, and the square of 60 is 3600. The Earth's pull upon the Moon, therefore, is almost exactly in the inverse square of the distance as compared with its pull on the stone. Kepler's book had found its "reader." His three laws were but three particular aspects of Newton's great discovery that the planets moved under the influence of a force, lodged in the Sun, which varied inversely as the square of their distances from it. But Newton's work went far beyond this, for he showed that the same law governed the motion of the Moon round the {34} Earth and the motions of the satellites revolving round the different planets, and also governed the fall of bodies upon the Earth itself. It was universal throughout the solar system. The law, therefore, is stated as of universal application. "Every particle of matter in the universe attracts every other particle with a force varying inversely as the square of the distance between them, and directly as the product of the masses of the two particles." And Newton further proved that if a body, projected in free space and moving with any velocity, became subject to a central force acting, like gravitation, inversely as the square of the distance, it must revolve in an ellipse, or in a closely allied curve.