Having developed and enunciated the true laws of motion, he was able to show that Kepler’s second law (that equal areas are described by the line from the planet to the sun in equal times) was only another way of saying that the centripetal force on a planet is always directed to the sun. Also that Kepler’s first law (elliptic orbits with the sun in one focus) was only another way of saying that the force urging a planet to the sun varies inversely as the square of the distance. Also (if these two be granted) it follows that Kepler’s third law is only another way of saying that the sun’s force on different planets (besides depending as above on distance) is proportional to their masses. Having further proved the, for that day, wonderful proposition that, with the law of inverse squares, the attraction by the separate particles of a sphere of uniform density (or one composed of concentric spherical shells, each of uniform density) acts as if the whole mass were collected at the centre, he was able to express the meaning of Kepler’s laws in propositions which have been summarised as follows:— The law of universal gravitation.—_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_.[2] But Newton did not commit himself to the law until he had answered that question about the apple; and the above proposition now enabled him to deal with the Moon and the apple. Gravity makes a stone fall 16.1 feet in a second. The moon is 60 times farther from the earth’s centre than the stone, so it ought to be drawn out of a straight course through 16.1 feet in a minute. Newton found the distance through which she is actually drawn as a fraction of the earth’s diameter. But when he first examined this matter he proceeded to use a wrong diameter for the earth, and he found a serious discrepancy. This, for a time, seemed to condemn his theory, and regretfully he laid that part of his work aside. Fortunately, before Newton wrote the _Principia_ the French astronomer Picard made a new and correct measure of an arc of the meridian, from which he obtained an accurate value of the earth’s diameter. Newton applied this value, and found, to his great joy, that when the distance of the moon is 60 times the radius of the earth she is attracted out of the straight course 16.1 feet per minute, and that the force acting on a stone or an apple follows the same law as the force acting upon the heavenly bodies.[3]