GRAVITATION. The law of gravitation is the law discovered by Newton, according to which every portion of matter attracts every other portion with a force directly proportional to the product of the two masses, and inversely proportional to the square of the distance be tween them. The motion of the planets round the sun in ellipses, each marking out the area of its orbit at a constant rate, and each having a year proportional to the square root of the cube of its mean distance from the sun, implies that there is such a force on each planet exactly pro portioned to its mass, directed toward, and in versely as the square of its distance from the sun. The lines of force radiate out from the sun on all sides equally, and always grasp any matter with a force proportional to its mass, whatever planet that matter belongs to. Since the force is always proportional to the mass acted on, and produces the same change of velocity whatever that mass may be, the change of velocity tells us nothing about the mass in which it takes place, but only about the mass which is pulling. If, however, we compare the accelerations due to different pulling bodies, as for instance that of the sun pulling the earth with that of the earth pulling the moon, or if we compare changes in motion due to the dif ferent planets pulling each other, then we can compare their masses and weigh them one against another and each against the sun.
All this was clearly seen by Newton, and was set forth in 11;- 'System of the World' (3d ed., p. 41). Kepler (q.v.) had indeed given the laws, deduced from observation, according to which the planets describe their orbits. From these Newton deduced the laws of the force in the case of the planets; and subsequently he generalized the statement of them, by showing the identity of the nature of the force that retains the moon in her orbit, and that which attracts matter near to the surface of the earth. Kepler's laws state, first, that every planet revolves around the sun in an ellipse, of which the sun occupies one focus; second, that the velocity of any' planet at different parts of its orbit is such that the radius vector from the sun to the planet sweeps over equal areas in equal times; and third, that the distances of the various planets are so re lated to the periods of their revolution that the squares of the periodic times are proportional to the cubes of the mean distances from the sun. From these laws Newton made the fol
lowing deductions: He inferred from the sec ond law that the planet is acted on by a central force that is always directed toward the sun. From Kepler's first law he deduced the law of variation of the force for any one planet, and found that the force varies inversely as the square of the distance of the planet from the sun. Lastly, he concluded from Kepler's third law a relation between the forces on the various planets; namely, that the forces on equal masses of the different planets are inversely propor tional to the squares of the distances of those planets from the sun. This law indicates the identity of the nature of the force that acts on the different planets. Newton next proceeded to consider the motions of the moon; and to ask the question, °Is not the force that causes the moon to fall toward the earth the same as that which influences failing bodies near to the earth's surface?" This question he attempted to put to the test of calculation. At first he was unsuccessful. The then received estimate of the dimensions of the earth were so far from correct that the comparison between the force of attraction in a stone and that in the moon at her distance from the earth did not exactly agree with his theory, and he was obliged to give it up for nearly 20 years. It was not till 1684, when he heard a paper of Picard read at the Royal Society of London, on new geodetical measurements of the earth, that he obtained ac curate data to work with; and, returning home, he set to work to examine the question afresh.