Page:Elementary Text-book of Physics (Anthony, 1897).djvu/85

§ 58] III. The squares of the periodic times of the planets are proportional to the cubes of the semi-major axes of their orbits.

Kepler could give no physical reason for the existence of such laws. Later in the century, after Huygens had discovered certain theorems relating to motion in a circle, it was seen that the third law would hold true for bodies moving in concentric circles, and attracted to the common centre by forces varying inversely as the squares of the radii of the circles. Several English philosophers, among them Hooke, Wren, and Halley, based a belief in the existence of an attraction between the sun and the planets upon this theorem.

The demonstration was by no means a rigorous one, and was not generally accepted. It was left for Newton to show that not only the third, but all, of Kepler's laws were completely satisfied by the assumption of the existence of an attraction acting between the sun and the planets, varying inversely as the square of the distance. The demonstrations which show that the law of universal attraction is consistent with Kepler's laws are given in §§48, 50.

Newton also showed that the attraction holding the moon in its orbit, which is presumably of the same nature as that existing between the sun and the planets, is of the same nature as that which causes heavy bodies to fall to the earth. This he accomplished by showing that the deviation of the moon from a rectilinear path is such as should occur if the force which at the earth's surface is the force of gravity were to extend outwards to the moon, and vary in intensity inversely as the square of the distance.

Two further steps were necessary before the final generalization could be reached. One was, to show the relation of the attraction to the masses of the attracting bodies; the other, to show that this attraction exists between all particles of matter, and not merely, as Huygens believed, between those particles and the centres of the sun and planets.

The first step was taken bj; Newton. By means of pendulums having the same length, but with bobs of different materials, he showed that the force acting on a body at the earth's surface is