It was quite clear, from the work of Kepler, that the force deflecting the planets from uniform motion in a {32} straight line lay in the Sun. The facts that the Sun lay in the plane of the orbits of all the planets, that the Sun was in one of the foci of each of the planetary ellipses, that the straight line joining the Sun and planet moved for each planet over equal areas in equal periods of time, established this fact clearly. But the amount of deflection was very different for different planets. Thus the orbit of Mercury is much smaller than that of the Earth, and is travelled over in a much shorter time, so that the distance by which Mercury is deflected in a course of an hour from movement in a straight line is much greater than that by which the Earth is deflected in the same time, Mercury falling towards the Sun by about 159 miles, whilst the fall of the Earth is only about 23.9 miles. The force drawing Mercury towards the Sun is therefore 6.66 times that drawing the Earth, but 6.66 is the square of 2.58, and the Earth is 2.58 times as far from the Sun as Mercury. Similarly, the fall in an hour of Jupiter towards the Sun is about 0.88 miles, so that the force drawing the Earth is 27 times that drawing Jupiter towards the Sun. But 27 is the square of 5.2, and Jupiter is 5.2 times as far from the Sun as the Earth. Similarly with the other planets. The force, therefore, which deflects the planets from motion in a straight line, and compels them to move round the Sun, is one which varies inversely as the square of the distance. But the Sun is not the only attracting body of which we know. The old Ptolemaic system was correct to a small extent; the Earth is the centre of motion for the Moon, which revolves round it at a mean distance of 238,800 miles, and in a period of 27 d. 7 h. 43 m. Hence the circumference of her orbit is 1,500,450 miles, and the length of the straight line which she would travel {33} in one second of time, if not deflected by the Earth, is 2828 feet. In this distance the deviation of a circle from a straight line is one inch divided by 18.66. But we know from experiment that a stone let fall from a height of 193 inches above the Earth's surface will reach the ground in exactly one second of time. The force drawing the stone to the Earth, therefore, is 193 x 18.66; _i.e._ 3601 times as great as that drawing the Moon. But the stone is only 1/330 of a mile from the Earth's surface, while the Moon is 238,800 miles away--more than 78 million times as far. The force, therefore, would seem not to be diminished in the proportion that the distance is increased--much less in the proportion of its square.