Experimenting still further, we might notice that on the surfaces of bodies rotating with respect to the earth, strange forces would make their appearance. We might eventually plot out the lay of these forces, and divide them into centrifugal and Coriolis forces. Later, a number of curious phenomena occurring on the earth’s surface would be discovered. We should notice that the trade winds and sea currents invariably followed slanting courses, that cyclones always whirled anti-clockwise in the northern hemisphere and clockwise in the southern hemisphere, that rivers flowing northward in the northern hemisphere had a tendency to eat into their east banks. The protuberance of the equator, and the decrease of weight, as we moved towards the tropics, would also be detected. Later still, curious experiments such as Foucault’s pendulum and the gyroscopic compass would be studied; and all these separate discoveries would remain disconnected unless we accumulated one hypothesis after another.
Finally, some genius would come along and say: “Why, all these phenomena will be in order if we assume the earth to be in rotation, the magnitude of this rotation being computed with reference to a system of axes fixed with respect to the stars. This rotation will entail the existence of a field of centrifugal and Coriolis forces on the earth’s surface as on all rotating bodies; and, as a result, all the strange, disconnected phenomena noted will fit quite naturally into a perfectly simple and consistent synthesis.”
Thus far we have seen that by assuming the earth to be in rotation and by referring motion to an extraterrestrial frame, a considerable simplification was introduced into our synthesis when purely mechanical experiments conducted on the earth’s surface were considered. But this simplification will be still more apparent when account is taken of the planetary motions. So long as in our description of these motions we refer our measurements to the earth frame, the wanderings of the various planets will appear very erratic. However, after long periods of observation certain uniformities would be disclosed, and we might succeed in constructing some highly complicated clockwork mechanism which would portray the motions of the sun, moon and planets. Such was indeed Ptolemy’s accomplishment. We might then, by accelerating the motion of our mechanism, foretell the positions of the sun, moon and planets at some future date. In this way the advent of eclipses might be forecast in a more or less accurate way. But the point is that this model could only yield us what we had put into it. We might predict the future positions of the planets because we had detected uniformity in their motions. But if perchance some stray comet were to wander into the solar system, it would be utterly impossible for us to anticipate its motion. Our powers of prevision would thus be extremely limited.
Then we have to consider another type of phenomenon first noticed by Hipparchus. We refer to the precession of the equinoxes, according to which the Pole Star appears to wander away gradually from the direction of true north, finally returning after having described a circle in the course of 28,000 years. To complete our model it would be necessary to take this phenomenon into consideration by assuming that the entire firmament was wobbling like a spinning top. All such phenomena and many others would appear as so many separate empirical discoveries, and no connection between them could be invoked unless one artificial hypothesis were piled up on another, until nature was deprived of all unity.[146] In short, we should merely have succeeded in describing phenomena just as we might describe the patterns on a butterfly’s wings, but our description would in the main be sterile. In a general way, prevision would be impossible; and any such discovery as that of Neptune by Leverrier, deduced from the peculiar motion of Uranus, would be completely out of the question, since no mathematical connection would have been found to exist between the motions of the various planets.
But just as all the difficulties we encountered in mechanics vanished when we substituted a description of motion in terms of the inertial frame (a frame fixed to the stars), so now, once again, by taking the same frame, we are enabled to overcome all the astronomical difficulties we have mentioned, and re-establish harmony and unity in nature. Kepler, as we know, referred the successive positions of the planets (as obtained from Tycho Brahe’s observations) to an inertial frame. He found that, as referred to this frame, each planet described an ellipse round the sun, the sun being situated at one of the foci of the ellipse. Kepler’s laws of planetary motions were then as follows:
1. The planets describe ellipses round the sun.
2. Their motions obey the law of areas, by which we mean that the radius vector joining the sun to a planet sweeps over equal areas in equal times.
3. The square of the time required for a planet to describe its orbit is proportional to the cube of the major axis of the ellipse described.
These are Kepler’s laws. They constitute a distinct advance over Ptolemy’s description, since in addition to the numerous advantages entailed by the choice of the inertial frame in terrestrial mechanics, these laws appear extremely simple and are capable of being expressed in concise mathematical form. But the great importance of Kepler’s laws is that they rendered Newton’s discoveries possible.
Newton argued that, since in an inertial frame free bodies appeared to follow rectilinear courses with constant speeds, it was probable that the planets were being acted on by forces which prevented them from following their natural courses. Now, Kepler’s second law, the law of areas, is compatible only with the existence of a force at all times directed along the line joining the sun and planet. Inasmuch as the planets described closed curves round the sun, this force was obviously one of attraction towards the sun. Kepler’s first and third laws, considered jointly, enabled Newton to determine the precise numerical law of solar attraction, the law of the inverse square. Further, the elliptical motion of the moon round the earth, as it appeared when referred to the inertial frame, connoted the existence of a similar law of attraction existing between moon and earth. It appeared probable, therefore, that we were in the presence of a general action of matter on matter, and Newton found that the phenomenon of weight could be accounted for, not only qualitatively, but also quantitatively, by assuming that matter always attracted matter. Hence, he was led to the formulation of his law of universal attraction.