I have given only a qualitative description of Einstein’s law of gravitation; to give its exact quantitative formulation is impossible without more mathematics than I am permitting myself. The most interesting point about it is that it makes the law no longer the result of action at a distance: the sun exerts no force on the planets whatever. Just as geometry has become physics, so, in a sense, physics has become geometry. The law of gravitation has become the geometrical law that every body pursues the easiest course from place to place, but this course is affected by the hills and valleys that are encountered on the road. CHAPTER IX: PROOFS OF EINSTEIN’S LAW OF GRAVITATION The reasons for accepting Einstein’s law of gravitation rather than Newton’s are partly empirical, partly logical. We will begin with the former. Einstein’s law of gravitation gives very nearly the same results as Newton’s, when applied to the calculation of the orbits of the planets and their satellites. If it did not, it could not be true, since the consequences deduced from Newton’s law have been found to be almost exactly verified by observation. When, in 1915, Einstein first published his new law, there was only one empirical fact to which he could point to show that his theory was better than Newton’s. This was what is called the “motion of the perihelion of Mercury.” The planet Mercury, like the other planets, moves round the sun in an ellipse, with the sun in one of the foci. At some points of its orbit it is nearer to the sun than at other points. The point where it is nearest to the sun is called its “perihelion.” Now it was found by observation that, from one occasion when Mercury is nearest to the sun until the next, Mercury does not go exactly once round the sun, but a little bit more. The discrepancy is very small; it amounts to an angle of forty-two seconds in a century. That is to say, in each year the planet has to move rather less than half a second of angle after it has finished a complete revolution from the last perihelion before it reaches the next perihelion. This very minute discrepancy from Newtonian theory had puzzled astronomers. There was a calculated effect due to perturbations caused by the other planets, but this small discrepancy was the residue after allowing for these perturbations. Einstein’s theory accounted for this residue, as well as for its absence in the case of the other planets. (In them it exists, but is too small to be observed.) This was, at first, his only empirical advantage over Newton.