Taking all this into account, and doing prodigies of mathematical skill of which we have sufficiently indicated the object, Einstein has succeeded in expressing the law of gravitation in a completely invariant form. In calculating, on the ground of Newton’s law, the “Interval” of two astronomical events—for instance, the successive falls of two meteorites into the sun—we should find that the “Interval” has not precisely the same value for observers who are moving at different velocities. With the new form given to the law by Einstein the difference disappears. The two laws, however, differ little from each other, as was to be expected in view of the accuracy with which astronomers found Newton’s law verified during a couple of centuries. The improvement made in Newton’s law by Einstein means, in a word (and to use the old language of the Euclidean universe), that we consider the law accurate with the reserve that the distances of the planets from the sun are measured by a scale which decreases slightly in length as the sun is approached. * * * * * It is surprising that Newton and Einstein agree in expressing the movements of gravitating stars in an _almost_ identical form, because their starting-points are very different. Newton starts from the hypothesis of absolute space, the empirical laws of the motions of the planets expressed in Kepler’s laws, and the belief that gravitational attraction is a force proportional to mass. Einstein, on the other hand, in making his calculations starts from the conditions of invariance which we indicated. He starts, in a sense, from the philosophical principle or postulate or impulse to hold that the laws of nature are invariant and independent of the point of view—irrelative, if I may use the word. Einstein even abandons the hypothesis which ascribed the curving of gravitational paths to a distinct force of attraction. Yet, starting from a point of view so different from that of Newton, and one that seems at first less overloaded with hypotheses, Einstein reaches a law of gravitation which is _almost_ identical with Newton’s. This “almost” is of immense interest, because it enables us to test which is the accurate law, that of Newton or that of Einstein. They give the same results when there is question of velocities that are feeble in comparison with that of light, but their results differ a little when there is question of very high velocities. We have already seen that, near the sun, light itself is bent out of its course in exact conformity with Einstein’s law, and in a way that Newton’s law did not predict as such. But there is another divergence between the two laws. According to the Newtonian law the planets revolving round the sun describe ellipses which—neglecting the small perturbations due to the other planets—have a rigorously fixed position.