Suppose we put on a table a slice of lemon cut through the longer diameter of the fruit, and imagine that the chief stars, the northern constellations, are painted on the vaulted roof of the vast hemispherical room in the middle of which we place our table. The slice of lemon has very nearly the form of an ellipse, and, if we take one of the pips to represent the sun, it will stand for the orbit of one of our planets. Newton’s law says that—after making due corrections—the planetary orbit keeps a fixed position relatively to the stars as long as the planet continues to revolve. This means that the slice of lemon remains stationary. Einstein’s law says, on the contrary, that the orbital ellipse turns very slowly amongst the stars while the planet traverses it. This means that our slice of lemon must turn slightly on the table, in such wise that the two ends of the lemon do not remain opposite the same stars painted on the wall. If we calculate, in virtue of Einstein’s law, the extent to which the elliptical orbits of the planets must thus turn, we find it so small as to be impossible of observation except in the case of one planet, the swiftest of all, Mercury. Mercury revolves completely round the sun in about eighty-eight days, and Einstein’s law shows that its orbit must at the same time turn by a small angle which amounts to forty-three seconds of an arc (43″) at the end of a century. Small as this quantity is, the refined methods of the modern astronomer can easily measure it. As a matter of fact, it had been noticed during the last century that Mercury was the only one of the planets to show a slight anomaly in its movements, which could not be explained by Newton’s law. Le Verrier made prodigious calculations in connection with it, as he thought that the anomaly might be due to the attraction of an unknown body lying between Mercury and the sun. He hoped that he would thus discover, by calculation, an intra-Mercurial planet, just as he had discovered the trans-Uranian planet Neptune. But no one ever observed his planet, and the anomaly of Mercury continued to be the despair of astronomers. Now, in what did the anomaly consist? Precisely in an abnormal rotation of the planetary orbit; a rotation which Le Verrier’s calculations showed to be forty-three seconds of an arc in a century. That is exactly the figure that we deduce, without using any hypothesis, from Einstein’s law of gravitation! It is true that, according to the recent calculations of Grossmann, the astronomical observations collected by Newcomb give as the recorded value of the secular displacement of the perihelion of Mercury, not 43″ as Le Verrier believed, but 38″ at the most. The agreement with Einstein’s theoretical result is, therefore, not perfect (which would have been extraordinary), but it is striking, and is within the limits of possible error of observation.