It must therefore suffice if we place the conception of approximation in the foreground here as in other parts of this book. Till quite recently Newton's Equations of Motion were used as a foundation for verifying astronomical occurrences. These are symbolical representations expressed as formulæ that contain in an exceedingly simple form the law of mass attraction. They express the comprehensive principle that the attraction is directly proportional to the mass and inversely proportional to the square of the distance; so that the moving force is doubled when the mass is doubled, whereas if the distance is double, the force is only a quarter as great, if the distance is trebled, the force becomes one-ninth as great. According to the Theory of Relativity this fundamental law is not wrong or invalid, but no longer holds fully if pursued to its last inferences. In applying corrections to it, new factors occur, such as the ratio of given velocities to the velocity of light, and the new geometry which operates with "world-lines" in space which, amalgamated with the dimension of time, is regarded as a quadruply extended continuum. Einstein has actually supplemented these fundamental equations for the motion of masses so that the original form states the true condition of affairs only approximately, whereas Einstein's equations give the motion with very great accuracy. The above-mentioned essay of Einstein is carried out as if the structure bequeathed to us by Newton required the addition of a final, very delicate pinnacle. For the mathematician this pinnacle is given as a combination of signs, representing a so-called "Elliptic Interval." Such an interval is a very weird construction, and the man who will make it apprehended by the general reader is yet to be born. When Lord Byron said: "And Coleridge, too, has lately taken wing. But like a hawk encumbered with his hood,-- Explaining Metaphysics to the nation-- _I wish he would explain his Explanation_." (_Dedication to "Don Juan._") he had still a sure footing in intelligibility, compared with the non-mathematician, who demands an explanation for such a construction. And what a complex of mathematical dangers must be overcome even before the question of the meaning of this integral is crystallized out! But now the explanation had arrived and could be evaluated, if only approximately. Before we give the result, let us just describe at least one technical term, namely, "Perihelion." It is that point of a planetary orbit which lies nearest the sun. This orbit is an ellipse, that is, an elongated curved fine in the interior of which one distinguishes a major axis in the direction of elongation, and a minor axis perpendicular to the former at its middle point. The perihelion of a planetary orbit is at one of the end points of the major axis.