Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space-time variables _x, y, z, t_ of the original coordinate system _K_, we introduce new space-time variables _x′, y′, z′, t′_ of a co-ordinate system _K′_. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or in brief: General laws of nature are co-variant with respect to Lorentz transformations. This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. If a general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced. XV. GENERAL RESULTS OF THE THEORY It is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, _i.e._ the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favour. Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter _v_ are not very small as compared with the velocity of light. We have experience of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice. We shall not consider the motion of stars until we come to speak of the general theory of relativity. In accordance with the theory of relativity the kinetic energy of a material point of mass _m_ is no longer given by the well-known expression image020 but by the expression image021 This expression approaches infinity as the velocity _v_ approaches the velocity of light _c_. The velocity must therefore always remain less than _c_, however great may be the energies used to produce the acceleration. If we develop the expression for the kinetic energy in the form of a series, we obtain image022 When image023