 Evidently these transformations preserve the velocity of light, but they do not preserve length and time. So the invariant quantities of Newtonian mechanics, which presuppose invariant measures of length and time, must now depend on the choice of inertial frame. In other words, acceleration is an invariant quantity only when it is zero, for the magnitude of a non-zero acceleration will differ for observers in relative motion. Therefore the notions of force, mass, and acceleration no longer provides an appropriate definition of an inertial frame, except in the ideal case of a frame in which no forces are acting. Einstein’s definition instead appeals to the invariant quantities of electrodynamics: an inertial frame is one in which light travels equal distances in equal times in arbitrary directions. What seems impossible, from the point of view of Galilean relativity, is that a frame that moves uniformly relative to one frame that satisfies Einstein’s definition should also satisfy the definition. But that seeming impossibility rests, again, on the assumption that two inertial frames will have a common measure of simultaneity. Einstein showed that light-signals provide an empirically and theoretically reasonable definition of simultaneity, in light of the empirical soundness of Maxwell’s equations and the apparent invariance of the velocity of light. In the absence of an empirically reasonable alternative compatible with Galilean invariance, there is no sound criterion of simultaneity that will give the same results in different inertial frames. Of course, it would remain true that in a given inertial frame, the motions of free particles would satisfy the requirements of Lange’s definition, and particles that move uniformly in one such frame would also move uniformly in any other. But such a definition is not a substitute for Einstein’s definition, since it must itself presuppose a definition of simultaneity. Otherwise, its appeal to the measurement and comparison of times and distances is without a sound empirical basis. Einstein’s definition places such measurements on an empirical basis. Their results, however, will depend on the choice of an inertial frame, and will vary systematically according to the relative velocities of different inertial frames.