are only dealing with the question as to how the energy of a point-mass depends on the velocity. We shall speak of its essential significance later.
The most important result of a general character to which the special theory of relativity has led is concerned with the conception of mass. Before the advent of relativity, physics recognised two conservation laws of fundamental importance, namely, the law of the conservation of energy and the law of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law. We shall now briefly consider how this unification came about, and what meaning is to be attached to it.
The principle of relativity requires that the law of the conservation of energy should hold not only with reference to a co-ordinate system , but also with respect to every co-ordinate system which is in a state of uniform motion of translation relative to , or, briefly, relative to every “Galileian” system of co-ordinates. In contrast to classical mechanics, the Lorentz transformation is the deciding factor in the transition from one such system to another.
By means of comparatively simple considerations we are led to draw the following conclusion from these premises, in conjunction with the
