Page:Relativity (1931).djvu/159



OR the relative orientation of the co-ordinate systems indicated in Fig. 2, the $$x$$-axes of both systems permanently coincide. In the present case we can divide the problem into parts by considering first only events which are localised on the $$x$$-axis. Any such event is represented with respect to the coordinate system $$K$$ by the abscissa $$x$$ and the time $$t$$, and with respect to the system $$K'$$ by the abscissa $$x'$$ and the time $$t'$$. We require to find $$x'$$ and $$t'$$ when $$x$$ and $$t$$ are given. A light-signal, which is proceeding along the positive axis of $$x$$, is transmitted according to the equation

or

Since the same light-signal has to be transmitted relative to $$K'$$ with the velocity $$c$$, the propagation