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APPENDIX I

SIMPLE DERIVATION OF THE LORENTZ TRANSFORMATION [Supplementary to Section XI]

FOR 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

$x=ct$

or

$x-ct=0$

(1).

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

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