The use of the C.G.S. system in this equation gives 2/k = 1.08 x 1027; ρ is the average density of the matter and k is a constant connected with the Newtonian constant of gravitation.
APPENDICES
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 co-ordinate 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 relative to the system K′ will be represented by the analogous formula
x′ – ct′ = 0 . . . . . (2)