-axis, we thus have
. It is easily seen that the Lorentz transformation really satisfies equation (11) for
; for (11) is a consequence of (8a) and (9), and hence also of (8) and (9). We have thus derived the Lorentz transformation.
The Lorentz transformation represented by (8) and (9) still requires to be generalised. Obviously it is immaterial whether the axes of
' be chosen so that they are spatially parallel to those of
. It is also not essential that the velocity of translation of