' with respect to
should be in the direction of the
-axis. A simple consideration shows that we are able to construct the Lorentz transformation in this general sense from two kinds of transformations, viz. from Lorentz transformations in the special sense and from purely spatial transformations, which corresponds to the replacement of the rectangular co-ordinate system by a new system with its axes pointing in other directions.
Mathematically, we can characterise the generalised Lorentz transformation thus:
It expresses
',