  It is demonstrated how the right hand sides of the Lorentz Transformation
equations may be written, in a Lorentz invariant manner, as 4--vector scalar
products. The formalism is shown to provide a short derivation, in which the
4--vector electromagnetic potential plays a crucial role, of the Lorentz force
law of classical electrodynamics, and the conventional definition of the
magnetic field in terms spatial derivatives of the 4--vector potential. The
time component of the relativistic generalisation of the Lorentz force law is
discussed. An important physical distinction between the space-time and
energy-momentum 4--vectors is also pointed out.
