This method of synchronization leads however to the non-equality of different inertial reference frames: the "preferred" inertial reference frame is such that got the first synchronization of the clocks.

where u is the velocity (it is directed along the x-axis) of the inertial reference frame K' with respect to the preferred inertial reference frame K, [gamma] = 1/[square root of 1 - [v.

It is obvious that the direct Tangherlini transformations have the sequel that time t' of a moving inertial reference frame has to delay in [gamma] times with respect to t that is the same that the transverse Doppler-effect in the Special Theory of Relativity.

This transformation holds for the volume dV of a material particle that is at rest in the inertial reference frame S'.

We consider an inertial reference frame S' (0', x',y', z', t')

moving with velocity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] with respect to the inertial reference frame S (0, x, y, z, t) of the previous paragraph.