If we divide by this magnitude, we obtain the four values

so that

(19) | . |

It is apparent that these four values, are determined by the vector and inversely the vector of magnitude follows from the 4 values , where are real, real and positive and condition (19) is fulfilled.

The meaning of here is, that they are the ratios of to

(20) |

The differentials denoting the displacements of matter occupying the spacetime point to the adjacent space-time point.

After the Lorentz-transfornation is accomplished the velocity of matter in the new system of reference for the same space-time point *x', y', z', t'* is the vector with the ratios as components.

Now it is quite apparent that the system of values

is transformed into the values

in virtue of the Lorentz-transformation (10), (11), (12).

The dashed system has got the same meaning for the velocity *after* the transformation as the first system of values has got for *before* transformation.