where denotes the differentiation with respect to a fixed material point (space point). Furthermore P is rotation, is divergence, is gradient,
.
§ 2. Transformation to a moving coordinate system and local time.
We decompose the velocities into a common translational velocity (which is constant with respect to time) of the whole system, and the "relative" velocity :
(3)
and we denote a differentiation with respect to time, in relation to a relatively stationary point, by :
(4)
Then it is given
.
(5)
Simultaneously, instead of the "general time" we introduce the "local time" . It is defined at a point whose radius vector is , by:
(6)
Differentiations with respect to relative coordinates, in which local time is assumed as the fourth independent variable, shall be denoted by an upper index prime. Then it is