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 § 4. The equations of motion.

In the mechanics of, the so-called "proper time" of a point occurs, i.e. a four-dimensional scalar $$(\tau)$$, defined by

If we differentiate (with respect to $$\tau$$) the four-dimensional radius vector of the point, and dividing by the speed of light ($$c$$), then it is resulting in the $$V^{4}$$-"velocity" of :

Obviously the four components of the $$V^{4}$$-"velocity" identically satisfy the equation:

We form now, by the $$V_{I}^{4}$$-"velocity" and "force" according to the scheme (2), the four-dimensional scalar

Introducing the ponderomotive force of electromagnetic fields, whose components are determined by (16), and taking into account equations (15) and (30), we find:

where $$Q$$ is the Joule-heat, developed in the unity of space and time.

Now, gives the equations of motion of an element of matter in the