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 and from $$V_{II}^{4}[-i\mathfrak{H},\ -\mathfrak{D}\}$$, when combined according to scheme (6), we obtain $$V_{I}^{4}$$, which is called the "magnetic rest force":

The vectors "electric rest force and magnetic rest force" are connected with $$V^{3}$$, which determine the ponderomotive forces on electric and magnetic poles in motion, and which I wrote down in the first paper as $$\mathfrak{E}'$$ and $$\mathfrak{H}'$$:

Evidently we have:

setting

From the two $$V_{I}^{4}$$

$\left\{ \mathfrak{R}^{e},\ U^{e}\right\}$ and $\left\{ \mathfrak{R}^{m},\ U^{m}\right\} $

which are composed according to formula (1a), we obtain the $$V_{II}^{4}$$:

$\begin{array}{l} \mathfrak{a}=k^{-2}[\mathfrak{E}'\mathfrak{H}']\\ \mathfrak{b}=ik^{-2}\left\{ \mathfrak{E}'(\mathfrak{qH}')-\mathfrak{H}'(\mathfrak{qE}')\right\} =ik^{-2}\left[\mathfrak{q}[\mathfrak{E}'\mathfrak{H}']\right]\end{array}$

By insertion of $$V^{3}$$:

the last $$V_{II}^{4}$$ can be written:

By multiplying the $$V^{3}\mathfrak{f}'$$ by the speed of light ($$c$$), we obtain the "relative radius" vector of my first paper [l. c.), equation IV].

Finally we combine $$V_{I}^{4}$$ which is represented by (11), with the $$V_{I}^{4}$$-"velocity" according to scheme (6). $$V_{I}^{4}$$ is calculated as follows:

$\begin{array}{l} \mathfrak{R}=ik^{-3}\left\{ \mathfrak{f}'+\left[\mathfrak{q}[\mathfrak{qf}']\right]\right\} \\ U=-k^{-3}(\mathfrak{qf}').\end{array}$

When multiplied by ($$-i$$), we arrive at the $$V_{I}^{4}$$-"rest radius" of :

{{MathForm1|(12)|$$\left\{ \begin{array}{l} \mathfrak{R}=k^{-1}\mathfrak{f}'+k^{-3}\mathfrak{q}[\mathfrak{qf}']\\ U=ik^{-3}(\mathfrak{qf}').\end{array}\right.$$}}

§ 3. Four-dimensional tensors.

A "Four-dimensional tensor" ($$T^{4}$$) is a set of ten variables, which are transformed into the orthogonal Lorentz transformations, such as we transform the squares and products of the coordinates $$x, y, z, u$$:

$x^{2},\ y^{2},\ z^{2},\ yz,\ zx,\ xy;\qquad xu,\ yu,\ zu;\qquad u^{2}.$