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 is indicated by $$\Delta'$$, to

and

To fulfill these conditions, we determine a function $$\omega$$ by

and put

i.e., values that really satisfy the fundamental equations (Ia) - (IVa).

From (Va) it also follows

so that the sought forces are found.

Without prejudice to generality, we may assume that the translation happens in the direction of the x-axis. It is then $$\mathfrak{p}_y= \mathfrak{p}_z = 0$$, and the formula for the determination of $$\omega$$ will be transformed into

§ 23. To clearly define the meaning of the above formulas, we will compare the considered system $$S_{1}$$ with a second one $$S_{2}$$. The latter should not be moved, and it arises from $$S_{1}$$ by increasing all the dimensions that have the direction of the x-axis (therefore the relevant dimensions of the ions as well), in the ratio $$\textstyle\sqrt{V^{2}-\mathfrak{p}^{2}}$$ to $$V$$, or: between the coordinates x, y, z of a point of $$S_{1}$$ and the coordinates $$x', y', z'$$ of the same corresponding point of $$S_{2}$$, we let remain the relations