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 (Ions, electrons), then these equations form the electromagnetic basis of Lorentz's electrodynamics and optics for moving bodies.

If these equations which hold in the system K, are transformed to the system k with the aid of the transformation-equations given in § 3 and § 6, then we obtain the equations :—

where

Since the vector $$(u_{\xi}, u_{\eta}, u_{\zeta})$$ is nothing but the velocity of the electrical mass measured in the system k, as can be easily seen from the addition-theorem of velocities in § 4—so it is hereby shown, that by taking