We have obtained the formula for U for the case when v and w have the same direction ; it can also be obtained by combining two transformations according to section § 3. If in addition to the systems K, and k, we introduce the system k', of which the initial point moves parallel to the ξ-axis with velocity w, then between the magnitudes, x, y, z, t and the corresponding magnitudes of k', we obtain a system of equations, which differ from the equations in §3, only in the respect that in place of v, we shall have to write,
We see that such a parallel transformation forms a group.
We have deduced the kinematics corresponding to our two fundamental principles for the laws necessary for us, and we shall now pass over to their application in electrodynamics.
II. — ELECTRODYNAMICAL PART.
§ 6. Transformation of Maxwell's equations for Pure Vacuum.
On the nature of the Electromotive Force caused by motion in a magnetic field.
The Maxwell-Hertz equations for pure vacuum may hold for the stationary system K, so that
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