Page:The principle of relativity (1920).djvu/52

 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, (v + w)/(1 + vw/c^2). 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

1/c [part]/[part]t [X, Y, Z] = | [part]/[part]x [part]/[part]y [part]/[part]z |
 * L M N |,