Page:SahaElectrodynamics.djvu/18

 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 &xi;-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,

$$(v+w)/\left(1+\frac{vw}{c^{2}}\right)$$

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.

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

$$\frac{1}{c}\frac{\partial}{\partial t}[X,\ Y,\ Z]=\left|\begin{array}{ccc} \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z}\\ \\L & M & N\end{array}\right|$$,