Page:SahaElectrodynamics.djvu/22

 It is further clear that the assymetry mentioned in the introduction which occurs when we treat of the current excited by the relative motion of a magnet and a conductor disappears. Also the question about the seat of electromagnetic energy is seen to be without any meaning.

§ 7. Theory of Döppler's Principle and Aberration.
In the system K, at a great distance from the origin of co-ordinates, let there be a source of electrodynamic waves, which is represented with sufficient approximation in a part of space not containing the origin, by the equations :—

$$\left. \begin{array}{c} X=X_{0}\sin\Phi\\ Y=Y_{0}\sin\Phi\\ Z=Z_{0}\sin\Phi\end{array} \right\} \left. \begin{array}{c} L=L_{0}\sin\Phi\\ M=M_{0}\sin\Phi\\ N=N_{0}\sin\Phi\end{array} \right\} \phi=\omega\left(t-\frac{lx+my+nz}{c}\right)$$

Here $$(X_0, Y_0, Z_0)$$ and $$(L_0, M_0, N_0)$$ are the vectors which determine the amplitudes of the train of waves, $$(l, m, n)$$ are the direction-cosines of the wave-normal.

Let us now ask ourselves about the composition of these waves, when they are investigated by an observer at rest in a moving medium k :— By applying the equations of transformation obtained in §6 for the electric and magnetic forces, and the equations of transformation obtained in § 3 for the co-ordinates, and time, we obtain immediately :—