Page:Zur Elektrodynamik bewegter Systeme I.djvu/5



or written in a different manner:

{{MathForm2|(L'2)|$$\left.\begin{matrix} P=(\eta)\{E+[wH]\} & & (\eta)=\left(1,\ k^{2},\ k^{2}\right)\eta\\ & where\\ P=(\sigma)\{E+[wH]\} & & (\sigma)=\left(1,\ k,\ k\right)\sigma\end{matrix}\right\} $$}}

The values from (L'2) are to be included into (L'1). The differential equations for $$E$$ and $$H$$ with given coefficients, will follow. These equations have, as independent variables, the coordinates $$xyz$$ and the time $$t$$.

Instead of them, we will introduce new variables $$x_0\dots t_0$$ by the equations

Furthermore, we denote by $$\rho_0$$ the magnitude $$\tfrac{\rho}{k}=\tfrac{de}{dx_{0}\cdot dy_{0}\cdot dz_{0}}$$, as well as by $$P_0$$ and $$\Gamma_0$$ the operators, which formally correspond to $$P$$ and $$\Gamma$$ in the system of the new variables. Eventually, we define the two new vectors E and M by:

from which it conversely follows due to (1)

Then it arises:

From (C') the following can be derived: E and M are functions of $$x_0\dots t_0 w$$, which contain $$t_0$$ and the translation velocity $$w$$ only in connection with:

$t_1 = t_0 -(w\cdot r_0 )$