Page:Zur Elektrodynamik bewegter Systeme II.djvu/6

(but no difference in the case of "stationary aether"). Whether one or the other kind of rotation actually has taken place, there can be (due to logical reasons) no optical, or more general, no electric means of testing. A material (mechanical or acoustical) protection or control is rather required. The scheme would be as follows: the two gears are located at the same shaft, which will be driven in the middle; then we must guarantee the phase equality of both ends up to ¹⁄₁₀₀₀₀ of the propagation time of light, which corresponds to the length of the axis.^[1]

What we have to understand under "electric and magnetic quantities", still needs a clarification. Those aren't concepts which (besides our equations or independently from them) must be introduced into electrodynamics. The are rather given from these equations as "integration constants". Equation I says, that for every closed surface $S$ which goes through invariable material particles, the surface integral of ${\mathfrak {M}}$ is a time-independent quantity; we will call this quantity the magnetic quantity within $S$. Equation II says the same with respect to the surface integral of ${\mathfrak {E}}$ for a surface extended in isolators, and it connects for an arbitrary surface the temporal change of this magnitude with the electric current through $S$ in the same way, as the content of a fluid is connected with the current of a fluid. We call this magnitude the quantity of electricity within $S$. In the definitions of both magnitudes, it is implicitly presupposed, that we can know the identical moments of time in the various points of the closed surface. From the preceding it follows: When we define identical times at different places, so that the propagation of light becomes uniform with respect to the fixed stars (time $t$), then electricity and magnetism express themselves as surface integrals of ${\mathfrak {E}}$ and ${\mathfrak {M}}$. When we define identical times at different places, so that the propagation of light becomes uniform with respect to Earth (time $t'$), then they express themselves as surface integrals of ${\mathsf {E}}{\mathsf {E}}$ and $\mu {\mathsf {M}}$.

From the equations, into which I', II', III pass for $u=p=const.$, it is given by means of (7):

${\begin{matrix}\Gamma ({\mathfrak {M}})=\Gamma '(\mu {\mathsf {M}})\\\\\Gamma ({\mathfrak {E}})=\Gamma '({\mathsf {E}}{\mathsf {E}})+(p\cdot \Lambda )\end{matrix}}$.

(10)

1. Also this procedure of course has only a meaning, as soon as we can be sure, that the laws of mechanics for the "general time" is strictly correct.