Page:Zur Elektrodynamik bewegter Systeme II.djvu/7

If we at first presuppose, that the field is static, then firstly it is ${\tfrac {d}{dt}}=0$ and consequently $\Gamma =\Gamma '$, and secondly $\Lambda =0$, thus

$\Gamma ({\mathfrak {E}})=\Gamma ({\mathsf {E}}{\boldsymbol {E}})$

and thus for an arbitrarily closed surface:

${N}dS=\int \limits _{t'=const.}{\mathsf {E}}{\mathsf {E}}_{N}dS$

If $S$ is extended in isolators, then the first integral is generally of the special value $t$, and the last integral is independent of the special value of $t'$. The once existing equality of both expressions thus remains during all changes of the field; that is:

$\Gamma ({\mathfrak {E}})=\Gamma '({\mathsf {E}}{\mathsf {E}}),$ in the isolator

(11)

$\int \limits _{t=const.}{\mathfrak {E}}_{N}dS=\int \limits _{t'=const.}{\mathsf {E}}{\mathsf {E}}_{N}dS$ for every conductor surface.

(12)

(10), (11) and (12) say, that the magnitudes which are to be denoted as magnetic density ($\rho _{0}$), electric density in the isolator ($\rho _{e}$) and total quantity of electricity of a conductor ($e$), have in general the same value in both representations. Thus the result is: identical data $\rho _{m}$, $\rho _{e}$, $e$ determine identical fields E, M, independent of the values of $p$.

Everything said in this paragraph applies to media, which are in relative rest with respect to a reference system that itself has a uniform translational velocity. By assuming this references system as being fixed in Earth, we neglect the rotation of axis. Theoretically spoken, the requirement of uniform propagation of light in all directions relative to earth cannot be satisfied by any "local time", because the velocity of diurnal motion has no potential. Namely, this has the consequence that the change which the propagation time of light suffers due to motion, depends on the light path, not on its start- and endpoint. However, if one considers that the diurnal motion (for one meter of distance from the axes each) varies by less than ¹⁄₁₀₀ ^cm⁄_sec, then it becomes clear, that no interference experiment can detect these local velocity differences. (One thinks of an interferometer whose two light paths are the halves of the square of one meter side length; let one side-couple be parallel to the direction of motion; Na-light shall be used. A rotation of the instrument around 180° would cause a replacement of the interference image by a millionth width of a fringe.) Also, that