Page:Zur Elektrodynamik bewegter Systeme II.djvu/4

By means of (5), (7) and (8), two equations emerge from I' II', which shall be simplified by putting:

$p\cdot v=0\,$

(9)

Then it is given:

$-{\mathsf {P'(E)}}={\frac {\delta {\mathfrak {M}}_{0}}{\delta t'}}+\Gamma '({\mathfrak {M}}_{0})v-{\mathsf {P}}'[v{\mathfrak {M}}_{0}]={\frac {\overline {d{\mathfrak {M}}_{0}}}{dt'}}$

I'a

$-{\mathsf {P'(M)}}={\frac {\delta {\mathfrak {E}}_{0}}{\delta t'}}+\Gamma '({\mathfrak {E}}_{0})v-{\mathsf {P}}'[v{\mathfrak {E}}_{0}]+\Lambda ={\frac {\overline {d{\mathfrak {E}}_{0}}}{dt'}}+\Lambda$

II'a

${\begin{cases}{\mathfrak {E}}_{0}=\epsilon {\mathsf {E}}-[v{\mathsf {M}}]\\\\{\mathfrak {M}}_{0}=\mu {\mathsf {M}}+[v{\mathsf {E}}]\\\\\Lambda =\lambda ({\mathsf {E-K}})\end{cases}}$

III'a

$\Sigma =[{\mathsf {EM}}]$

IV'a

§ 3. The field in relatively resting media.

Let the only velocity of the system be $p$, or which is the same, let it be in relative rest. Then $v=0$, and the following equations – in all rigor – shall apply:

$-{\mathsf {P'(E)}}={\frac {d{\mathfrak {M}}_{0}}{dt'}}$

I'b

${\mathsf {P'(M)}}={\frac {d{\mathfrak {E}}_{0}}{dt'}}+\Lambda$

II'b

${\begin{cases}{\mathfrak {E}}_{0}=\epsilon {\mathsf {E}}\\\\{\mathfrak {M}}_{0}=\mu {\mathsf {M}}\\\\\Lambda =\lambda [{\mathsf {E-K}}]\end{cases}}$

IIIb

$\Sigma =[{\mathsf {EM}}]$

IVb

These equations have exactly the same form, as Maxwell's equations for a stationary system. Only by those equations, however, the field E, M and thus also the radiation relative to matter $\Sigma$ is determined, as far as certain quantities – "electric and magnetic quantities" – which are invariable according to those very equations, are required.^[1] Thus for a while we postpone the consideration of these processes in which electromagnetic energy goes over into other forms of energy, especially mechanical work,^[2] and then we can say:

---

1. See in this respect, below p. 1409 f.
2. See below § 5.