aus Wikisource, der freien Quellensammlung
Aus II. folgt dann, wegen (18) und (17) Nr. 10
(9)
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{\displaystyle \mathrm {rot} '{\mathfrak {H}}'-4\pi {\frac {\partial {\mathfrak {D}}'}{\partial t'}}+{\frac {(p-1)}{pqn}}{\mathfrak {c}}_{0}\cdot \mathrm {div} '{\mathfrak {D}}'=}
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{\displaystyle =\mathrm {rot} {\mathfrak {H}}-4\pi {\frac {\partial {\mathfrak {D}}}{\partial t}}-{\frac {(p-1)}{pqn}}{\mathfrak {c}}_{0}\cdot \mathrm {div} {\mathfrak {D}}}
und
(10)
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{\displaystyle \mathrm {rot} '{\mathfrak {E}}'+{\frac {\partial {\mathfrak {B}}'}{\partial t'}}-{\frac {(p-1)}{pqn}}{\mathfrak {c}}_{0}\cdot \mathrm {div} '{\mathfrak {B}}'=}
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{\displaystyle =\mathrm {rot} {\mathfrak {E}}+{\frac {\partial {\mathfrak {B}}}{\partial t}}+{\frac {p-1}{pqn}}{\mathfrak {c}}_{0}\cdot \mathrm {div} {\mathfrak {B}}}
und
(11)
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{\displaystyle {\mathfrak {J}}'={\mathfrak {J}}+{\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {J}}-pq{\mathfrak {c}}_{0}\varrho }
Woraus sich wegen (7) Nr. 10 ergibt
(12)
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{\displaystyle {\mathfrak {J}}'+{\frac {p-1}{pqn}}\varrho '{\mathfrak {c}}_{0}={\mathfrak {J}}-{\frac {p-1}{pqn}}{\mathfrak {c}}_{0}\cdot \varrho }
Da nun allgemein
(13)
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{\displaystyle \left\{{\begin{aligned}\varrho '&=\mathrm {div} '{\mathfrak {D}}'\\\varrho &=\mathrm {div} \ {\mathfrak {D}}\end{aligned}}\right.}
ist, so folgt aus (9) wegen (12)
(14)
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{\displaystyle \mathrm {rot} '{\mathfrak {H}}'-4\pi {\frac {\partial {\mathfrak {D}}'}{\partial t'}}-4\pi {\mathfrak {J}}'=\mathrm {rot} {\mathfrak {H}}-4\pi {\frac {\partial {\mathfrak {D}}}{\partial t}}-4\pi {\mathfrak {J}}}
Aus II. haben wir ganz allgemein
(15)
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{\displaystyle \left\{{\begin{aligned}&{\mathfrak {H}}'=p{\mathfrak {H}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {H}}+4\pi pq\left[{\mathfrak {D}}{\mathfrak {c}}_{0}\right]\\&{\frac {4\pi {\mathfrak {D}}'}{n}}={\frac {4\pi p{\mathfrak {D}}}{n}}-{\frac {4\pi }{n}}(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {D}}-pq\left[{\mathfrak {H}}{\mathfrak {c}}_{0}\right]\end{aligned}}\right.}
und
(16)
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{\displaystyle \left\{{\begin{aligned}{\mathfrak {B}}'&=p{\mathfrak {B}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {B}}+pqn\left[{\mathfrak {E}}{\mathfrak {c}}_{0}\right]\\{\mathfrak {E}}'&=p{\mathfrak {E}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {E}}-pq\left[{\mathfrak {B}}{\mathfrak {c}}_{0}\right]\end{aligned}}\right.}
Ersetzen wir in (8) Nr. 9 die gestrichenen Größen durch die ungestrichenen und
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Nr. 9
(17)
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{\displaystyle \mathrm {div} {\mathfrak {B}}=p\ \mathrm {div} '{\mathfrak {B}}'-pgn{\mathfrak {c}}_{0}\mathrm {rot} '{\mathfrak {E}}'-pqn{\frac {\partial {\mathfrak {B}}'{\mathfrak {c}}_{0}}{\partial t'}}}
Transformieren wir jetzt auf Ruhe, so verschwindet infolge I. die rechte Seite von (17), und es folgt
(18)
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{\displaystyle \mathrm {div} {\mathfrak {B}}=0}
![{\displaystyle \left\{{\begin{aligned}&{\mathfrak {H}}'=p{\mathfrak {H}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {H}}+4\pi pq\left[{\mathfrak {D}}{\mathfrak {c}}_{0}\right]\\&{\frac {4\pi {\mathfrak {D}}'}{n}}={\frac {4\pi p{\mathfrak {D}}}{n}}-{\frac {4\pi }{n}}(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {D}}-pq\left[{\mathfrak {H}}{\mathfrak {c}}_{0}\right]\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4b493f7f86a4f28e5c8ae8ce47ccfafe21973c98)
![{\displaystyle \left\{{\begin{aligned}{\mathfrak {B}}'&=p{\mathfrak {B}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {B}}+pqn\left[{\mathfrak {E}}{\mathfrak {c}}_{0}\right]\\{\mathfrak {E}}'&=p{\mathfrak {E}}-(p-1){\mathfrak {c}}_{0}\cdot {\mathfrak {c}}_{0}{\mathfrak {E}}-pq\left[{\mathfrak {B}}{\mathfrak {c}}_{0}\right]\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/959b2461d8de7f77f45ced4884c14240f5ea76fd)
