# Page:Grundgleichungen (Minkowski).djvu/25

Now by putting $\mathfrak{H}=\mathfrak{B}$, the differential equation (29) is transformed into the same form as eq. (1) here when $\mathfrak{m}-[\mathfrak{we}]=\mathfrak{M}-[\mathfrak{wE}]$. Therefore it so happens that by a compensation of two contradictions to the relativity principle, the differential equations of Lorentz for moving non-magnetised bodies at last agree with the relativity postulate.

If we make use of (30) for non-magnetic bodies, and put accordingly $\mathfrak{H}=\mathfrak{B}+[\mathfrak{w},\ \mathfrak{D}-\mathfrak{E}]$, then in consequence of (C) in §8,

$(\epsilon-1)(\mathfrak{E}+(\mathfrak{wB}])=\mathfrak{D}-\mathfrak{E}+(\mathfrak{w}[\mathfrak{w},\ \mathfrak{D}-\mathfrak{E}])$

,

i.e. for the direction of $\mathfrak{w}$

$(\epsilon-1)(\mathfrak{E}+(\mathfrak{wB}])_{\mathfrak{w}}=(\mathfrak{D}-\mathfrak{E})_{\mathfrak{w}}$,

and for a perpendicular direction $\mathfrak{\bar{w}}$,

$(\epsilon-1)(\mathfrak{E}+(\mathfrak{wB}])_{\mathfrak{\bar{w}}}=(1-\mathfrak{w}^{2})(\mathfrak{D}-\mathfrak{E})_{\mathfrak{\bar{w}}}$,

i.e. it coincides with Lorentz's assumption, if we neglect $\mathfrak{w}^2$ in comparison to 1.

Also to the same order of approximation, Lorentz's form for $\mathfrak{F}$ corresponds to the conditions imposed by the relativity principle [comp. (E) § 8] — that the components of $\mathfrak{F_{w}}$, $\mathfrak{F_{\bar{w}}}$ are equal to the components of $\sigma(\mathfrak{E}+(\mathfrak{wB}])$ multiplied by $\sqrt{1-\mathfrak{w}^{2}}$ or $\frac{1}{\sqrt{1-\mathfrak{w}^{2}}}$ respectively.

### § 10. Fundamental Equations of E. Cohn.

E. Cohn[1] assumes the following fundamental equations

 (31) $\begin{array}{c} curl\ (M+[\mathfrak{wE}])=\frac{\partial\mathfrak{E}}{\partial t}+\mathfrak{w}\ div\ \mathfrak{E}+\mathfrak{F},\\ \\-curl\ (\mathfrak{E}-[\mathfrak{wM}])=\frac{\partial\mathfrak{M}}{\partial t}+\mathfrak{w}\ div\ \mathfrak{M},\end{array}$
 (32) $\mathfrak{F}=\sigma E,\ \mathfrak{E}=\epsilon E-[\mathfrak{w}M],\ \mathfrak{M}=\mu M+[\mathfrak{w}E]$,

where E, M are the electric and magnetic field intensities (forces), $\mathfrak{E,M}$ are the electric and magnetic polarisation (induction).

1. Gött. Nachr. 1901, w. 74 (also in Ann. d. Phys. 7 (4), 1902, p. 29).