# Page:AbrahamMinkowski1.djvu/12

From them it follows, that when $\dot{\epsilon}$ and $\dot{\mu}$ are set equal to zero:

$\begin{array}{l} \mathfrak{E'\dot{D}-D\dot{E}'=\dot{q}[E'H']+q[E'\dot{H}']+q[\dot{E}'H']},\\ \mathfrak{H'\dot{B}-B\dot{H}'=\dot{q}[E'H']+q[\dot{E}'H']+q[E'\dot{H}']},\end{array}$

Now, since relation (18) requires

$2\mathfrak{\dot{q}}c\mathfrak{g=E'\dot{D}-D\dot{E}'+H'\dot{B}-B\dot{H}}'$

one thus places Cohn's theory in our system, by setting

 (27) $c\mathfrak{g=[E'H']=}\frac{\mathfrak{S}'}{c}$

In Cohn's electrodynamics, the momentum density has to be set equal to the relative ray divided by $c^{2}$.

That relation (18a) is satisfied by (26) and (27), can easily be confirmed by considering, that the identity

$\mathfrak{\left[q[E'H']\right]=\left[E'[qH']\right]-\left[H'[qE']\right]}$

exists. From (19) it follows now for the electromagnetic energy density.

 (28) $\psi=\frac{1}{2}\mathfrak{E'D}+\frac{1}{2}\mathfrak{H'B}+\mathfrak{q[E'H']}$,

an expression, which according to (26) can also be written

 (28a) $\psi=\frac{1}{2}\epsilon\mathfrak{E}'^{2}+\frac{1}{2}\mu\mathfrak{H}'^{2}+2\mathfrak{q[E'H']}$;

it is in agreement with E. Cohns approach.

 (29) $\begin{cases} \mathfrak{D}=\epsilon\mathfrak{E}'-[\mathfrak{qH}],\\ \mathfrak{B}=\mu\mathfrak{H}'+[\mathfrak{qE}];\end{cases}$
 (30) $\begin{cases} \mathfrak{E'}=\mathfrak{E}+[\mathfrak{qH}],\\ \mathfrak{H'}=\mathfrak{H}-[\mathfrak{qE}].\end{cases}$
Besides four vectors contained in the main equations, two new vectors $\mathfrak{E,H}$ occur here. This circumstance makes Lorentz's theory more complicated than Cohn's one. The latter directly connects the components of $\mathfrak{D,B}$ with those of $\mathfrak{E',H'}$ by equations, which are linear in the velocity components; at this one, however, the connecting equations (§ 10, eq. 37b) given by elimination of $\mathfrak{EH}$, are not linear in the velocity components any more.