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

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

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

In '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.

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

it is in agreement with s approach.

I later return to the calculation of the ponderomotive force.

§ 8. Theory of H. A. Lorentz.

When we modify the connecting equations of the theory of, so that symmetry exists between the electric and magnetic vectors, then we arrive at the approach:

Besides four vectors contained in the main equations, two new vectors $$\mathfrak{E,H}$$ occur here. This circumstance makes 's theory more complicated than '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.