Page:Elektrische und Optische Erscheinungen (Lorentz) 016.jpg

certain point of space, constitutes an electric current (Maxwell's displacement current) that can be represented by ${\dot {\mathfrak {d}}}$. We assume that it exists also in the interior of charged matter. Yet additionally we find a convection current ${\mathfrak {C}}$ there. This is considered by me, when ${\mathfrak {v}}$ is the velocity of ponderable matter, as given in magnitude and direction by

${\mathfrak {C}}=\rho {\mathfrak {v}}$

and I put for the total current

${\mathfrak {S}}={\mathfrak {C}}+{\mathfrak {\dot {d}}}=\rho {\mathfrak {v}}+{\dot {\mathfrak {d}}}.$

(4)

In charged matter, ${\mathfrak {v}}$ shall continuously vary from point to point^[1]. Additionally the charge of every mass element shall stay unchanged during the motion. Thus $\rho \omega$ must be constant, when $\omega$ is the — maybe variable — volume of the element.

From this assumption we derive the property of solenoid distribution for the total current, which will be expressed by

$Div\ {\mathfrak {S}}=0.$

(5)

§ 7. The second deviation of the equilibrium state of the aether will be determined by the magnetic force ${\mathfrak {H}}$. It depends on the instantaneous current distribution, and satisfies the requirements

$Div\ {\mathfrak {H}}=0{,}$

(II)

$Rot\ {\mathfrak {H}}=4\pi {\mathfrak {S}},$

(III)

whose applicability we also presuppose for the interior of ponderable matter^[2].

Eventually we also assume the relation, for the interior of the ions^[3] as well as for the interspaces, by which in Maxwell's theory the dielectric displacement

1. By that it is of course not excluded, that mutually separated ions can often have very different velocities.
2. The justification of this lies in equation (5)
3. We neglect special magnetic properties of ponderable matter — which by the way would be explained by the motion of ions. Consequently we don't have to distinguish between the magnetic force and the magnetic induction.