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not only in the outer points, but also, at least with respect to the averages of the forces, in the interior of the conductor.

I want to call this charge A the compensation charge. Once generated, the conductor does not cause any electricity motion in a neighboring body. A stationary current in a wire moving with the Earth therefore exerts no inductive action on a circuit which is also at rest with respect to Earth, regardless of Earth's motion^[1].

It should be noted now that in the finally occurring state of the system, ρ and ${\mathfrak {d}}$ have certain values of order ${\mathfrak {p}}$ . Neglecting the magnitudes of second order, then it really follows from (4_a)

${\overline {\mathfrak {S}}}={\overline {\rho {\mathfrak {v}}}}.$

Interaction between a charged body K and a conductor.

§ 26. After the foregoing, we have to assume that in the conductor next to the current ${\overline {\mathfrak {S}}}$ , a compensation charge does exist, and also (at the surface of the conductor) the electrostatic induction-charge B caused by K. For simplicity, we imagine that ${\overline {\mathfrak {S}}}$ , $A$ and $B$ co-exist as independent ion systems^[2].

↑ It should be remembered that Mr. Budde (Wied. Ann., Vol 10, p. 553, 1880), on the basis of Clausius' law, reached the same conclusions, as it was drawn here by me. His value for the density of the compensation current even completely agrees with the above-found, if ${\mathfrak {p}}^{2}$ is neglected.
↑ This mode of imagination, however, is in no way necessary. To show that the considerations communicated in the texts are correct, we don't need to assume, that the ions which form the charges A and B, were remaining at rest and were altogether uninfluenced by the adjacent existing current. We can also imagine that all ions are moving, similar to an electrolyte, in a most irregular manner. But a constant, non-zero mean value ${\bar {\ ho}}$ is very well possible; because this constitutes the charges designated by A and B (i.e., ${\bar {\rho }}$ is composed of two terms of a sum ${\bar {\rho _{A}}}$ and ${\bar {\rho _{B}}}$ ), while the current ${\overline {\mathfrak {S}}}$ is determined by ${\overline {\rho {\mathfrak {v}}}}$ . If in (A) and (B) all members are replaced by the mean values, one easily sees that each of the vectors ${\overline {\mathfrak {d}}}$ and ${\overline {\mathfrak {H}}}$ consists of two parts, where one of them only depends on ${\bar {\rho }}$ and the other one only depends on ${\overline {\rho {\mathfrak {v}}}}$ . Now, as the actions to the outside were determined by those vectors, then they are just so, as if the charge and the current were not connected with each other at all. The same is true for the actions exerted on the conductor. Namely, if ${\mathfrak {d}}$ and ${\mathfrak {H}}$ are the variations caused by external causes in the aether, then by (V_a) the force acting on a volume element is given by

$4\pi V^{2}\rho {\mathfrak {d}}\ d\ \tau +\rho [{\mathfrak {p.H}}]\ d\ \tau +\rho [{\mathfrak {v.H}}]\ d\ \tau .$

The action, to which a noticeable part of the body is subjected, can thus be calculated in a manner, by which we put as unit volume

$4\pi V^{2}{\bar {\rho }}{\mathfrak {d}}+{\bar {\rho }}[{\mathfrak {p.H}}]+[{\bar {\rho {\mathfrak {v}}}}.{\mathfrak {H}}]{,}$

which again decomposes into two parts ${\bar {\rho }}$ and ${\overline {\rho {\mathfrak {v}}}}$ .
Strictly taken, also a third charge would have to be taken into account. The current can not exist without a potential gradient, and this cannot exist without electric charges of the parts of the conductor. These charges, however, play in the considered questions no essential role, and could even more be left out, as we can think of them as vanishingly small if we assume a very high conductivity.

[1] It should be remembered that Mr. Budde (Wied. Ann., Vol 10, p. 553, 1880), on the basis of Clausius' law, reached the same conclusions, as it was drawn here by me. His value for the density of the compensation current even completely agrees with the above-found, if ${\mathfrak {p}}^{2}$ is neglected.

[2] This mode of imagination, however, is in no way necessary. To show that the considerations communicated in the texts are correct, we don't need to assume, that the ions which form the charges A and B, were remaining at rest and were altogether uninfluenced by the adjacent existing current. We can also imagine that all ions are moving, similar to an electrolyte, in a most irregular manner. But a constant, non-zero mean value ${\bar {\ ho}}$ is very well possible; because this constitutes the charges designated by A and B (i.e., ${\bar {\rho }}$ is composed of two terms of a sum ${\bar {\rho _{A}}}$ and ${\bar {\rho _{B}}}$ ), while the current ${\overline {\mathfrak {S}}}$ is determined by ${\overline {\rho {\mathfrak {v}}}}$ . If in (A) and (B) all members are replaced by the mean values, one easily sees that each of the vectors ${\overline {\mathfrak {d}}}$ and ${\overline {\mathfrak {H}}}$ consists of two parts, where one of them only depends on ${\bar {\rho }}$ and the other one only depends on ${\overline {\rho {\mathfrak {v}}}}$ . Now, as the actions to the outside were determined by those vectors, then they are just so, as if the charge and the current were not connected with each other at all. The same is true for the actions exerted on the conductor. Namely, if ${\mathfrak {d}}$ and ${\mathfrak {H}}$ are the variations caused by external causes in the aether, then by (V_a) the force acting on a volume element is given by

$4\pi V^{2}\rho {\mathfrak {d}}\ d\ \tau +\rho [{\mathfrak {p.H}}]\ d\ \tau +\rho [{\mathfrak {v.H}}]\ d\ \tau .$

The action, to which a noticeable part of the body is subjected, can thus be calculated in a manner, by which we put as unit volume

$4\pi V^{2}{\bar {\rho }}{\mathfrak {d}}+{\bar {\rho }}[{\mathfrak {p.H}}]+[{\bar {\rho {\mathfrak {v}}}}.{\mathfrak {H}}]{,}$

which again decomposes into two parts ${\bar {\rho }}$ and ${\overline {\rho {\mathfrak {v}}}}$ .
Strictly taken, also a third charge would have to be taken into account. The current can not exist without a potential gradient, and this cannot exist without electric charges of the parts of the conductor. These charges, however, play in the considered questions no essential role, and could even more be left out, as we can think of them as vanishingly small if we assume a very high conductivity.

[1]

[2]