Page:Elektrische und Optische Erscheinungen (Lorentz) 040.jpg

and by (V_a) the electric force acting on stationary ions,

${\overline {{\mathfrak {E}}_{x}}}=-4\pi {\frac {\partial }{\partial x}}\left({\mathfrak {p}}_{x}\chi _{x}+{\mathfrak {p}}_{y}\chi _{y}+{\mathfrak {p}}_{z}\chi _{z}\right){\text{, etc.}}$

(27)

At first glance, it therefore seems as if a current that streams through a conductor, is acting on a stationary ion with a force of first order. However, on closer reflection we find that the force (27) is just being compensated by another force.

The values (27) are in fact in perfect agreement with the expressions (22), if we substitute

$\omega =-{\frac {{\mathfrak {p}}_{x}\chi _{x}+{\mathfrak {p}}_{y}\chi _{y}+{\mathfrak {p}}_{z}\chi _{z}}{V^{2}-{\mathfrak {p}}^{2}}}$

(28)

By § 22, ω would belong to an electric charge, its density is

$\rho =\Delta '\omega {,}$

or by the given formulas

$\rho =-{\frac {{\mathfrak {p}}_{x}{\overline {{\mathfrak {S}}_{x}}}+{\mathfrak {p}}_{y}{\overline {{\mathfrak {S}}_{y}}}+{\mathfrak {p}}_{z}{\overline {{\mathfrak {S}}_{z}}}}{V^{2}-{\mathfrak {p}}^{2}}}$

(29)

Let us imagine for a moment that the current does not exist, but there is a charge with the average density ρ. This would of course exist only in the conductor, and the total sum would be zero, as it follows from (29) and

$\Delta {\overline {\mathfrak {S}}}=0$

Obviously this ion distribution would completely vanish, if it is left alone. This can also be expressed by saying that the charge will set them in motion by virtue of its action on resting ions, and that therefore eventually another charge with the average density -ρ occurs besides it, or

${\frac {{\mathfrak {p}}_{x}{\overline {{\mathfrak {S}}_{x}}}+{\mathfrak {p}}_{y}{\overline {{\mathfrak {S}}_{y}}}+{\mathfrak {p}}_{z}{\overline {{\mathfrak {S}}_{z}}}}{V^{2}-{\mathfrak {p}}^{2}}}$

Since the current that we considered initially, exactly acts on resting ions as the charge (29), it will also generate the charge A after a short time; this eliminates the effects on stationary ions, namely