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#### §5. –ELECTRIC CURRENTS

**WALTER RITZ **

##### Translated from Recherches
critiques sur l'Ėlectrodynamique Générale,

*Annales de Chimie et de Physique*, Vol. 13, p. 145, 1908.

The theory of electrons considers currents of conduction
in metals as well as in electrolytes and gases, as a transport of electric
charges, the positive ions going in the opposite direction from the negative
ions. Let us consider an element of volume *d*τ of ponderable matter
which is a seat of current, an element containing a large number of ions**. **Let
*V* be its speed, *N*_{i}, e_{i} the numbers, by unit
of volume, and the charge of one of the diverse sorts of ions, which make up
the current. The relative speed of an ion in relation to the ponderable matter
will be *v-V*. This is

Annales 231

what characterizes the current, the intensity of which, measured in
(Oeuvres 389) electrostatic units is, by hypothesis

_{}

The electrostatic charge *Ed*τ of the
element is

_{}

and the vector

_{}

constitutes the *convection current*, whose effects have been
studied by Rowland and others.

Nearby ions have a complicated effect on the ions
in motion, and we admit that this results on the average in a resistance *–KJ*_{x},
-KJ_{y}, -KJ_{z}, proportional to the relative speeds, *K*
being a constant. In the expression of *J*, irregular molecular movements
are without appreciable influence. The ions cannot leave the surface of the
conductor, except at a point of contact with another conductor.

This having been posed, formulas (13) and (20) contain, beside the electrostatic term,
only terms divided by the excessively large number_{}. These terms will be perceptible only if the speeds or
accelerations are extremely large, or if the quantities of electricity brought
into play are incomparably greater than those we get in electrostatics. The
study of electrolytes and of the Hall phenomenon have shown that the speeds of
ions and electrons are such that *v/c* is very small,

Annales 232

on the order of 10^{-10}. This result considerably simplifies
the theory. The electrostatic charge *Ed*τ of the element of volume
appears as the difference of two incomparably greater charges: its positive
charge *E*_{1}dτ and its negative charge –*E*_{2}dτ,
both of the order of 10^{10}*Ed*τ. We will designate such a
current by the name of *neutral current*.

(Oeuvres 390) We considerably simplify the
calculations without noticeably changing the results by admitting that there
are only two sorts of ions, one positive, the other negative; and that the
latter is the only one in relative motion in relation to the substance of the
conductor, while the positive charges stay attached to this substance and have,
like it, the speed V. We therefore have

_{}

The reader will be warned when this hypothesis is
affecting the results.

We know that in the application of the classical
theories, the distinction between closed and non-closed currents was essential.
It will still be so here. Only the former may remain

stationary (in fixed paths). As for the latter, the hypotheses made on *E*_{1},
E_{2} show that the extremities of these currents will carry, after
a very short time, very extensive free electric charges, which will profoundly
modify the conditions of the (current’s) motion. In general, non-closed
currents vary therefore extremely rapidly, unless very sensitive tools permit
us to bring into play very inferior quantities of electricity.

We will assume, as the theory of electrons demands
and in accordance with the views of Ampère, that *magnets are systems of
closed neutral currents*.