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Translated from Recherches critiques sur l'Ėlectrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.

Annales 230 (Oeuvres 388)

     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 dτ of ponderable matter which is a seat of current, an element containing a large number of ions. Let V be its speed, Ni, ei 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[1]

     The electrostatic charge Edτ 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 –KJx, -KJy, -KJz, 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 Edτ of the element of volume appears as the difference of two incomparably greater charges: its positive charge E1dτ and its negative charge –E2dτ, both of the order of 1010Edτ. 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 E1, E2 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.

[1] Lorentz, Electronentheorie, §29, p.206.

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