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WALTER RITZ

#### Annales 240 (Oeuvres 396)

Lastly let us consider an electrostatic chargeswept along with a speed V' by the body which carries it and acting on a magnetized needle, that is to say on a system of closed and neutral currents, of nil electrostatic charge, whose positive ions are motionless, the negative ions having the speed v. An element ds of one of these currents will be subject to a force dRx, dRy, dRz, which is the sum of the actions of on its positive charge E'ds and its negative charge –E1ds, and expression (13) will give

The ensemble of terms proportional to V
' and v have the form already obtained several times; we have besides

(Oeuvres 397)  which we can integrate in relation to ds (this current being closed), as previously done in relation to ds', and we find again the formula which would be deduced from Lorentz’s theory. A transformation of this type will always be

possible as soon as at least one of the currents is closed. The additive terms in  would give a resultant force and no couple for the magnet, a force whose intensity, always very small, which depends on the hypotheses made on the movement of the ions in the magnet and is negligible in relation to the couple if v is small in relation to V, whether the negative electricity by itself is mobile or not.

When a dielectric is polarized by electrostatic forces there results in its surface identical electric charges according to both theories. If the electrostatic field varies, or if the dielectric is mobile, the movement of these charges will still be the same from both points of view and, we have just seen that these mobile charges will have the same action on a magnet. In the theories of Hertz and Lorentz, another action is added to this action, that of the displacement current relative to the ether which is proportional to the speed of the change of the electric force in one point of the ether. As in Röntgen’s experiment[1], the same as in those of Eichenwald[2], this action is nil in Lorentz’s theory, which consequently will give the same results, consistent with the experiment, as our formula.

To obtain an action dependent on k, that is to say an experimentum crucis, one has to be able to observe electrodynamic or electromagnetic forces between both non-closed or non-neutral currents. This has not yet been achieved.

[1] Annalen der Physik u. Chemie, t. XXXV, 1888, p. 264.

[2] Ann. der Physik, 4 série, t. XI, 1903, p. 1 et 421.