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where $$i\ d\ s$$ is to be considered as a vector in the direction of the current.

The second part of the force acting on ponderable matter
§ 12. A current element as the one previously considered, may be located in a magnetic field generated by external causes. According to a known law it suffers an electrodynamic force

for which we also can write now

or

This action results (according to our view) from the forces, which will be exerted by the aether upon the ions of the current element. It is thus near at hand, to assume for the force acting on a single ion

a hypothesis, which we still want to extend in a way, so that we generally assume a force acting on ponderable matter of the volume element $$d\tau$$

In unit charge this would be

By putting this vector together with $$\mathfrak{E}_{1}$$ that was considered earlier (§ 9), we obtain for the total force exerted on the unit of charge, i.e. for the electric force,