However that may be, these two hypotheses, together with the experiments on closed currents, suffice to determine completely the law of the mutual action of two elements. But then most of the simple laws we have met in the case of closed currents are no longer true.
In the first place, there is no electrodynamic potential; nor was there any, as we have seen, in the case of a closed current acting on an open current.
Next there is, properly speaking, no magnetic force.
And, in fact, we have given above three different definitions of this force:
1º By the action on a magnetic pole;
2º By the director couple which orientates the magnetic needle;
3º By the action on an element of current.
But in the case which now occupies us, not only these three definitions are no longer in harmony, but each has lost its meaning, and in fact:
1º A magnetic pole is no longer acted upon simply by a single force applied to this pole. We have seen in fact that the force due to the action of an element of current on a pole is not applied to the pole, but to the element; it may moreover be replaced by a force applied to the pole and by a couple;
2º The couple which acts on the magnetic needle is no longer a simple director couple, for its moment with respect to the axis of the needle is not null. It breaks up into a director couple, properly so called, and a supplementary couple which tends to produce the continuous rotation of which we have above spoken;