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;
3º Finally the force acting on an element of current is not normal to this element.
In other words, the unity of the magnetic force has disappeared.
Let us see in what this unity consists. Two systems which exercise the same action on a magnetic pole will exert also the same action on an indefinitely small magnetic needle, or on an element of current placed at the same point of space as this pole.
Well, this is true if these two systems contain only closed currents; this would no longer be true if these two systems contained open currents.
It suffices to remark, for instance, that, if a magnetic pole is