How is it possible? If it were a question of two circuits of invariable form, the one C fixed, the other C´ movable about an axis, this latter could never take on continuous rotation; in fact there is an electrodynamic potential; there must therefore be necessarily a position of equilibrium when this potential is a maximum.
Continuous rotations are therefore possible only when the circuit C´ is composed of two parts: one fixed, the other movable about an axis, as is the case in Faraday's experiment. Here again it is convenient to draw a distinction. The passage from the fixed to the movable part, or inversely, may take place either by simple contact (the same point of the movable part remaining constantly in contact with the same point of the fixed part), or by a sliding contact (the same point of the movable part coming successively in contact with diverse points of the fixed part).
It is only in the second case that there can be continuous rotation. This is what then happens: The system tends to take a position of equilibrium; but, when at the point of reaching that position, the sliding contact puts the movable part in communication with a new point of the fixed part; it changes the connections, it changes therefore the conditions of equilibrium, so that the position of equilibrium fleeing, so to say, before the system which seeks to attain it, rotation may take place indefinitely.
Ampère assumes that the action of the circuit on the movable part of C´ is the same as if the fixed part of C´ did not exist, and therefore as if the current passing through the movable part were open.
He concludes therefore that the action of a closed on an open current, or inversely that of an open current on a closed current, may give rise to a continuous rotation.
But this conclusion depends on the hypothesis I have enunciated and which, as I said above, is not admitted by Helmholtz.
4. Mutual Action of Two Open Currents.—In what concerns the mutual actions of two open currents, and in particular that of two elements of current, all experiment breaks down. Ampère has recourse to hypothesis. He supposes:
1º That the mutual action of two elements reduces to a force acting along their join;
2º That the action of two closed currents is the resultant of the mutual actions of their diverse elements, which are besides the same as if these elements were isolated.
What is remarkable is that here again Ampère makes these hypotheses unconsciously.