say from A´ to B´ along the movable wire, and it afterwards returned from B´ to B, then from B to A, then finally from A to A´, always following the fixed wire. The current was therefore also closed.
If a like current is subjected to the action of a closed current C, the movable part will be displaced just as if it were acted upon by a force. Ampère assumes that the apparent force to which this movable part AB seems thus subjected, representing the action of the C on the portion αβ of the current, is the same as if αβ were traversed by an open current, stopping at α and β, in place of being traversed by a closed current which after arriving at β returns to α through the fixed part of the circuit.
This hypothesis seems natural enough, and Ampère made it unconsciously; nevertheless it is not necessary, since we shall see further on that Helmholtz rejected it. However that may be, it permitted Ampère, though he had never been able to produce an open current, to enunciate the laws of the action of a closed current on an open current, or even on an element of current.
The laws are simple:
1º The force which acts on an element of current is applied to this element; it is normal to the element and to the magnetic force, and proportional to the component of this magnetic force which is normal to the element.
2º The action of a closed solenoid on an element of current is null.
But the electrodynamic potential has disappeared, that is to say that, when a closed current and an open current, whose intensities have been maintained constant, return to their initial positions, the total