but he could operate on neither because they were not strong enough or because their duration was too short.
Experiment therefore could only show him the action of a closed current on a closed current, or, more accurately, the action of a closed current on a portion of a current, because a current can be made to describe a closed circuit composed of a moving part and a fixed part. It is possible then to study the displacements of the moving part under the action of another closed current.
On the other hand, Ampère had no means of studying the action of an open current, either on a closed current or another open current.
- The Case of Closed Currents.—In the case of the mutual action of two closed currents, experiment revealed to Ampère remarkably simple laws.
I recall rapidly here those which will be useful to us in the sequel:
1º If the intensity of the currents is kept constant, and if the two circuits, after having undergone any deformations and displacements whatsoever, return finally to their initial positions, the total work of the electrodynamic actions will be null.
In other words, there is an electrodynamic potential of the two circuits, proportional to the product of the intensities, and depending on the form and relative position of the circuits; the work of the electrodynamic actions is equal to the variation of this potential.
2º The action of a closed solenoid is null.
3º The action of a circuit C on another voltaic circuit C´ depends only on the 'magnetic field' developed by this circuit. At each point in space we can in fact define in magnitude and direction a certain force called magnetic force, which enjoys the following properties:
(a) The force exercised by C on a