The Foundations of Science: Science and Hypothesis, The...

Ampère entitled his immortal work, 'Théorie des phénomènes électrodynamiques, uniquement fondée sur l'expérience.' He therefore imagined that he had made no hypothesis, but he had made them, as we shall soon see; only he made them without being conscious of it.

His successors, on the other hand, perceived them, since their attention was attracted by the weak points in Ampère's solution. They made new hypotheses, of which this time they were fully conscious; but how many times it was necessary to change them before arriving at the classic system of to-day which is perhaps not yet final; this we shall see.

It was not that he denied the possibility of open currents. If two conductors are charged with positive and negative electricity and brought into communication by a wire, a current is established going from one to the other, which continues until the two potentials are equal. According to the ideas of Ampère's time this was an open current; the current was known to go from the first conductor to the second, it was not seen to return from the second to the first.

Another sort of open current may also be imagined. I suppose two conductors, A and B, connected by a wire AMB. Small conducting masses in motion first come in contact with the conductor B, take from it an electric charge, leave contact with B and move along the path BNA, and, transporting with them their charge, come into contact with A and give to it their charge, which returns then to B along the wire AMB.

Now there we have in a sense a closed circuit, since the electricity describes the closed circuit BNAMB; but the two parts of this current are very different. In the wire AMB, the electricity is displaced through a fixed conductor, like a voltaic current, overcoming an ohmic resistance and developing heat; we say that it is displaced by conduction. In the part BNA, the electricity is carried by a moving conductor; it is said to be displaced by convection.

If then the current of convection is considered as altogether analogous to the current of conduction, the circuit BNAMB is closed; if, on the contrary, the convection current is not 'a true current' and, for example, does not act on the magnet, there remains only the conduction current AMB, which is open.

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.

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.

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:

This was by operating on a circuit C composed of two parts, the one fixed, the other movable. The movable part was, for instance, a movable wire αβ whose extremities α and β could slide along a fixed wire. In one of the positions of the movable wire, the end α rested on the A of the fixed wire and the extremity β on the point B of the fixed wire. The current circulated from α to β, that is to say, from A to B along the movable wire, and then it returned from B to A along the fixed wire. This current was therefore closed.

In a second position, the movable wire having slipped, the extremity α rested on another point A´ of the fixed wire, and the extremity β on another point B´ of the fixed wire. The current circulated then from α to β, that is to 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.

3. Continuous Rotations.—Among electrodynamic experiments, the most remarkable are those in which continuous rotations are produced and which are sometimes called unipolar induction experiments. A magnet may turn about its axis; a current passes first through a fixed wire, enters the magnet by the pole N, for example, passes through half the magnet, emerges by a sliding contact and reenters the fixed wire.

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.