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.
So Ampère considered as open currents of this nature, for example, the currents of discharge of condensers; but he could not make them the objects of his experiments because their duration is too short.
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.
For example, if we connect by a wire the two poles of a Holtz machine, the charged rotating disc transfers the electricity by convection from one pole to the other, and it returns to the first pole by conduction through the wire.
But currents of this sort are very difficult to produce with appreciable intensity. With the means at Ampère's disposal, we may say that this was impossible.
To sum up, Ampère could conceive of the existence of two kinds of open currents, 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.