glass tube or a simple cylinder of wood, which is left a little longer than the helix itself, when we wish to hold it in the hand and present it, as was done with the magnet, either to a compass needle or to another movable helix (Fig. 95. a.). In the latter case we obtain with the two helices, each traversed by currents, all the same effects as are produced by the mutual action of two magnets. We may easily procure a current movable in a helix for imitating a magnetised needle, either by adjusting the conductor of the little floating pile into the form of a helix (Fig. 96.), or by terminating the two extremities of a helix formed of a silk-covered wire by a plate of zinc and one of copper, each thrust into a cork floating upon acidulated water.

Fig. 96.

We are indebted to M. G. de la Rive for an experiment, which evidences in a remarkable manner Ampère's hypothesis of the constitution of magnets. It consists in presenting to the floating electrical ring that we have described (Fig. 84.), a magnetised bar held by one of its extremities, whilst the other is placed in the centre of the ring. When the hypothetical current of the magnet and the real currents of the ring are moving in the same direction, we perceive the ring advance parallel to itself, until it has arrived at the middle of the magnet, and when once there it remains there. But if we withdraw the magnet and turn it round, that is to say, if we replace it exactly in the same position, but taking the precaution of merely changing the position of the poles, we immediately perceive the ring recede parallel to itself,—an effect that is due to its currents and those of the magnet being directed in a contrary way. What is curious in this is, that, when once arrived beyond the extremity of the bar, the ring, instead of continuing to be repelled, turns upon itself, describing an angle of 180°, presents itself to the magnet with its currents then moving in the same direction with its own, and returns by a rapid movement to the middle of the bar, where it again remains in equilibrio. We also obtain all

these same effects by substituting an electrical helix for the magnetised bar. They may easily be explained by the attraction and repulsion that are exercised, according as they are in a direction which is relatively similar or different, by the currents of the magnet or the helix upon the currents of the movable ring. With regard to the turning round that is executed by the ring when it goes off from the magnet after having been repelled, it is due to its plane never being perfectly perpendicular to the axis of the bar: the repulsive actions upon the different sides are not equal, and are transformed into a change of direction, which is necessarily followed by an attraction, as soon as the currents of the magnet and those of the ring are moving in the same direction. It is also easy to understand why the ring stops at the middle of the magnet; it is that evidently, in Ampère's theory, the middle of the magnet is, like the middle of the helix, the point of application of the resultant of all the parallel currents perpendicular to the axis, and moving in the same direction from one extremity to the other; it is therefore the point where the action exercised upon an exterior current must be at its maximum.

We may here inquire, why it is not the same when a magnet, instead of acting upon one or several currents forming a ring, acts upon iron or upon another magnet: we know, in fact, that in that case the action, on the contrary, is at its minimum at the middle of the magnet, and at its maximum at the poles, namely, at the points situated quite near to its extremities. Further: if we move a vertical electric current along and very near to one of the small vertical faces of a compass needle, we find that when this current is exactly opposite to one or other pole, it exercises no action; and that, if its action is of a certain nature, repulsive for example, upon all the points of the face of the magnet comprised between the two poles, it is of a contrary nature (attractive in this case) upon all the points of this same face that are situated beyond the poles, which, as we know, are never at the extremities themselves. The same effect is presented in a contrary direction upon the opposite face.

Thus, if the vertical current is directed upwards from below, it attracts all those points of the west face of the needle that are situated between the two poles, and repels those that are situated beyond; on the contrary, it repels all the points of the east face situated between the poles, and attracts all those that are situated beyond. A convenient and elegant manner of making this kind of action manifest consists in presenting to M. G. de la Rive's floating ring, and parallel to its plane, one of the lateral faces of a magnetised bar, taking the precaution that the centre of the ring be nearer to one of the extremities than to the middle of the bar. We then see the ring slide along the face of the magnet, resting against it on its two vertical sides; and as soon as one of them has passed the end of the bar the ring itself turns, describing an angle of 90°, and returns as before to the middle of the magnet. Thus, although in one of the vertical sides of the ring the currents are moving in a direction contrary to that which they have in the other, yet they are both attracted by points of the same face of the magnet, situated, it is true, on different sides of the pole.

The effects that we have just been describing, which were discovered and described by Faraday and by G. de la Rive, at first appeared very contrary to Ampère's theory of the nature of magnets; in fact, according to this theory, the electrical currents, the association of which forms a magnet, ought all to have had the same direction upon the same face of a magnetised bar, and, consequently, could not have exercised contrary actions, according as they were situated between the two poles, or beyond them. Finally, how are we to explain the nullity of action at the two poles themselves?

The objections that we have been pointing out did not arrest Ampère; he succeeded in overcoming them all, and established his theory upon such a solid basis that it is at the present time generally admitted. He set out from the principle that the electric currents to which, according to his view, magnets owe their properties, are molecular, that is, that they circulate around each particle. These electric currents pre-exist in all magnetic bodies, even although they

have not been magnetised, only they are arranged in an irregular manner so that they neutralise each other. Magnetisation is the operation by which a common direction is impressed upon them; whence it follows that the series of the exterior portions of the molecular currents which are all moving in the same direction, constitutes a finished current around the magnet, whilst the interior portions are neutralised by the exterior ones, moving in the contrary direction, of the following molecular stratum. In order to follow out these effects well, we must decompose the magnet into concentric and similar strata: Fig. 97. represents the section of a cylin

1

Fig. 97.

drical magnet, and the magnet itself. The direction impressed upon the currents by magnetisation is maintained in bodies that are endowed with coercitive force, and ceases in others, such as soft iron, as soon as the force that determined it ceases; because then all the molecular currents, being free to obey their mutual action, take the relative position that produces equilibrium, or the neutralisation of every exterior effect.

In order to submit this hypothesis to calculation, and thus to deduce from it all the effects of the mutual action of magnets upon currents, and currents upon each other, it would be necessary to commence by calculating the mutual action of two molecular currents alone, or, which amounts to the same thing, of two infinitely small portions of current. Now, this calculation required for starting points, besides the general law of attraction and repulsion according to the

direction of the currents, and which we have already established, certain principles furnished by experiment; and experiment cannot be made upon infinitely small portions of currents. But, by means of a calculation which is as rigorous as it is ingenious, M. Ampère has been able to deduce the principles that are necessary to be established in respect to infinitely small currents, from the cases of equilibrium that are furnished by the mutual action of finite currents. These cases

of equilibrium, to the number of four, enable us to determine the laws which the mutual action of infinitely small electric currents must necessarily obey, in order that they may be realised. And when these laws are once obtained, the calculation, on being applied to the consideration of infinitely small currents, leads to consequences perfectly conformable with experiment, in regard to the effects that must be produced by the assemblage of these currents, such as occurs in magnets and electric helices.

Let us now look into the four cases of equilibrium, furnished by experiment, which have served as the basis to the calculations upon infinitely small currents.

First Case of Equilibrium.

Two equal and contrary finite currents exercise upon a third, situated at the same distance from the two former, no action, the attractive action of the one being equal to the repulsive action of the other. In order to demonstrate this principle, we must employ a wire covered with silk, which is bent in the middle upon itself, so that its two halves, which are parallel to each other, may be in contact throughout their whole extent: the two extremities, which are situated one beside the other, are placed in communication one with the positive, the other with the negative pole of the pile, so that the two halves are traversed by the same current in opposite directions. To the vertical or horizontal astatic current of the float we present this double current, composed of two equal and contrary currents situated at the same distance from the movable current, and the action is alto