very great in respect to this diameter, like magnets, whose poles would be situated at the very extremities of these cylinders. This result therefore established a complete identity between a solenoïd and a magnetic filament; for the latter being composed of molecular currents, it is clear that, whatever be the distance at which it acts, the diameter of these currents is always infinitely small in relation to this distance. We will not follow M. Savary into the other consequences which he has deduced from his calculations; we shall confine ourselves to saying that they all agree with the results that had been already furnished by the experimental study of magnetism in the hands of Coulomb and other philosophers who have been engaged on this subject; so that, under the conditions laid down, a solenoïd represents a true magnet. Thus, in particular, they established by calculation, founded upon the laws of electro-dynamics alone, that the poles of two solenoïds repel each other if they are of the same name, namely, if the currents move in them in the same direction, and attract each other, if they are of contrary names. They also succeeded in establishing, that a solenoïd has no action when its direction is a closed curve; a result that agrees with what is furnished by a magnetised steel plate, which, when it is rolled into the form of a closed ring, ceases to present any traces of magnetism.

Ampère's theory, therefore, when regarded simply under the relation of the properties of magnets and of their mutual action, is found as satisfactory as that of Coulomb; but it has further this great superiority over the latter, that it accounts, upon the same principle, for all the phenomena of electrodynamics, that is to say, the mutual action of magnets and currents, and the mutual action of magnets upon each other. It is true it also rests upon an hypothesis, that of the existence of electric currents around the particles of magnetic bodies: but this hypothesis is quite as admissible as that of the existence of two magnetisms in each particle; we shall even see further on that recent facts seem to give it a further degree of probability, although there are others which we shall also point out, that are less easily reconciled

with it. It accords perfectly well with all the theoretical mathematical labours that have been gone through by M. Poisson, and by other philosophers, resting upon that of Coulomb; and cannot, therefore, but be advantageously substituted for it. With regard to the anomalies that we have pointed out, and which consist in the opposite actions that are exercised upon a current by the parts of a magnet situated on the different sides of the poles, and the nullity of action observed at the poles themselves, Ampère has shown that they are merely due to a magnet's not being able to be completely assimilated to a solenoïd, which represents only a simple magnetic filament; and that in a magnet, properly so called, the molecular currents exercise upon each other a reaction that modifies their relative arrangement, and takes from the extremities the regularity that exists in the central part. He showed, in particular, that the nullity of action at the poles proceeds from the poles being the points where the actions of the contrary currents are equal; and he has thus connected their position with the arrangement of currents, that depends itself on the general form of the magnet.

It would be easy for us, by returning to the study of the magnetic phenomena which are contained in our First Chapter, to show directly that Ampère's theory satisfies all cases. We will quote only one example. It is borrowed from the experiment in which, by breaking a magnetised needle through the middle, we thus create two new and contrary poles at the extremities that have just been disjoined. If we separate a solenoïd into two fragments by cutting it perpendicularly to its axis, we evidently obtain upon the two separated faces two currents, which, although moving in the same direction when they are one after the other, are moving in a contrary direction in regard to each other for the observer who looks at them both in front (Fig. 102.), or are in respect to him the two currents by which a solenoïd is terminated at each of its extremities. These currents, therefore, will determine upon the two new faces of the solenoïd opposite and contrary poles to those which are already found at the opposite extremity of the same fragment. Thus we see that this

experiment, when made upon a solenoïd, by giving the same result as when made upon a magnet, is explained perfectly well in the theory which admits that magnets are an assemblage of electric currents, distributed as we have pointed out.

Fig. 102.

Phenomena of continuous Rotation, arising from the mutual Action of Magnets and Currents, and of Currents upon each other.

By attentively observing the contrary action that is exercised upon a movable vertical current, either by the corresponding parts of a magnet taken on its two opposite faces, or by the points which, though situated on the same face, are on the different side of either pole, Mr. Faraday concluded that, if the current could turn freely around the

S

Fig. 103

pole, it would execute a continuous rotatory movement (Fig. 103.); and this he succeeded in realising. In order to obtain this in a decided manner, a cylindrical magnet must be placed in the centre of a capsule filled with mercury, taking care that the surface of this liquid is a little below the pole of the magnet; we then lead from a movable axis fixed vertically by means of two points between the summit of the magnet, and a piece of steel fixed to a metal support, a thin brass wire bent square, and the vertical position of which is terminated by a fine point, plunging slightly into the mercury,

so as scarcely to graze its surface (Fig. 104.). A voltaic current is transmitted through this movable conductor by

Fig 104.

means of the mercury on the one hand and the metal support on the other. The wire is immediately seen to be set in motion, and it turns rapidly around the magnet. The direction of the rotation depends at once on the direction of the current, and the nature of the pole of the magnet around which this rotation occurs. If the pole and the direction of the current are both changed at the same time, the direction of the rotation remains the same: in order that it may vary, we must change only one or the other of these circumstances at the same time.

Mr. Faraday also succeeded in determining a continuous rotatory movement in a magnet under the influence of a current, by plunging vertically into a vessel filled with mercury, by means of a ballast weight of platinum, a small magnetised bar, the summit alone of which appears above the liquid (Fig. 105.). A metal rod, communicating with one of the poles of the pile, descends vertically to the centre of the surface of the mercury, which is itself placed in communication with the other pole by means of a point of its circumference.

Fig. 105.

Im

mediately the current was established, the magnet commenced turning around a right line formed by the prolongation of the vertical rod beneath the surface of the mercury. We must

here observe that the magnet describes not a cylinder but a cone, provided its lower extremity is placed upon the axis of rotation, and remains there while its upper extremity describes a circle around the point where the vertical conductor touches the surface of the mercury. The direction of the motion in this case, as in the preceding, depends upon the direction of the current, and upon which of the two magnetic poles is on the top of the magnet.

In this experiment, as in the preceding one, the rotation goes on accelerating up to a certain point, at which its velocity becomes uniform, which is due to the resistance opposed by the mercury to the effect of the evidently accelerating force that produces the motion.

Faraday's experiments, at the time they were made, appeared irreconcileable with Ampère's ideas; but this philosopher had not at that period made known his law of angular currents, by means of which he soon succeeded in easily explaining the phenomena observed by Faraday, and adding to them certain others that are no less curious. Then, in order to add an experimental proof to the theoretic demonstration that he had given, that all these facts were not contrary to his hypothesis of the nature of magnets, he repeated them all, by supplying the place of the magnets by electro-dynamic helices or cylinders, or assemblages of parallel circular electric currents.

In order thoroughly to comprehend how an attraction or repulsion between currents can give rise to a rotatory action, we must set out from the distinction that Ampère established between closed and open currents. A closed current is that which, setting out from a point, returns to the same point, after having described a figure of any form (no matter what the form may be). It is not necessary, in order that the current be closed, that the whole circuit, including that of the pile, should form part of it, as occurs in floats. It is equally closed in movable conductors, one of the extremities of which sets out from a