compartments do not flow together across the little wooden partitions.

When the apparatus is in the position shown in fig. 83, a current enters by z1, passes along the semicircular mercury channel Q, to the immersed end of the wire circuit B, up the right-hand side of the circuit, along the top, down the left hand side, through Q, and out by the wire z. The action between this current and the system of lines of force passing from N to S causes the circuit to be urged in the sense indicated by the dotted arrows, that is counterclockwise as seen from above.

2

The current-conductor continues to experience a rotational impulse under the influence of the fixed magnetic field until it has reached the position in which it embraces the maximum number of lines of force-that is, until its plane has become perpendicular to the direction of the field NS. Since the ring, moreover, possesses some inertia, the kinetic energy which it has acquired will cause it to turn some way beyond this middle position. But in order that the rotation may still be helped forward in the same direction, the field of the current must have its direction reversed. This result is automatically effected; for that end E of the wire circuit which previously dipped into Q2 passes across the intervening gap so as to reach Q1, and conversely. thus the current is made to flow up that side of the circuit which it previously flowed down, and the field of the magnet seeks to turn the circuit right about, which corresponds to a continuation of the existing motion in the same sense. At the next time of passing through the mean position (dead point) the direction of the current is once more automatically reversed in the movable part of the circuit; and so on.

If, instead of a single circuit of wire, we arrange a large number of such circuits upon one axis with their planes intersecting one another, the result is a drum-shaped surface entirely built up of these circuits, with currents flowing up one side and down the other. Such a drum when provided with a suitable commutator and placed in

a magnetic field, is set in rotation, the separate windings, which follow closely one after another, all helping to increase the effect (drum armature ').

In order to gather as many lines of force as possible through the windings, the wires are wound upon an iron drum, not made in one continuous mass but built up of thin plates of iron, insulated from one another and closely bound up together (laminated armature). The reason for this 'lamination will appear later. We need not speak here of the special arrangements which serve to reverse the current in the separate windings just at the right instant. They will be described in connection with dynamo machines, which are exactly the opposite of electro-motors in action.

192. Rotation of radial currents. In all cases where we have spoken of the axial system of lines of force of a galvanic current, we have assumed that the annular lines of force of these systems are, as it were, bound up with the material of the current-conductor, just as we saw, in the case of ordinary magnets, that the issuing and re-entering lines of force are definitely attached to the steel. The correctness of our assumption is shown in a specially instructive manner when we consider those continuous rotations which occur in the case of so-called radial currents, flowing within the fields of fixed magnets.

Experiment 65.-A circular disc of copper has its edge amalgamated, and is mounted upon a horizontal axle about which it can rotate freely, the lowest point of its circumference dipping into a drop of mercury in a hollow placed beneath. A strong current enters the disc at its centre and passes to the drop of mercury below, from which it is led away by a conducting wire. This current flows principally along that radius of the disc which terminates in the mercury, producing around it an axial system of lines of force. If the lines of force of a powerful horse-shoe magnet are made to pass perpendicularly through the lower part of the disc, this latter will be set in rotation (BARLOW'S wheel). Those parts of the wheel through which the current flows will be driven out of the magnetic field

T

in accordance with the left-hand rule. As soon as this happens, however, they cease to be traversed by the current, a new portion of the rim of the disc becoming immersed in the mercury; but the deflecting influence is now exerted on that radius of the wheel which has newly assumed the function of current-conductor, and which in consequence is also driven out of the field, and so on, the result being a continuous rotation of the disc.

Experiment 66.-The same effect is still more strikingly shown when a flat circular dish filled with mercury is placed upon one pole of a powerful electro-magnet, the internal margin of the dish being covered with an annular strip of sheet copper. If a metallic current-conductor be dipped into the middle of the mercury, the current being led away from the annular copper strip by a second conducting wire, the current spreads out radially from the centre, and is uniformly distributed in all horizontal directions through the mercury. Since the lines of force of the magnet pass upwards or downwards through the entire movable mass, the whole will acquire a rotatory motion, whose direction is given by the left-hand rule.

In the centre the rotation is strongest, for there the annular lines of force due to the current are most closely packed together. The level of the more central portion of the mercury surface becomes depressed, owing to the action of centrifugal' forces. The phenomenon may be rendered visible to an audience by allowing flat corks, carrying little candles, to float on the surface of the mercury.

In this experiment, as in those previously described, a commutator should be introduced into the circuit of the current, so that the direction of the current may be reversible, as well as that of the magnetic field. We have thus the opportunity of applying the left-hand rule in cases of the most varied kind.

193. Movements of a flexible conductor in the field of a bar magnet. The electro-magnetic actions assume a peculiar form when the current-conductor is flexible and is allowed to hang freely near to a fixed bar magnet, and parallel to

it. An arrangement suitable for this purpose is due to HELMHOLTZ.

To a square base-board B (fig. 84) is fastened a wooden stem H, supporting by means of a brass clamp the strong bar magnet M, with poles

n and s. Also attached to H is a thick copper wire D, which arches upwards as shown in the figure, and ends, vertically above the magnet, in a piece bent downwards. The extremity of this piece, which should not be too near to the pole n, is split so as to receive the end of a thin gold strip SS, which is firmly gripped by it, and hangs close beside the magnet reaching fully down to the baseboard B. A wire conveying a current is attached to the lower end of the gold strip by means of a binding screw, a corresponding wire being attached to D, and a commutator being placed in the circuit.

Experiment 67.- Let

the gold strip SS (fig. 84)

be supported at the middle

FIG. 84

so that it hangs loosely in the neighbourhood of the two ends of M, and then let the circuit of the current (about ten ampères) be closed. The strip becomes wound round the upper and lower portions of the magnet so as to form a continuous helix. If the direction of the current be reversed, the strip becomes unwound, and rewound in the

opposite direction. The unwinding and rewinding arising from repeated reversals of the current are especially striking. Here again, if the polarity of the magnet has been determined, the direction of the force acting upon each element of the movable conductor may be deduced from the left-hand rule.

For example, we find on applying the rule, that at the upper end of the rod, where the lines of force leaving the pole n are proceeding towards the observer, the strip conveying a current in the direction of the arrows, when in front of the magnet M will be urged towards the left (direction of the thumb), when behind the magnet to the right. This is apparent from the figure. At the lower end, that portion of the strip which lies in front of the magnet will be urged towards the right, that which lies behind towards the left.

194. Quantitative law of the mechanical action upon a movable current-conductor in a stationary magnetic field.—We have now followed out qualitatively in a variety of cases the action of a magnetic field upon a movable conductor. We saw that the left-hand rule could always be applied to determine the direction of the resulting motion, and we even deduced the law itself from a consideration of the symmetry which characterises the interaction of the fields concerned. We must now formulate the quantitative relations which hold good in such cases.

In all cases where quantitative relations between measurable quantities are concerned, the most general expression of the relation is that derived from the law of energy. From the expression idN, for the electro-magnetic energy of the field of a current (§ 170), by making use of the principle of energy, we may calculate the mechanical force P exerted upon a current-conductor by a magnet, owing to the mutual action of their respective fields.

In fig. 80, for example, let us suppose the rails, on which slides the movable conductor T, to run vertically upwards, and to have their upper ends connected to conducting wires so that they form part of a closed circuit. Thus when T