left in the sense of the current, following the rule given in § 160. 189. Mechanical interpretation of the dynamical forces.In Chapter II. we explained the mutual action of two magnets, not by supposing that their poles exerted forces of attraction or repulsion on one another, but by means of tensions and pressures in the intervening medium, that is in the field common to the two magnets. We shall now show that the forces which currents and magnets exert upon one another may be deduced from the structure of the resultant field, without any necessity for further assumptions. If a rectilinear current-conductor is brought into a magnetic field, which for the sake of simplicity we may suppose to be uniform, the lines of force belonging to the two fields will have the same direction on one side of the conductor, and contrary directions on the opposite side, provided the current does not coincide in direction with lines of force of the magnetic field. In accordance, then, with § 123, the effects of the lines of force become strengthened on one side of the current and weakened on the opposite side, and hence the conductor must experience a force tending to move it through the magnetic field. That the direction of the force is that which corresponds to the left-hand rule will be evident when we remember in which sense the current is embraced by its lines of force. The model, fig. 80, exemplifies very clearly the superposition of two fields in the present case. The two parallel limbs of a wooden framework are marked respectively N (red) and S (blue), and represent for example the poles of a horse-shoe magnet. To represent the lines of force hh of the uniform field between N and S, a number of indiarubber tubes are stretched across, their ends being secured to pegs, and arrows being marked upon them as in fig. 39. Within the field thus represented, we lay a model of the system of lines of force surrounding a current, fig. 65. T is the cross-section of the conductor, the direction of the current being towards the observer, and rr are the concentric ring-shaped tubes of force. To represent the possibility of sending a current through T, this conductor must be capable of moving parallel to itself along a pair of rails, parallel to N and S (that is, vertical), one in front of the magnetic system and the other behind. The rings of lines of force surrounding the current run counter-clockwise as seen in the figure, corresponding to the direction in which the current flows. Hence the rotational motions are towards the observer through the apertures of the rings, as indicated by the little arrows. Above the conductor T, fig. 80, each element of volume is traversed in opposite directions by lines of force due to the two fields, so that the two effects are antagonistic, the resultant J h 71 S h n FIG. 80 energy per unit volume and the pressure across the lines of force being correspondingly diminished. Thus below the conductor there is a pressure acting, which tends to thrust the conductor away, and is not compensated by an equal pressure above. Hence the resultant force on T is directed upwards as indicated by the arrow B. The effect is further increased by those parts of the lines of force which lie more to the two sides, since in the lower parts of the lines the components of the resultant rotational motion are greater than in the corresponding upper parts. If the forefinger of the left hand be laid upon the lines of force hh in the direction (N-S) of the arrows, and if the middle finger be extended in the direction of the current (i.e. from the plane of the figure towards the observer), the thumb will point upwards, in the direction of motion B (left-hand rule.) The special form of the mechanism in motion is here of less importance than the energy content of the various portions of the field, as exemplified by means of the mechanism. For we saw in § 170 that there must be a certain quantity of this fieldenergy to produce such mechanical forces as those now considered, the resulting displacements causing a change in the number of lines of force embraced by the current. Compare also § 194 below. 190. Electro-magnetic rotations. If we limit the freedom of motion of the current-conductor by constraining one point of it to occupy a fixed position in space, and if we arrange the movable portion of the conductor and the magnetic field so as to be symmetrical about this point, the mutual action between the current and the magnet may be made to produce a continuous rotation. Of the large number of mechanisms which have been constructed to show this rotation of a movable currentconductor in a magnetic field, we shall describe only a few typical examples, some of which are chiefly of historical interest, while others have important practical applications. (a) Faraday's rotating wire. This oldest and simplest of all such devices is still found the most convenient with currents of moderate strength. A movable piece of conducting wire has an eye at one end, by which it hangs in the field of a fixed magnet, whose axis passes through the point of suspension. The lower end of the wire dips into mercury, and when the circuit of the current is closed the wire rotates round the magnet. An ordinary cylindrical lamp-chimney G, fig. 81, 24 cm. in length and 4.5 cm. internal diameter, is closed by corks S and T above and below. Through the centre of the lower cork the bar magnet M is stuck so that one of its ends n projects to a distance of about 8 cm. into the interior of the cylinder. A conducting wire also passes up through the lower cork into the mercury. Another copper wire passes through T, and ends in an amalgamated loop H. From this hangs the straight piece of wire D, to which a small paper vane is attached. The lower part of the cylinder contains just enough mercury to ensure that the lower amalgamated end of the wire D shall dip well into it. The bar magnet M is fixed in a vertical position in a stand. If a current is sent through the movable wire D (fig. 81), from below upwards, and if the north pole of the magnet M is uppermost, the movement impressed upon the wire D, when it occupies the position indicated in the figure, will be away from the observer, and the continued action of the two fields upon one another will produce a rotation in the sense of the dotted arrow,that is, counter-clockwise as seen from above. (b) Rotating hoop of wire.-A more symmetrical arrangement may be made. by dividing the current, and making it pass down through the two legs of a wire hoop, one on each side of a bar magnet, fig. 82. 2 FIG. 81 The pole n of a powerful bar magnet or electro-magnet is surmounted by a wooden cap H, round the lower part of which runs an annular groove RR containing mercury, to which the conducting wire Z is connected. The pointed pivot s, directed vertically upwards, is fixed exactly in the centre of the cap, and upon it turns the wire hoop BB fitted with the bearing N. The two limbs of this hoop pass vertically downwards, and dip into the mercury channel RR on either side. The upper side of the bearing N is hollowed out and contains mercury, into which dips the amalgamated point of the wire D, held in an ordinary clip. Thus a current can enter the hoop through D. The current entering at N (fig. 82) becomes divided and flows along the two limbs of the hoop BB down to the mercury in the channel RR, from which it is led away by the wire Z. If it is the north pole n of the magnet which projects into the field of the current, the right-hand limb will be urged towards, and the left-hand limb away from the observer, so that the hoop of conducting wire will rotate in the sense indicated by the dotted arrows, that is in the clockwise direction as seen from above. This rotational direction, combined with the (upward) direction of the magnetic lines of force, constitutes a left-handed screw. 191. Magneto-electric motor.-The rotational movements experienced by current-conductors in the fields of fixed magnets are applied in the construction of machines which overcome frictional resistances at the expense of the energy of the electro-magnetic field, maintaining their moving parts in continuous rotation and having a capacity for performing mechanical work. This is the principle of magneto-electric motors, or electro-motors.' In all technical applications the movements directly produced are rotatory, though in some cases they are converted by suitable mechanism into a progressive or a reciprocating motion. The steam engine primarily produces only a reciprocating backward and forward motion, which is transformed into a rotatory motion by an intermediate mechanism of connecting rods and cranks. Herein lies the principal advantage of the electro-motor over the steam engine, the former producing directly the desired rotatory motion. Fig. 83 represents an arrangement which may serve as a |