other hand the more remote lines, owing to the pressure of the inner ones, are bowed out excentrically into widely spreading curves. In the neighbourhood of the axis of the coil, the field is approximately uniform.

The line-of-force diagram, fig. 71, was obtained in the following way. Upon a ring-shaped wooden frame, 17 cm. broad, 2.0 cm. deep, and 11 cm. internal diameter, many turns are wound of covered copper wire 1 mm. in diameter, and the frame is supported vertically upon a stand. A piece of thick cardboard, with a rectangular hole cut in it, is slipped over the ring and arranged so that its upper face is horizontal, and passes exactly through the centre of the ring. Upon the cardboard is laid a sheet of paper, with rectangular notches cut in one edge, to receive the cross-sections Sp of the coil, another sheet of paper with a straight edge being laid with this edge in contact with the notched edge of the former sheet. Thus we obtain even the central portions of the diagram, and by separately removing the two sheets from their positions and joining them together again, we are enabled to photograph the diagram without any obstruction from the upper part of the coil. Where the two sheets of paper meet, a dark line appears in the figure, running just above Sp Sp.

176. Multipliers. These are devices for detecting and measuring even feeble currents, and depend upon the principle of collecting together as many as possible of the lines of force due to the current. To produce more considerable effects upon a magnetic needle than would be possible with a simple current loop, the lines of force are augmented in number, by superposing many turns of wire. It was in this way that the first sensitive instruments for detecting and measuring currents were constructed (SCHWEIGGER and POGGENDORFF, 1820).

The effect may be still further increased by using, instead of a simple needle at the centre of the coil, an astatic pair of needles, one of which lies within the coil while the other, oppositely magnetised, lies above them. This arrangement of needles diminishes the influence of the earth's magnetism, which tends to restore the suspended system to its position of rest (§ 45), while it adds together

the effects produced by the windings upon the inner and outer needles, as may be easily verified by means of the 'thumb rule' (§ 160); the right hand, pointing in the sense of the current, being laid upon the upper part of the windings, first with the palm turned towards the inner needle, then towards the outer.

Since those ends of the needles which point in either one direction are of opposite polarity, the effects produced upon them by the field of the current will reinforce one another.

177. Galvanometer. The measurement of a current by deflection of a magnetic needle may be made more accurate when, instead of a single coil of wire, two coils side by side are used, the lines of force proceeding from the one being immediately taken up and kept together by the other. In this way we avoid a divergence of the lines of force at the place where their effect is to be compared with that of the earth's magnetism, the field between the two coils being nearly uniform. Here the magnet hangs, suspended by a cocoon fibre or thin quartz fibre; it may conveniently be in the form of a thin circular disc made of steel, and so magnetised that when it is suspended its magnetic axis is horizontal. If one face of the disc is polished, the deflections of the reflecting magnet may be very accurately read through the aperture of the coil by means of a scale and telescope (G. WIEDEMANN's mirror galvanometer). In place of the steel mirror, SIEMENS introduced a bell magnet, to whose stem a mirror was attached. For reasons to be explained later, the steel disc or bell magnet is surrounded by a mass of copper, and the suspended system is protected from draughts by a glass case.

More recently systems of several needles have been employed, arranged between two pairs of coils. A light silvered glass mirror is attached to the middle of a flattened aluminium wire. Above and below the mirror, on both sides of the wire, short slender pieces of magnetised watchspring are fastened, all the magnets belonging to the upper set having their north poles turned in one direction, while all those in the lower set have their north poles turned in

the opposite direction. If there are the same number of magnets above and below the mirror, and if all the individual magnets are about equally strongly magnetised, the whole system is very nearly astatic, the effect of terrestrial magnetism on the upper system being almost exactly neutralised by its opposite effect on the lower system. On the other hand, the magnetic moment of either system is relatively large, if we take account of its lightness. Each system of needles lies between a pair of coils, one pair being traversed by the current in one sense, and the other pair being traversed in the opposite sense. If the suspension is made by means of a thin quartz fibre, these instruments may attain to great sensitiveness, detecting even the billionth of an ampère. (Lord KELVIN, H. E. J. G. DU BOIS and RUBENS.)

178. Solenoids.-Let a long stiff wire be wound in the form of a helix, a certain space being left between consecutive turns, so that we may easily see what goes on in the interior. The wire tube thus formed is called a 'solenoid,' and must not be confused with the unit solenoids' spoken of in § 84, the two uses of the term being entirely distinct. We will investigate the disposition of the lines of force in the neighbourhood of such a coil when it is made the axis of a concentric distribution of force.

G

a

A

62

FIG. 72

In a board AA, fig. 72, 12 cm. by 25 cm. and furnished with a projecting rim, two small hollows a, b are sunk, and are filled with mercury, into which wires from without are made to dip. A

series of oblique parallel grooves r, to r, are also cut in the board and filled with mercury. Upon the board AA is laid another of equal size, which is kept in position by resting upon the projecting rim of the former; two semicircular openings being cut in this. rim to allow the upper board to be conveniently lifted off. The upper board is pierced perpendicularly with a series of holes (numbered from 1 to 16), and through these are thrust wire hoops B1 . . . . Bg. The free ends of these hoops are straight, and amalgamated at the tips, which dip into the mercury troughs (or cups) in the manner shown in the figure. Thus the hoops represent the upper portions of eight turns of a solenoid, the mercury troughs representing the lower portions. The phenomena will be very little influenced by the fact that the lower portions of the windings are not curved like the upper.

Upon the upper board is laid a sheet of paper pierced with corresponding holes. Over this fine iron dust is evenly scattered, and then the wire hoops B are arranged in position, so that they dip into the mercury below and establish a continuous metallic connection between a and b. After the current has been stopped, the wire hoops may be carefully lifted out again, and the line-offorce diagram rendered permanent, either by means of a spray of one of the solutions mentioned in § 7, or by transferring the iron particles to gummed paper, or by photography. It was by this last method that fig. 73 was prepared.

Line-of-force diagram in a plane through the axis of a solenoid (fig. 73).-Each of the black dots in the figure represents a cross-section of the conductor, and may be recognised as such by the encircling lines of force which are collected about it. But since the current has the same direction in adjacent windings, the more remote lines of force merge in

FIG. 73

to one another. Thus within the solenoid there is a continuous flow of lines of force which are bent into a sinuous form in the immediate neighbourhood of the current-conductor. Each turn of the solenoid encompasses fresh lines of force and carries forward the flux of force

from the preceding turn. Thus within the solenoid the magnetic force is very strong, while outside there are hardly any lines of force. The more nearly we approach the axis of the solenoid, the more exact is the parallelism between the lines of force; the field is uniform. Fig. 73 further illustrates the cross-pressure which the lines of force exert upon one another. The outer lines of the system bulge out into the spaces between the turns of wire, like elastic threads tied up tightly into a bundle, while just under the wire they are closely crowded together. Such a solenoid has far greater field-energy than its separate windings. At its ends, the lines of force diverge in all directions.

179. Equivalence of solenoids and bar magnets.--At one end of a solenoid lines of force emerge as they do from the north pole of a permanent magnet, while at the other end they re-enter the solenoid, as would be the case at the south pole. Thus a solenoid, so far as concerns the external disposition of its lines of force, behaves exactly like a bar magnet.

If we follow out the direction of the current, we have at once a sufficient datum for determining from which end of the solenoid the lines of force emerge, which end, that is, corresponds to the north pole of a magnet, as well as the end where the lines re-enter, that is, the magnetic south end. Since the current-conductor embraces the lines of force in the clockwise sense, these lines will be passing into the interior of the solenoid at that end which, viewed from the outside, corresponds to a clockwise circulation of the current. On the other hand, that end which corresponds to a counter-clockwise circulation must appear as a source of lines of force, that is, as a north magnetic pole.

Model of the solenoid with its lines of force.-A helix, 30 cm. long and 5 cm. in diameter, is wound from thick copper wire overwound with red cotton or silk, the direction of the current in the wire being indicated by means of red arrows. Through the helix are threaded a number of model tubes of force (fig. 39), which are bent round into the form of closed curves (§ 127), their arrangement being such that the rotatory motions corresponding to the magnetic forces follow the same direction as the current.