regions, especially the most outlying parts of all, N and S, though no particular point can be specified as the exclusive origin of the lines of force.

The lines of force issuing from one polar region into the surrounding field curve round in wider and wider circuits until they reach the other polar region, where they terminate.

We find, therefore, the same properties which led us to distinguish between the two polar regions of a magnet with polepieces, when we painted them red and blue.

At the middle of the bar there is a region J where hardly any lines of force begin or terminate; the magnetic force in the immediate neighbourhood of this place is determined only by the lines which pass from the red to the blue end, and which here run parallel to the bar. This portion of the bar, then, contributes nothing directly to the strength of the field; it is called the indifferent zone.

If we give the bar magnet a half turn, more or less, about its axis, we still obtain the same line-of-force diagram in a plane parallel to the axis. Hence it follows that the field is symmetrical with respect to this axis (approximately when the cross-section is angular, accurately when it is circular). If a round bar magnet is supported in a vertical position, the line-of-force diagram fig. 5 will be obtained in a horizontal plane. This figure corresponds, therefore, to a plane cutting through the field perpendicularly to the axis of the magnet, all the lines being seen to run radially outward. To form a picture of the true disposition of the field (in three dimensions) we must imagine a series of planes, each drawn through one of these lines and the axis of symmetry of the magnet, and each corresponding to a distribution of lines like that depicted in fig. 4.

Since many lines of force originate at the circumference of the end of the magnet, there is in the diagram a correspondingly denser aggregation of iron particles, forming a black ring in the middle. The neighbouring portions of the diagram, within and just without this ring, have very few particles remaining, the

greater part having moved away to the annular region in question. Similar appearances are always to be observed in line-of-force figures when the magnetic force has a very strong component in the plane of the paper.

In the case of longer and thinner bar magnets, it is found that the lines of force diverge from two points whose distance apart is equal to about five-sixths of the length of the bar.

The case of very long thin bars is especially important. If such a bar be magnetised, iron filings will be found to attach themselves to the ends almost exclusively, assuming the form of nearly spherical tufts. Line-of-force diagrams show that directing forces are only appreciably exerted on iron particles lying near to the extremities, or poles. The lines of force in the neighbourhood of each pole follow a course which is not appreciably influenced by the more distant pole, the indifferent zone is much longer, and the particles surrounding either pole are not perceptibly acted upon by the other pole. In this way we are able to arrive at the conception of a single isolated pole; a conception which we shall frequently have occasion to employ.

FIG. 5

The field at either end of a long bar magnet of this kind is called unipolar.' For almost all forms of the crosssection of the magnet the lines of force proceed radially, as in fig. 5.

22. Compound magnets. As we have already explained, the magnetic effect of a magnet depends upon the number of lines of force which issue from it: the greater the number of lines proceeding from a magnetically active place, the greater their effect. To increase the effect due to a bar magnet, we may combine it with similar bars, magnetised in the same way; since the lines of force all diverge from one end, and converge again to the other end, the bars must

be so arranged with regard to one another that all the ends having the same kind of magnetism are together; that is, all the poles marked red are to be at one end, and those marked blue at the other end. (In § 27 we shall explain a simple criterion for distinguishing between the two kinds of polarity.) Combining in this way a number of bar magnets, each of which has been previously magnetised as highly as possible, we obtain a compound magnet.

The magnetic effect due to a compound magnet is not proportional to the number of rods of which it is built up. There is no simple relation between the weight of the compound magnet and its strength; the explanation of this being found in the influence exerted upon one another by magnets laid side by side with like ends together.

23. Magnets of special forms. From bar magnets we may pass on to magnets of some special forms, which it will be convenient to mention in this connection, some being of great practical importance, while some are more of theoretical interest, and are destined to play a most important part in the sequel. Very thin magnets may be made out of clock-spring. If we cut from a long thin strip of steel a piece in the form of a very elongated rhombus, and magnetise it by stroking with another magnet, so that the poles are at the acute corners, the result is a so-called magnetic needle.

Again, let a short thick bar of steel be magnetised perpendicularly to its axis. The transversely magnetised body so obtained has polar regions on the two sides of its bounding surface. If we imagine the length of the bar to be made. excessively small, we have a plate with poles at opposite points of its circumference. Small bell-shaped pieces of steel tube, closed at one end, are sometimes magnetised so that their poles are at opposite sides of the cylindrical bounding surface. A steel ring may be magnetised so as to have poles at opposite ends of a diameter. All these forms are of importance in connection with certain electrical and magnetic measuring instruments, which will be described later.

If a rod is strongly magnetic at both ends, and if we sufficiently reduce the length in the direction of the axis, we finally obtain a plate which has a distribution of magnetism on each face, so that the lines of force proceeding from one face bend round, embracing the rim of the plate, and finally reach the other face, where they terminate. A magnet of this kind is called a magnetic shell.' We may, if we choose, regard a long bar magnet as made up of a succession of magnetic shells placed face to face; all the faces of one kind looking in the same direction.

We shall find in Section II. that magnetic shells are of great theoretical importance, on account of the analogy between them and certain electro-magnetic arrangements (circuits in which currents are flowing). In view of the important applications which we shall afterwards have to make of them, we shall now construct circular, square, and rectangular cardboard models of magnetic shells, one side being covered with red paper and the other with blue.

24. The horse-shoe magnet. Since the effects produced by a bar magnet are strongest at the ends, where the lines of force are most numerous, we may conveniently obtain stronger fields by bending a bar into the form of a horseshoe or an incomplete ring, so as to bring the two ends near together. The ends of the horse-shoe are then finished by filing, so as to make their terminal faces lie in one plane, and the bar is magnetised along its entire length. If a horse-shoe magnet of this kind be supported in a vertical position, with its ends upwards, and if a line-of-force figure be then formed upon a sheet of paper held just above, the diagram obtained will be similar to that shown in fig. 3. In a plane drawn through the curved axis, that is, in the 'median plane' of the magnet, or in a neighbouring parallel plane (fig. 6), the lines of force proceeding from the ends n and s are seen to be closely crowded together, while in the space between the limbs of the horse-shoe they pass from one side to the other by very nearly the straightest and shortest path. Outside this space the lines are bowed out into wider and wider arcs, those proceeding from the outer