they re-enter the magnet at other places. Many lines do not turn back again, but appear to lose themselves in remote parts of the field.

The field of a magnet is extended in three dimensions, since it occupies a certain region of space. The term 'field' is hardly a correct expression of our meaning, when we ordinarily think of something two dimensional-that is, a distribution of lines of force over a surface.

B.-Natural magnets with iron armatures

In studying magnetic relations by means of natural magnets, there are difficulties arising from irregularity of shape, and irregular distribution of polarity. We must therefore find some means of directing the magnetic influences, and concentrating them in small determinate regions; to attain which object we may avail ourselves of the property possessed by soft iron, of taking up and transmitting the magnetic state.

13. Transmission of magnetic influence by soft iron.—Experiment 5.-Let a rod of soft annealed iron be held in a vertical position by means of a wooden clamp, and then let a vessel filled with iron filings be brought near to its lower end. Even if the filings are brought into contact with the rod, very few of them are found to adhere. If, however, a magnetically active corner of a lodestone be held touching the upper end of the rod, a tuft of filings will remain hanging to the lower end, the separate strings of particles diverging from one another. It is thus seen that in the present case magnetic lines of force issue from the lower end of the rod, and these have been transmitted downwards through the iron from the natural magnet above. When the magnet is removed, the iron filings fall from the rod.

14. Magnetic permeability.-We shall better understand the transmission of magnetic effects through the soft iron if we apply soft iron bars to the two poles of a natural magnet (figs. 2a, 2b).

Experiment 6.-Place a piece of lodestone on a horizontal

plane, uniformly sprinkled with iron dust, arranging it so that two poles may lie as close together as possible, producing the line-of-force diagram (fig. 2a). There are poles

above a and b as is shown in the figure by the numerous lines curved downwards, and passing from one point to the other, though not very easily discernible. The lines of force which diverge from a converge again towards b. At points more remote from the poles, such as c and d, the directing influence of the magnetic force is no longer appreciable.

Now place the lodestone on a second piece of paper as thickly dusted over with iron as the first. At the two poles (al and b', fig. 2b) lay two elongated pieces of soft iron upon the paper, underneath the magnet, and direct them so that their free ends c' and d' approach one another more and more closely, actual contact between them being prevented by a small piece of cork attached to the end of one rod. On tapping the paper, the iron dust becomes arranged as

in fig. 2b. A comparison of the two diagrams shows that:

a. The lines of force are attracted to the iron rods, many of them beginning or ending on the rods.

B. In particular, the lines of force proceeding directly from the poles a and b appear to be collected together and transmitted by the iron.

FIG. 2b

7. Accordingly the number of lines of force passing across from one iron rod to the other, but especially the number of lines issuing from the free ends c' and d', is much greater than it would be at corresponding parts of the field, when no iron is present.1 The magnetic effects which arise from the poles a and b are rendered perceptible at more distant points of the field c', d' when they are transmitted there by means of

soft iron.

Borrowing a term from an analogous problem in fluid motion, we say that the iron has considerable magnetic permeability.'

15. Magnetic permeability of different substances.-Experiment 7.-Let experiment 6 be repeated with rods of wood, glass, copper and brass of the same size as the iron rods. The influence of any of these on the transmission of magnetic influence from the lodestone is not appreciable, the substances in question having a permeability far less than that of iron.

The little rods of iron used in producing fig. 2b had previously acquired some magnetism of their own.

Under the influence of very strong magnetic fields, however, these substances exhibit in a slight degree properties which are in some respects similar to those of soft iron.

16. Natural magnets fitted with pole-pieces.--The high permeability of soft iron enables us to modify the field of a natural magnet in a convenient way. The polar regions of a lodestone are furnished with closely-fitting iron pieces which are continued in the form of massive iron blocks, and from these very powerful effects are obtained.

The polarity is transmitted to the exterior of these socalled 'pole-pieces,' which serve to concentrate the magnetic effect.

Experiment 8.-Let one of the natural magnets used in experiment 1 be furnished with pole-pieces in the manner described above. On dipping the points of the pole-pieces into iron filings, the adhering tufts will be found to be much longer and stronger than could be obtained at any part of the magnet in its natural condition.

Experiment 9.-Let a magnet furnished with pole-pieces be supported in a wooden stand, with the ends of the pole-pieces facing upwards. To effect this a block of wood, with a cavity cut to receive the magnet, is fixed to a board of sufficient width, while four wooden supports, attached to this board, serve to carry a wooden frame, whose upper edge is at the same height as the pole-pieces of the magnet. The sheet of paper or of glass on

FIG. 3

which the magnetic pictures are to be formed is laid upon this frame, and when the experiment is not proceeding a piece of soft iron is placed joining the two poles. The line-of-force diagram in fig. 3 shows how the lines of force pass from the one pole (n) to the other (s). The crowding together of the lines near the poles shows how the magnetic force is concentrated at these places.

We shall find it convenient in future to mark the poles in some definite manner, one with red and the other with blue (preferably with enamel colours). Accordingly the lines of force will be spoken of as issuing from the red pole (n) and entering the blue one (s).

17. The keeper.-If a piece of soft iron, whose length is equal to the distance between the pole-pieces, is brought near to the latter, many of the lines of force leave the surrounding space, and pass through the iron. Just as chains of little iron particles were previously held fast, so now the entire mass of iron will be supported, when we arrange it as a bridge connecting the pole-pieces. On turning the magnet round, the soft iron is found to remain hanging to it, the attraction due to magnetic influences overcoming gravity. The piece of soft iron is called the keeper, because the closing of the magnetic circuit in the manner described has an important influence in preserving the properties of the magnet.

Experiment 10.-Effect of closing the magnetic circuit.—Let a magnet provided with pole-pieces be laid in a horizontal position, then form and fix the line-of-force figure just over the pole-pieces. Next place the keeper near to the pole-pieces, form another figure, bring the keeper nearer, once more form a figure, and so on. A comparison of the different figures shows how the keeper gathers together and transmits through its substance the lines of force which pass from pole to pole. The nearer it is brought to the magnet, the more numerous are the lines of force which enter and leave it, nearly all the lines passing to the end of the keeper from the nearest magnet-pole across the shallow intervening gap, where they follow approximately the shortest possible path. If the keeper is brought into actual contact with the poles, it is held fast by them.

C.-Artificial magnets of various forms and their fields

We should make but slow progress in the knowledge of magnetic phenomena if all our investigations were to be made with natural magnets, with or without pole-pieces. In