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We shall afterwards have to consider more closely the analogous property of the polar regions of our earth; from one of these, magnetic lines of force proceed outwards into space, while at the other the lines pass back into the interior of the earth.

10. Localisation of the poles of a natural magnet.Experiment 4'.-Take several sheets of paper, and in each cut an opening of such shape and size that some particular cross-section of the magnet will just fix within it. Disposing the sheets in different places, but keeping them all horizontal, obtain on each one a figure of lines of force. By comparing these figures one with another, we shall be able to discover how the polar regions are distributed over the magnet.

11. The magnetic field. The entire space surrounding a magnet, as far as the force exerted has any perceptible magnitude, is referred to as the 'field' of the magnet.

Since for the present at least we are unable to trace the course of the magnetic influence within the substance of the magnet itself, we may consider the field to be confined to the external region. We may also consider it to be limited by a spherical surface enclosing the magnet, and of so great a radius that the magnetic force at all points external to the surface is not perceptible to the tests which we have so far employed. The field occupies the hollow region which lies between this spherical surface and the external surface of the magnet, a remark which is of importance in view of subsequent developments. As our means of detecting magnetic influences become more refined, the outer limits of the field become more extended; and strictly speaking there are no limits at all, the field extending indefinitely into space.

12. Course of the lines of force in the field of a natural magnet. To obtain a picture of the field of a natural magnet, we must combine together the line-of-force diagrams obtained in § 10. Each of them evidently gives no more than a plane sectional view of the field. We remark, then, how bundles of lines of force start from the boundary of the field (surface of the magnet) in certain polar regions, and after becoming more or less widely spread out as they run their course, are once more closely crowded together as

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

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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 (a1 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 c1 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

y. 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 c1, d' when they are transmitted there by of soft iron.

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means

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

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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.

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