upon one another. We speak, therefore, of a certain condition of magnetic polarisation which obtains in steel, soft iron, or any other substance exposed to magnetic influences. The question arises whether we can so conceive of this condition of stress in a magnetically polarised medium, as to obtain an explanation of the tension and pressure which we have already shown to exist along and across the lines of force respectively. We proceed to consider two elements lying side by side and polarised in the same sense.

Experiment 49.-Two thin soft iron rods, only a few centimetres in length, have each a loop at one end, to which a long thin silk thread is attached. The rods are suspended by means of the threads, so that they hang side by side at the same height, and a pole of a strong bar magnet is then brought near to them. They are seen to move away from one another. Through each of the rods passes a part of the flux of force which issues from the pole of the magnet, the upper ends of the rods thus acquiring the same polarity as the exciting pole, and their lower ends the contrary polarity. The two pairs of like poles, above and below, cause a repulsion between the two rods-that is to say, there is a pressure between them, and they accordingly separate until the restoring force due to gravity is great enough to preserve equilibrium.

If we conceive of a medium as made up of chains of such elements, which are joined end to end, the chains lying side by side, the separate chains must similarly exert lateral pressure on one another. But these chains indicate the course of the lines of force through the medium. From the polarisation of the separate elements, therefore, there arises a pressure across the direction of the lines of force.

We may similarly infer the existence of a tension along the lines of force. For we know that lines of force proceeding from the pole of the bar magnet pass along the small iron bars from one pole to the other, and since two poles of the same bar are of opposite polarity, they necessarily attract one another. When the chains of iron filings between two strong unlike poles continue to crowd more and

more into the middle of the field as the paper supporting them is tapped, some part of the effect may be attributed to the shortening of the chains of polarised particles, owing to the tension in the direction of their length.

This explanation is, however, only apparent, since we have assumed the existence of that tension along the lines of force which we set out to explain. Thus the assumption of a polarisation is not by itself sufficient to afford a mechanical explanation of the pressures and tensions in the field. It has therefore been necessary to subject the phenomena to a further analysis, by means of mechanical modes of representation which will be described later.

105. Paramagnetic and diamagnetic substances. All substances do not behave like soft iron towards the lines of force, collecting the lines more closely together, so that fewer are left to traverse the surrounding air. We have already (§ 14) ascribed this phenomenon to the greater permeability of soft iron to the lines of force. Certain substances, such as bismuth for example, have a magnetic permeability smaller than that of air. Lines of force proceeding through the air give way as they approach such a substance, bending round it so that fewer pass through than if the same space had been filled with air. Media which behave in this manner are called diamagnetic,' to distinguish them from paramagnetic media which behave like soft iron.

Models of paramagnetic and diamagnetic bodies in uniform fields. We will now describe two models, illustrating the greater permeability of paramagnetic substances, the lesser permeability of the diamagnetic, and the corresponding changes produced in the distribution of lines of force in a uniform field.

Along the shorter sides of two rectangular boards, 48 cm. long and 24 cm. broad (fig. 32), laths 2 cm. in thickness are fastened, one lath on each board being painted red and the other blue, to represent the north and south poles of a magnet. In the middle of each board is fastened a wooden block about 15 cm. long and 10 cm. broad. Through holes in the marginal laths wires are passed, and to these arrow-heads are attached, pointing from the north towards the south pole. The wires are to represent the

lines of force. The outermost wires pass directly across from one lath to the other, but in the middle of the series there are some short wires which are joined to the wooden blocks. All the wires are bent in the manner indicated in the figure.

From the disposition of lines of force in fig. 32 we conclude:

(a) That in the case of a paramagnetic substance such as iron (Fe), the lines of force issuing from the north pole are collected together

force tends to set it parallel to the direction n-s in the figure: axial' or 'polar setting.'

(b) That in the case of a diamagnetic substance such as bismuth (Bi) the lines of force issuing from the north pole are diverted on encountering the nearer end of the body, just as if there were a pole of like name there. They pass mostly through the surrounding medium, which they can traverse more easily. At the other side of the diamagnetic body the lines of force once more converge, just as if they were sucked in by the presence of a sink there.

The end of the body facing the north-seeking pole of the magnet is a source, and therefore also north-seeking, the end opposite the south-seeking pole being a sink, that is, south-seeking. When the diamagnetic body is free to

K

turn, the pressure across the direction of the lines of force will tend to set it perpendicular to the direction n―s: 'equatorial setting.'

The polar setting of paramagnetic and equatorial setting of diamagnetic substances may be demonstrated by preparing short bars of suitable materials, and suspending them by thin cocoon fibres. Very strong magnetic fields are necessary for the experiment, and the way in which these may be obtained will be described in Section II.

The behaviour of the two classes of substances towards the lines of force may be illustrated from the following example in fluid motion. If the bed of a straight broad flat stream is thickly overgrown with rushes, so that the flow of the water is considerably resisted, and if the rushes are cut away from a rectangular patch in the middle, so that within that patch there is no obstacle to the flow, the stream lines will be gathered together and pass more thickly through this place of greater permeability, just as the magnetic lines of force do through soft iron. If, however, there are no obstacles in the bed of the stream except a patch of rushes in the middle, the stream lines bend round so as to avoid the place of greater resistance, just as the lines of force do in the case of bismuth.

If the permeability of the surrounding medium is changed, a paramagnetic body may be thereby converted into a diamagnetic one, or vice versâ; so that one and the same body may set axially or equatorially between the poles of a magnet, according to the nature of the surrounding medium.

C.-Flux of magnetic induction

106. Magnetic induction. In the interior of a magnetised body the lines of force are propagated from molecule to molecule. If the magnetisation is uniform, it is to be measured by the intensity I ($ 99). Suppose the body to be placed in a magnetic field of strength , measured by the number of lines of force per square centimetre of cross section; this strength of field is then added to that already existing within the body.

We shall later on become acquainted with very simple methods of superposing two or more magnetic fields.

The magnetic condition is determined by the total number of lines of force per unit of cross-sectional area, the important magnitude thus measured being called the 'magnetic induction.' To show its significance as clearly as possible, we shall make use of a simple example. Let there be a toroid, uniformly magnetised with intensity I, and let this toroid be cut through at one place, so as to leave two free ends separated by an air-gap. We shall suppose the gap to be so narrow as not to disturb the uniformity of magnetisation. Then in accordance with § 99, there will be 473 lines of force passing across each square centimetre of the gap, and these continue their course to the same number through the substance of the toroid. Upon this system of lines of force we have to superpose whatever system may be due to external causes. latter let there be lines of force per cm.2, so that strength of the external field in absolute measure.

In the

is the

Then within the air gap there will be 473+ lines of force per cm.2, and the same lines continue their course uninterrupted through the substance of the toroid. The magnetic condition is characterised by the magnetic induction

Since all substances placed in a magnetic field become magnetised to some intensity I, we see that B is always to be distinguished from 5; when we have confined our attention to the strength of field 5, we have tacitly assumed J=0; this being justified by the small magnetisability of air, with which medium we were usually concerned.

107. Dimensions of the magnetic induction. Since the numerical factor 47 is without dimensions, it follows that B is the sum of two quantities, each of which has the dimensions cm. gr. sec. (§ 100 and $70). In other words, magnetic induction, intensity of magnetisation, and strength of field are all of the same dimensions. When we write

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