thirdly, a stage when increase of H only produces a small increase in the alignment of the magnets. Thus with only two magnets an indication of the chief peculiarities of the magnetisation curve can be obtained.

By considering much larger numbers of such pivoted magnets a much nearer approach to the phenomena actually found in the case of the magnetisation of a magnetic metal can be obtained. We have, however, said enough to indicate the line of argument by means of which Ewing supports his theory, and for further details we must refer the reader to his original papers on the subject.

In order to account for the heat developed in iron, due to hysteresis, when it is taken through a cycle of magnetisation, Ewing supposes that, on the decrease of the magnetising force, the molecular magnets return towards their undisturbed positions, and in doing so acquire kinetic energy, so that instead of immediately coming to rest they will execute oscillations about their position of rest till the kinetic energy thus acquired is converted into heat due to the currents induced in neighbouring molecules (see § 516).

In the above molecular theory of magnetism no supposition has been made as to the cause of the molecules being magnets. To account for this Ampère put forward the hypothesis that the magnetism of the molecule was really the field of an electric current which circulates continuously within it. In order to account for the fact that these molecular currents must continue without diminution, it is necessary to suppose that the molecule offers no resistance to the circulation of these intra-molecular currents such as occurs when a current passes between one molecule and another in the phenomenon of conduction.

The direction in which the Ampèrian molecular currents must be supposed to circulate can at once be obtained from either of the rules given in § 471. Since if we face a north pole the lines of force run from the pole towards us, and in a circle conveying a current the lines of force flow towards the spectator when the current circulates in the anticlockwise direction, it follows that when facing the north pole of a magnet the molecular currents must circulate in the anticlockwise direction.

In the same way, if we suppose that the earth's magnetic field is due to currents circulating round the earth, since the pole near the geographical north pole is what we call in magnetism a south pole, it follows that the currents must flow in the east to west direction, that is, in the same direction as the apparent motion of the sun.

508. Paramagnetic and Diamagnetic Bodies.-Iron, nickel, and cobalt, the so-called magnetic metals, are materials in which the permeability is greater than unity, that is, greater than the permeability of air. In addition to these bodies there are others in which the permeability is only very little greater than that of air. All these substances are classed together as paramagnetic bodies. The great majority of substances, however, have permeabilities less than that of air, and are called diamagnetic.

The extent to which bodies exhibit diamagnetism is, however, very much smaller than the paramagnetism of iron, nickel, and cobalt. Thus bismuth, the most strongly diamagnetic body known, has a permeability of 0.9998, while the permeability of iron under certain conditions is as high as 2000. If a rod of a diamagnetic material is introduced into a magnetic field, it will become magnetised by induction, but the poles will be in the opposite direction to what they would be in the case of a paramagnetic body, so that the south pole is turned towards the direction in which the lines of force of the magnetising field are running.

The fact that in diamagnetic bodies the permeability is less than it is in air means that the induction, Â, through the body is less than the value of the field which would exist if the body were removed. This can only hold if the tubes of force due to the magnetism induced in the body run, within the body, in the opposite direction to the tubes of force of the field. In order that the tubes of force due to the induced magnetism of the body may, in the body, run in the opposite direction to the tubes of force of the inducing field, a north pole, that is, a place where tubes of force leave the body, must be formed at the end of the body which is turned towards the direction from which the tubes of force of the field enter the body. Hence, when a diamagnetic body is introduced into a uniform

FIG. 487.

magnetic field, the lines of force within the space occupied by the body are fewer than there would be in this space were the body removed. On the other hand, outside the body the lines of force will be more closely packed than they would be in the absence of the body, for outside the body the tubes of force due to the induced magnetisation of the dia

magnetic body are, on the whole, in the same direction as the tubes of force in the field. In Fig. 487, the lines of force of a uniform field in which a sphere of a strongly diamagnetic material has been

FIG. 488.

introduced are shown. The corresponding case, where the sphere is composed of a paramagnetic material, is shown in Fig. 488. It will be noticed how in this case the lines of force crowd into the sphere, and are more widely spaced in the region outside the equatorial portion of the sphere.

Suppose that a bar of a para

magnetic material AB (Fig. 489) is placed in a magnetic field of strength H, the direction of which makes with the length of the bar an angle . We

A

Hcos

H

Hsin.0

may resolve the field H into a component H cos parallel to the axis of the cylinder, and a component H sin perpendicular to the axis. If I is the intensity of the magnetisation parallel to the axis induced by the component H cos 0, and if k is the susceptibility of the iron, and the length of the cylinder is so great that the demagnetising force due to the induced poles can be neglected, we have I1=kH cos 0. If the length of the cylinder is / and its cross-section is s, the volume is sl, and since the magnetic moment of a magnet is equal to the product of its volume into the intensity of magnetisation, the moment of the cylinder due to the magnetisation induced by the component of the field parallel to the axis is sl. kH cos 0. Now in § 425 it was shown that the couple acting on a magnet, of which the moment is M, tending to turn it into parallelism with a field of strength H, when its axis makes an angle with the direction of the field, is MH sin 0. Hence the couple, due to the magnetism induced by the component parallel to the axis, tending to turn the cylinder is slk H2 cos 0 sin 0.

FIG. 489.

The component of the magnetising field at right angles to the axis will also induce a magnetisation in its own direction. In this case the magnetising force will be much less than H sin 0, on account of the demagnetising force exerted by the ends, and it has not yet been found possible to calculate exactly what this effect will be in such a case as that we are considering. If we consider the bar as a spheroid, of which the major axis is very much greater than the minor axis, the intensity of the transverse magnetisation can be shown to be given by

and is in the opposite direction to the moment due to the longitudinal magnetisation. The total turning moment is therefore given by

In the case of iron in a magnetising field about equal to that of the

earth in these latitudes is about 30, so that the term

1.6, and so is small compared to the term k. The cylinder of iron thus tends to set itself parallel to the direction of the field.

In the case of a diamagnetic body the value of k is so small that 1+2k is practically unity, and the term

k is very nearly equal to ¿, I +2πk so that in a uniform field there is no measurable directive force exerted upon even a cylinder of bismuth (k=0.6 106). The manner in which a diamagnetic cylinder will set itself in a very strong magnetic field can, however, be at once foreseen. Since there will be a south pole induced at A (Fig. 489), and a north pole at B, the cylinder will tend to turn round in the anticlockwise direction. When it got beyond the position where its axis was at right angles to the direction of the field the polarity would be reversed, so that in such a position as A'B' there would be a north pole at A' and a south pole at B', and hence the cylinder would tend to return into the position where its axis is at right angles to the direction of the field. Diamagnetic bodies therefore tend to turn, so that their longer axis is at right angles to the direction of the field.

Solids are not the only bodies which exhibit magnetic properties; thus oxygen and some solutions of iron salts are paramagnetic, while water and alcohol are diamagnetic.

By means of these liquids it can be shown that the direction in which a cylindrical tube filled with, say, a paramagnetic liquid tends to set itself depends on the susceptibility of the surrounding medium. Thus a tube containing a weak solution of ferric chloride will in air or water set itself parallel to the direction of the field, since its susceptibility is greater than that of either air or water. If, however, it is surrounded by a stronger solution of ferric chloride, it will behave like a diamagnetic body and set itself with its length perpendicular to the direction of the lines of force of the field. This effect is at once explainable if we consider that when the tube containing the weak solution is placed in the stronger solution, since the permeability of the contents of the tube is less than that of the surrounding medium, the induction through the tube will be less than that which would exist if the tube were removed, and the tube is practically diamagnetic with respect to the surrounding stronger solution.

It is therefore evident that in order to account for diamagnetism it is not necessary to assume that these bodies have a negative susceptibility, but only that their susceptibility is less than that of air, or, since the susceptibility of air and of a vacuum are very nearly the same, less than that of a vacuum. Since the susceptibility and the permeability are related by the equation

μ = 1 +4πk,

and that for the most diamagnetic body known the susceptibility is less than 1/4, the permeability will in all cases be greater than zero.

PART VI.-ELECTRO-MAGNETISM

CHAPTER XII

FORCES ACTING ON CONDUCTORS CONVEYING

CURRENTS

509. Force acting on a Straight Conductor conveying a Current when placed in a Magnetic Field.—If a straight conductor, in which a current is flowing, is placed in a magnetic field, so that it is at right angles to the lines of force of the field, then, owing to the magnetic field due to the current, the distribution of the lines of force of the field will be altered. In Fig. 490 are shown the lines of force due to a conductor which is perpendicular to the plane of the paper and passes through the point A when placed in a uniform magnetic field in which the lines of force ran parallel to the line CD. Remembering that we have every reason to suppose that there exists a tension along the lines of force, and a pressure at right angles, while the lines of force act as if they were connected with the body by which they are produced, it is evident that, as a result of the crowding of the lines of force on one side of the conductor, and their separation on the other, the conductor conveying the current will be acted upon by a force in the direction of the arrow.

If the current flows downwards, the lines of force are circles which run in the clockwise direction, and at the upper part of the diagram they strengthen the magnetic field, since they run in the same direction as the lines of force of the field. In the lower part of the diagram the lines of force due to the current and to the field are in opposite directions, and therefore the resultant magnetic field is the difference of the fields due to the two causes. The direction in which the conductor tends to move is therefore at right angles to the direction of the lines of the field, and towards the part of the field where the lines of force due to the current are in the opposite direction to the lines of force of the field. Since the direction of the lines of force of the current can at once be remembered by one of the rules given in § 472, the direction of the force acting on a conductor in a magnetic field can at once be remembered. Fleming has given a convenient rule for remembering the direction in which a conductor conveying a current in a magnetic field will tend to move. If the index finger of the left hand is held pointing in the direction of the lines