The curve of temporary magnetization is at first a straight line from X0 to XL. It then rises more rapidly till X = D, and as X increases it approaches its horizontal asymptote.

The curve of residual magnetization begins when X = L, and approaches an asymptote at a distance = .81 M.

It must be remembered that the residual magnetism thus found corresponds to the case in which, when the external force is removed, there is no demagnetizing force arising from the distribution of magnetism in the body itself. The calculations are therefore applicable only to very elongated bodies magnetized longitudinally. In the case of short, thick bodies the residual magnetism will be diminished by the reaction of the free magnetism in the same way as if an external reversed magnetizing force were made to act upon it.

446.] The scientific value of a theory of this kind, in which we make so many assumptions, and introduce so many adjustable constants, cannot be estimated merely by its numerical agreement with certain sets of experiments. If it has any value it is because it enables us to form a mental image of what takes place in a piece of iron during magnetization. To test the theory, we shall apply it to the case in which a piece of iron, after being subjected to a magnetizing force X, is again subjected to a magnetizing force X1.

If the new force X, acts in the same direction in which X acted, which we shall call the positive direction, then, if X, is less than X, it will produce no permanent set of the molecules, and when I is removed the residual magnetization will be the same as

that produced by X. If X, is greater than X, then it will produce exactly the same effect as if X, had not acted.

But let us suppose X, to act in the negative direction, and let us suppose - L cosec 01.

Xo = L cosec 0%, and X1

As X increases numerically, 0, diminishes. The first molecules on which I will produce a permanent deflexion are those which form the fringe of the cone round A, and these have an inclination when undeflected of 0.+ Bo.

As soon as 01-Bo becomes less than 0+3, the process of demagnetization will commence. Since, at this instant, 0, 0, +2ẞo, X1, the force required to begin the demagnetization, is less than Xo, the force which produced the magnetization.

If the value of D and of I were the same for all the molecules, the slightest increase of X1 would wrench the whole of the fringe of molecules whose axes have the inclination 0+3, into a position. in which their axes are inclined 0, +ẞ, to the negative axis OB.

Though the demagnetization does not take place in a manner so sudden as this, it takes place so rapidly as to afford some confirmation of this mode of explaining the process.

Let us now suppose that by giving a proper value to the reverse force X, we have exactly demagnetized the piece of iron.

The axes of the molecules will not now be arranged indifferently in all directions, as in a piece of iron which has never been magnetized, but will form three groups.

(1) Within a cone of semiangle 01-ẞo surrounding the positive pole, the axes of the molecules remain in their primitive positions. (2) The same is the case within a cone of semiangle surrounding the negative pole.

(3) The directions of the axes of all the other molecules form a conical sheet surrounding the negative pole, and are at an inclination + Bo⋅

When X is greater than D the second group is absent. When I is greater than D the first group is also absent.

The state of the iron, therefore, though apparently demagnetized, is in a different state from that of a piece of iron which has never been magnetized.

To shew this, let us consider the effect of a magnetizing force X acting in either the positive or the negative direction. The first permanent effect of such a force will be on the third group of molecules, whose axes make angles= 01+ So with the negative

axis.

447.]

MAGNETISM AND TORSION.

85

If the force X2 acts in the negative direction it will begin to produce a permanent effect as soon as 2+B becomes less than 01+B, that is, as soon as X, becomes greater than X. But if X acts in the positive direction it will begin to remagnetize the iron as soon as 02-ẞ becomes less than 01+ Bo, that is, when 02 = 01+2ẞo, or while X is still much less than X1.

It appears therefore from our hypothesis that

When a piece of iron is magnetized by means of a force X, its magnetism cannot be increased without the application of a force greater than X. A reverse force, less than X, is sufficient to diminish its magnetization.

If the iron is exactly demagnetized by a reversed force X1, then it cannot be magnetized in the reversed direction without the application of a force greater than X1, but a positive force less than I is sufficient to begin to remagnetize the iron in its original direction.

These results are consistent with what has been actually observed by Ritchie, Jacobi †, Marianini ‡, and Joule §.

A very complete account of the relations of the magnetization of iron and steel to magnetic forces and to mechanical strains is given by Wiedemann in his Galvanismus. By a detailed comparison of the effects of magnetization with those of torsion, he shews that the ideas of elasticity and plasticity which we derive from experiments on the temporary and permanent torsion of wires can be applied with equal propriety to the temporary and permanent magnetization of iron and steel.

447.] Matteucci || found that the extension of a hard iron bar during the action of the magnetizing force increases its temporary magnetism. This has been confirmed by Wertheim. In the case of soft bars the magnetism is diminished by extension.

The permanent magnetism of a bar increases when it is extended, and diminishes when it is compressed.

Hence, if a piece of iron is first magnetized in one direction, and then extended in another direction, the direction of magnetization will tend to approach the direction of extension. If it be compressed, the direction of magnetization will tend to become normål to the direction of compression.

This explains the result of an experiment of Wiedemann's. A

*Phil. Mag., 1833.

Pog., Ann., 1834.

‡ Ann. de Chimie et de Physique, 1846. § Phil. Trans., 1855, p. 287.
Ann. de Chimie et de Physique, 1858.

current was passed downward through a vertical wire. If, either during the passage of the current or after it has ceased, the wire be twisted in the direction of a right-handed screw, the lower end becomes a north pole.

Here the downward current magnetizes every part of the wire in a tangential direction, as indicated by the letters NS.

The twisting of the wire in the direction of a right-handed screw causes the portion ABCD to be extended along the diagonal AC and compressed along the diagonal BD. The direction of magnetization therefore tends to approach AC and to recede from BD, and thus the lower end becomes a north pole and the upper end a south pole.

Effect of Magnetization on the Dimensions of the Magnet.

448.] Joule *, in.1842, found that an iron bar becomes lengthened when it is rendered magnetic by an electric current in a coil which surrounds it. He afterwards † shewed, by placing the bar in water within a glass tube, that the volume of the iron is not augmented by this magnetization, and concluded that its transverse dimensions were contracted.

Finally, he passed an electric current through the axis of an iron tube, and back outside the tube, so as to make the tube into a closed magnetic solenoid, the magnetization being at right angles to the axis of the tube. The length of the axis of the tube was found in this case to be shortened.

He found that an iron rod under longitudinal pressure is also elongated when it is magnetized. When, however, the rod is under considerable longitudinal tension, the effect of magnetization is to shorten it.

448.]

CHANGE OF FORM.

87

This was the case with a wire of a quarter of an inch diameter when the tension exceeded 600 pounds weight.

In the case of a hard steel wire the effect of the magnetizing force was in every case to shorten the wire, whether the wire was under tension or pressure. The change of length lasted only as long as the magnetizing force was in action, no alteration of length was observed due to the permanent magnetization of the steel.

Joule found the elongation of iron wires to be nearly proportional to the square of the actual magnetization, so that the first effect of a demagnetizing current was to shorten the wire.

On the other hand, he found that the shortening effect on wires under tension, and on steel, varied as the product of the magnetization and the magnetizing current.

Wiedemann found that if a vertical wire is magnetized with its north end uppermost, and if a current is then passed downwards through the wire, the lower end of the wire, if free, twists in the direction of the hands of a watch as seen from above, or, in other words, the wire becomes twisted like a right-handed screw.

In this case the magnetization due to the action of the current on the previously existing magnetization is in the direction of a left-handed screw round the wire. Hence the twisting would indicate that when the iron is magnetized it contracts in the direction of magnetization and expands in directions at right angles to the magnetization. This, however, seems not to agree with Joule's results.

For further developments of the theory of magnetization, see Arts. 832-845.