somewhat as in fig. iii. Hence there will be a couple acting on each sphere; and this will be in such a direction that the whole cylinder will be urged to lie along the lines of force. In this position the internal and external inductions act against one another, and the magnetisation is at a minimum.

When the cylinder is perpendicular to the field there is unstable equilibrium, and the magnetisation is at a maximum.

Hence a diamagnetic (see § 6, end) cylinder tends to set along the lines of a uniform field; that is, to assume the position in which its magnetisation is minimum.

We may, however, add that with diamagnetic bodies the above action is very feeble; and no observation has as yet detected any 'setting' of such bodies in a uniform field.

§ 9. A Long Body in a Non-Uniform Field.-When a magnetic cylinder is suspended in such a non-uniform field as that between the two poles of a powerful magnet, the results of §§ 7 and 8 concur to show that it will set along the lines running between the two poles.

When a diamagnetic cylinder is so suspended, the action described in § 7 would urge it to stand in the weakest part of the field; i.e. at right angles to the lines of force between the poles. But the action given in § 8 would tend to make it set along these lines. In all cases that occur in practice, the former action gives rise to the greater couple; and so the diamagnetic cylinder stands at right angles to the lines running between the poles.

To exhibit these phenomena, very powerful magnets are needed. We therefore proceed to consider how powerful temporary magnets may be obtained.

§ 10. Solenoid With, and Without, an Iron Core.-According to the view that appears to be most in accord with experiment, magnetic matter possesses innate magnetism. This magnetism is, however, molecular; and we have evident magnetism, or an external field, only when the molecules are suitably arranged.

We see that, on this view, there is nothing very surprising in a moderate field 'producing' a strong magnet; for the magnetism is in the soft iron already, and the field may be able to arrange the molecules suitably.

We may contrast the magnetic action of an ordinary solenoid

with that of one in which there is a soft iron core. It is often said 'the core strengthens the solenoid.' But it is perhaps more in accordance with facts to say 'the solenoid renders evident the innate magnetism of the iron.'

Experiments.--(i.) We can compare the action of the two on a balanced

needle.

(ii.) We can examine the fields of the two respectively by placing them under glass and sprinkling steel filings above. It will be seen that in the case of the solenoid the field is weak, and that some of the lines of force 'leak out' between the turns of the wire. In the case of the solenoid with iron core, the field is far stronger, and the strength is more concentrated at the poles.

The iron is, from its symmetrical position, magnetised in the direction of the lines of force due to the solenoid; ie. in the direction of the solenoid's axis. The north pole of the core will be that at the north end of the solenoid, where the current, to one facing the end, appears to run counter-clockwise.

§ II. Electro-Magnets. Thus, when a soft iron core is wrapped round with many turns of wire, and a current is passed through the wire, the core becomes temporarily a magnet. Such magnets are called electro-magnets, and can be made far more powerful, mass for mass, than can any permanent steel magnets.

We may regard the external field to be made up of two components; the one due to 'evident magnetism' now evoked in the iron, the other due to the spiral or solenoidal current. These two fields are superimposed upon one another. As long as the iron is far from saturation, the field due to it is approximately proportional to the field-strength (see § 6) and therefore to the currentstrength. But when saturation is reached, any further increase in current will only increase the comparatively insignificant component field due to the spiral alone. In winding the wire about an iron core, and in passing a current through the wire, it is necessary to have regard to the following considerations.

(i.) The wire must not be too thick, or it will not be possible to give a number of turns sufficient for the production of a strong field with a current of reasonable magnitude.

(ii.) The wire must not be so thin as to give great resistance and consequent loss of energy in heat.

(iii.) It is of little use producing a field-strength greater than that necessary to magnetise the iron nearly to saturation.

(iv.) The distribution of the wire about the core must be adapted to the shape and dimensions of this latter.

DUJARDINS

The accompanying figure shows one form of electro

magnet.

Experiment. It is possible, in the case of a powerful electromagnet, to trace the lines of force in a very striking manner. Instead of filings we may use small pieces of steel knitting-needles. If the field be powerful, the effect of gravity on these pieces of steel will be relatively insignificant; and we may cause them to attach themselves end to end to one another, and so trace out the lines of force in any direction in space, while with permanent magnets we were able to trace the lines only over a horizontal plane.

Note.-Field due to an electromagnet.-In calculating the field due to an electro-magnet we can consider the solenoid, and the core which has become a cylindrical

magnet, separately. But in general the field due to the former is relatively insignificant, and we need only regard the core.

§ 12. Paramagnetic and Diamagnetic Phenomena.-When powerful electro-magnets are employed it is found that all bodies are influenced by the magnetic field (see § 6).

If pellets of various materials are suspended, by means of a light and long thread, near one of the poles of such a magnet, it is found that certain substances are attracted by the pole, while others are repelled.

Those bodies which are attracted are called paramagnetic, or magnetic; such are iron, nickel, cobalt, manganese, platinum, carbon, many salts of magnetic metals, solutions of such salts, and oxygen gas.

Those bodies which are repelled are called diamagnetic; such are bismuth, antimony, zinc, tin, mercury, lead, silver, copper,

gold, phosphorus, glass, quartz, alum, sulphur, sugar, hydrogen, nitrogen, water, alcohol, and most other liquids and gases not here named.

Iron is the most strongly magnetic, and bismuth the most strongly diamagnetic, body known.

If we make bars of various substances, those which are magnetic will set axially, or in a line with the poles; while those which are diamagnetic will set equatorially, or at right angles to the line joining the poles (see § 9).

The accompanying figure represents experiments with magnetic and diamagnetic liquids respectively. The liquid is placed in a watch-glass and rests on the poles. When

the current is passed, the magnetic liquid B rises up in a heap over each of the two poles; while the diamagnetic liquid A is repelled into a heap between the two poles. Such effects are very small, and must be magnified by means of reflected light if they are to be made clear. The difference between the two classes of liquids is clearer if we employ thin glass

B

tubes filled with the one or the other respectively, and observe whether these set axially or equatorially. It must, however, be remembered in this case that the glass itself is diamagnetic; its action can be allowed for.

§ 13. Pseudo-Diamagnetic Phenomena.--In certain cases a bar may set equatorially when its material is magnetic, or axially when its material is diamagnetic, owing to peculiarity of structure.

Thus, a bar inay be made composed of short steel needles separated from each other, lying side by side, running transverse to the length of the bar. Such an arrangement will, as a whole, set equatorially; each little needle lying axially. So again, if in a bar of bismuth the crystallisation have a certain direction with respect to the length of the bar, this may set axially. The repulsion or attraction of pellets from or to a pole is the best way of dividing bodies into the two classes.

§14. Relative Magnetism or Diamagnetism.-By Archimedes' principle we know that bodies immersed in any fluid medium appear to have a +, zero, or weight according as they

displace less than their own, their own, or more than their own weight of that medium respectively. By this principle we can predict, e.g., whether a body immersed in water will sink, remain where it is, or be forced upwards.

Similar reasoning applied to the case of a magnetic field leads us to predict-what can be verified by experiment-that when a body, whose coefficient of magnetisation with respect to vacuum iş k, is immersed in a medium whose coefficient is h, the body will behave as though it were in vacuo and had a coefficient k' equal to k-h. If this be true reasoning, then if k>h the body will appear to be magnetic; if k = h it will be neutral, and if k <h it will appear to be diamagnetic.

These predictions have been experimentally tested and verified. Thus, a weaker solution of ferric chloride appears diamagnetic when in the midst of a stronger solution, though in vacuo it is distinctly paramagnetic.

The question

$15. Is there Absolute Diamagnetism? naturally arises: 'Is there then such a thing as true diamagnetism, or is it merely that some bodies are less magnetic than that which we call "vacuum"?'

Some bodies which appear diamagnetic in the magnetic medium oxygen, may very well be found to be magnetic when tested in vacuo. But most diamagnetic bodies (e.g. bismuth) are still diamagnetic in vacuo.

It can be shown that all phenomena of repulsion and of equatorial-setting with which we are acquainted could be accounted for by supposing 'vacuum' to be a medium slightly magnetic.

But the phenomenon referred to in § 16, viz. the contrary directions in which a ray of plane polarised light is rotated in different media, seems to imply an essential difference in the sign of k for the two classes of media respectively. Before, therefore, we can accept unreservedly the view that all phenomena come under the head of paramagnetism or relative paramagnetism, it will be necessary to show that such a view can be reconciled with the fact quoted.

The whole question is at present unsettled. Quite recently (1886) experiments have been tried tending to show that bodies may change from diamagnetic to paramagnetic behaviour, or vice versa, according to the strength of the field in which they are