As in the case of bar magnets, we can obtain a horseshoe magnet of greater strength by binding together a number of pieces of thin steel plate, cut in the form of a horse-shoe and separately magnetised. If a piece of soft iron (the keeper) be brought into contact with the two ends, it will be strongly held by the magnet (§ 17).

Here again the lifting strength is not proportional to the number of separate magnets used in building up the combination. The formula which have been obtained involve quantities depending on the quality of steel and the method of tempering and magnetising it. They need not be further considered in this place.

25. Determination of the spacial distribution of lines of force in strong fields.-When we have to deal with strong magnetic forces, for example those due to compound magnets, we can determine directly the course of the lines of force, not only in a plane, but in three dimensions.

(a) Fixation of the finest iron dust in the form of the lines of force by burning.-Sprinkle the finest iron dust between the poles of a powerful magnet; the particles adhere together and build up a stable bridge between the two poles, the separate chains following the form of the lines of force (very approximately at least where the force is strong, though in weaker parts of the field the disturbance of form arising from gravity may be considerable). On setting fire to the iron it becomes oxidised, and coheres so as to form a solid mass which reproduces the structure of the field of force. We may then remove the slag, and, by making sections of it, follow out the structure of the field.

(b) Fixation by imbedding in gelatine.-Let coarse iron particles be imbedded in a semi-fluid body, such as gelatine, which does not interfere with the rotation of the particles or with their displacement through small distances, and leaving the whole exposed to the influence of a magnet, allow the gelatine to harden.

Experiment 17.-Suspend a horse-shoe magnet with its poles pointing downwards, and arrange a card-board box so that the

poles dip into it. Dissolve some fine transparent gelatine, then warm the solution and stir in a considerable quantity of iron filings. Any fine dust which may be present, and which would render the gelatine opaque, should be removed by sifting it away. The gelatine solution is now to be poured into the cardboard box, so as to surround entirely the lower part of the magnet, and there allowed to stiffen.

On removing the cardboard box, and cutting away the outer layers of gelatine in which the filings are rusted, we obtain a transparent mass in which the course of the lines of force can be clearly followed from every side, especially when a strong light is allowed to shine through. The iron filings in the interior of the mass do not rust very quickly.

If the form of the lines of force is to be projected by means of the lantern, it is better to immerse the particles of iron in some viscous transparent fluid.

Let ferrum redactum be stirred into glycerine or paraffin oil, contained in a thin glass vessel, which is then placed horizontally in the beam of a lecture lantern, so that an image of the iron particles is projected on the screen. When a strong magnet is brought near, the particles arrange themselves along the lines of force; and if a piece of soft iron be immersed in the trough, the lines of force are seen to become concentrated in its neighbourhood.

26. Uniform magnetic field. Generally speaking, the lines of force are curved; but if we examine the field of a horse-shoe magnet, we find that there are places between the limbs of the horse-shoe where the course of the lines is very nearly rectilinear. Here they are evenly distributed with the same degree of closeness throughout the field. Fields of this kind are of great importance and are called ' uniform fields.'

Such fields are similar to the earth's gravitational field within a restricted region, for example in a room; there the weight of a body is everywhere the same, and at all points the direction of the force is vertical, the gravitational lines of force being parallel to one another.

D.-Magnets with one degree of freedom

All the magnets so far employed we have supposed to be held fixed. We shall now consider the case where the axis joining the poles of the magnet is free to rotate in a horizontal plane about its middle point.

In the case of a horse-shoe magnet, this is accomplished by hanging it up by a thread attached to the middle of the bend. Bar magnets may be suspended by means of a brass loop furnished above with a hook to which a thread is attached, the adjustment being so made that the magnet swings freely in a horizontal plane. The suspending threads must first be untwisted by leaving a weight suspended from them. Small light magnets (magnetic needles) are sometimes fitted at the middle with a cap in which a hollow piece of agate is set, so that the needle may be supported with as little friction as possible on a vertically directed steel point.

We thus give to the magnet' one degree of freedom,' as it is called; that is to say: Out of the infinitely numerous positions which the axis could occupy in space, we confine ourselves to those (singly infinite in number) which the axis could occupy in a horizontal plane when one point of the magnet is fixed. Further on we shall consider the effect of giving more than one degree of liberty to the magnet, which we shall suppose free to set with its axis in any direction, horizontal or otherwise; the point of suspension alone being fixed relatively to the earth's surface.

27. South-to-north direction of a freely turning magnet.A magnet, suspended by a thread or supported upon a steel point, can turn freely in any direction in a horizontal plane; but there is an experimental law, which is of fundamental importance in regard to magnetic phenomena, and which may be stated as follows:

If the axis of a magnet is free to turn in a horizontal plane, it will set itself in a determinate direction.

If the magnet is displaced from this position, and left free to move, it executes vibrations of gradually diminishing

amplitude, and finally comes to rest in the same position again. If we examine the phenomenon in relation to the points of the compass, we find that one pole points to the north (this is the north pole' or north-seeking pole), the other pole to the south (south pole). This furnishes a means of specifying the poles of a magnet without ambiguity, and of distinguishing one from the other.

For example, we may verify in this way that in the method of magnetisation by double touch (§ 19 b) the end rubbed with the north pole of the exciting magnet becomes a south pole, and vice

versa.

The phenomenon of the south-to-north pointing of a suspended magnet was made known to the world in the seventeenth century, though as early as the year 121 A.D. it was mentioned in a Chinese dictionary (PESCHEL).

We shall consider later the significance of the phenomenon as touching the physical constitution of our planet.

We shall distinguish all north poles by red, and south poles by blue (cf. § 16). In order to render the polarity immediately recognisable in the figures, north poles are ordinarily shaded perpendicularly to the magnetic axis, and south poles parallel to this axis (AIRY).

Like poles are those which tend to point in the same direction at any given place; unlike poles are those which tend to point in opposite directions.

31

CHAPTER II

THE MUTUAL ACTION OF TWO MAGNETS

A.-Mechanical force exerted by a fixed upon a movable magnet. Direction of the lines of force

In this chapter we shall become acquainted with new properties of the lines of force, relating to the effects produced upon a movable magnet under their influence. For the present we leave out of account the system of lines of force. arising from the movable pole, using this only to investigate the course of the lines of force in the field of a fixed magnet.

28. One pole of a long straight movable bar magnet in the field of a fixed magnet; mechanical effects.-We saw above (§ 21) that in long thin bar magnets (regularly magnetised) the magnetic effectiveness is concentrated almost exclusively at the ends. This fact enables us to subject a single pole to the influence of a fixed magnet, the movable bar magnet being supposed made so long that the second pole lies outside the region where the field of the fixed magnet is appreciable.

Experiment 18.-To one end of a long strongly-magnetised steel wire, a loop or eye of brass is affixed, so that the steel wire may be hung up by a thread, and will then rest in a vertical position with its lower end just above the table.

The steel wire should not be too flexible, and must be made quite straight. The suspending thread must be untwisted, thin and not too long, or the wire will too easily acquire an oscillatory motion. It will be best, indeed, to load the wire somewhat at its