instrument stands on a cork base, which has a small depression to receive the point F.

If we desire to map out the lines of force of a magnet (for example, of a horse-shoe magnet), we place it over a sheet of paper, supporting it on a wooden block so as

to raise its 'median plane' to the same height as the magnetic needle G. By looking vertically down upon G, it is easy so to move the foot A, that the tangent to its path is always parallel to G. We have thus a very fairly accurate graphic construction for the course of a line of force, so far as it corresponds to the median plane of the magnet under examination.

One of the most comprehensive collections of such systems of curves, for magnets of the most various forms (bar-, horse-shoeand ring-magnets) was brought out in 1844, by J. E. HERGER, with a preface by ERMAN. It was published by E. PÖNICKE and Son, of Leipzig, and contains thirty-seven large diagrams of lines of force, in thirty-one folio plates.

FIG. 7

A

Specification of the magnetic force as a directed quantity.— Two data are necessary for the complete specification of the effect produced upon a movable pole when placed in a magnetic field.

(1) A determinate direction. This will be at each point coincident with that of the lines of force passing through the point, and is to be determined by drawing the corresponding tangent to the line of force, or more simply by taking an element of the curve which includes the point itself and is short enough to be regarded as straight. The complete specification of a direction includes also a determinate sense. Lines of force at a given position in space may lie along the same curve and yet differ from one another in direction, a north-seeking pole being urged one way along the one line of force, and the contrary way along the other. It is therefore essential to know the sense in which a line of force proceeds, as well as the form of the curve which it follows.

(2) A determinate strength.-We have already seen that the magnetic effects in the more remote parts of the field are weaker than those in the neighbourhood of the poles. We shall learn later from quantitative experiments that the same is true of the mechanical force exerted upon a movable pole. Thus the effects observed at different places in the same field differ also in intensity.

Quantities which have direction (including sense) and magnitude are called vectors'; they may be represented geometrically by a straight line of definite length drawn from a point in a definite direction. The magnetic force is a vector, or directed quantity.

The simplest vector quantity is the displacement of a point from one position to another along a straight line of determinate length drawn in a determinate direction; hence the name (vehere to carry). Velocity and acceleration are also vectors. The part played by vector quantities in physics is very important. We shall find that rotations about axes are also included in the same category.

32. Faraday's representation of the distribution of magnetic force by means of the lines of force.-The lines of force furnish us with sufficient data for the complete determination of the magnetic force at each point of the field. The course followed by the lines shows immediately the direction of the force; while by introducing a movable north pole into the field, we can discover which is the positive sense along any line of force. It would seem, perhaps, more difficult to express the magnitude of the magnetic force by means of the distribution of lines. But the density or closeness with which these lines are packed together in any given part of the field may be made to furnish a measure of the intensity of the corresponding force. This density is most simply measured by the number of lines of force intersecting some area whose plane is at right angles to their course, for example, the number of lines per square centimetre; this last-named quantity being called the field intensity at the corresponding point.

It will be shown later on that this mode of representation

leads to an absolute and not merely to a relative measure of the magnetic force. As the principle of the method is somewhat unfamiliar, we shall here introduce a simple example which may help to make it clearer.

Experiment 24.—Examination of the distribution of the lines of force in three dimensions.—Cut down upon one of the gelatine blocks described in § 25, and count the lines of force which intersect the different sections.

In the neighbourhood of the pole of the magnet, a square centimetre of surface, taken perpendicularly to the direction of the lines of force, will be marked with many points where these lines intersect it (considerable strength of field); while in places more remote from the pole the intersections per square centimetre will be few (small strength of field). The numbers thus obtained are not directly comparable, because the formation of the chains of iron filings is influenced by numerous accidental circumstances; the method will only become exact when we suppose the lines of force to be built up and distributed according to a definite law. The example is merely intended to illustrate the possibility of using the method to show graphically the magnitude of the magnetic force.

B.-Mechanical action between two movable magnets.

We shall next consider the case where two magnets, subject to one another's influence, are both movable. One of them (,) we shall suppose to have one degree of freedom, the constraints imposed upon it being such that it can only move to and fro in the direction of its axis, or at right angles to it; or we shall suppose it suspended by a thread or mounted on a needle-point, so that it can turn freely in a horizontal plane. In its position of equilibrium in the last-mentioned case, it will point north and south. The second magnet is to be entirely free; it is to be held in the hand, so that it can be approached to the first magnet from every possible side.

We shall now dispense with the condition that the distance from pole to pole of a magnet is to be very great; on the contrary we shall suppose both pairs of poles to take part in the effects observed, and shall seek to determine how

the lines of force of the one magnet are influenced by those of the other.

33. Reciprocal action of the fields of two neighbouring coaxal bar magnets. To render a bar magnet freely movable in the direction of its own axis, it is placed in a little boat made of sheet-brass (fig. 8) and suspended by threads from the ceiling.

A rectangular piece of sheet brass about 12 cm. long is bent round the bar magnet m1, which is about 25 cm. in length and of circular section. At the four corners S-shaped hooks are inserted into holes drilled in the brass. The hooks are fastened to long thin threads, which are passed in pairs over other hooks fixed in the ceiling. Beneath one end of the bar magnet is a block of wood K, which carries a pointer Z.

Experiment 25.-Let the pole n of the magnet m, be brought axially towards the pole n of m1; m, recedes from

m2, as indicated in the figure by the arrows. If the pole s of m, is approached to the pole s of m1, a similar repulsion is observed. The receding of the magnet m, causes it to rise somewhat above its original height, so that a certain amount of work is necessarily done against gravity.

The field due to a magnet-pole is in some degree impenetrable by the like pole of another magnet.

When we stretch out our hand, and suddenly feel a resistance to its movement, we say that there is something there.'

To this something, which resists the penetration of other bodies into the space which it occupies, we give the name of 'matter.' The effect observed is also summed up by saying that the region in question is filled with a certain form of energy, which resists a diminution of volume. The knowledge that a magnetic field is a region filled with energy of a special kind is of very great importance.

The phenomenon observed in our experiment is most simply described by saying that the fields due to poles of the same name repel one another.

Experiment 26.-Let the pole s of m, be brought near to the pole n of m, and vice versa: the magnets will be attracted together. The fields due to poles of unlike name attract one another provided they are brought near enough to exert mutual influence. The masses of the bars themselves have no part in the mutual action; the origin of the effect must lie entirely in the lines of force emerging from or converging to the poles; for in all the foregoing experiments these have shown themselves to be the true cause of magnetic effects. The masses of magnetic matter' thus appear to be inseparably attached to their lines of force, so that mechanical attractions and repulsions are exerted between the two magnets.

6

Experiment 27.-Between the two mutually attracting or repelling magnets interpose successively a number of screens made of different substances: cardboard, wood, glass, brass and iron. Through all but the last the action is transmitted without perceptible change: the iron, however, screens each magnet almost entirely from the influence of the other.

34. Course of the lines of force in the field of two neighbouring coaxal magnets; representation of the pressures and tensions in the field.--The mechanical forces described in the last paragraph will be more easily understood if we consider the changes of form experienced by the two superposed fields. In order to see these conveniently, we form the lineof-force diagram in a plane parallel to the axis of two coaxal bar magnets.