The entire distribution of the flux of force originating at N is deflected somewhat towards the right by the presence of the unlike pole s. Owing to the tension along the lines of force and the pressure across them, the two poles will be urged towards one another (attraction). If the two poles are free to move, they will mutually approach one another.

[The forces which they exert upon one another will be equal and opposite, in accordance with the third law of motion, and it should be noticed that though all the lines of force attached to and pulling s are pulling N more directly along the axis, there are also a considerable number of lines pulling N away from s.]

Here as before we can calculate at once the field-intensity at any place when we know the breadth b between consecutive lines and the distance r from the axis.

(b) Diagram of two like poles.-Let the strength of one pole be as before = 1.592 unit, that of the other pole being

5

20

4π

= 0.3979, so that the two poles in this case are of the 4π same name, a north pole N being placed at a determinate distance from a weaker north pole n. At the points of intersection of the lines corresponding to the two unipolar fields, the forces to be compounded are both directed We have a network of interaway from their poles. secting lines precisely like that of fig. 28, but through each of the meshes we have now to draw the other diagonal, so that we obtain the result shown in fig. 29. The lines of force, as they approach one another from the two poles, bend round so as to avoid meeting. There is one line which separates the two systems from one another, and does not pass through either pole. Where this line meets the axis of the diagram, there is an indifferent point, or point of zero magnetic force, J. The 20 units of flux of force proceeding from the pole N all pass outwards into the surrounding space, and so likewise do the 5 units from the pole n, no intermixture of the two taking place.

Owing to the pressure across the direction of the lines

of force, there will be a force on each pole urging it away from the other; that is, the two poles will repel one another.

If we suppose pressure and tension to be interchanged, so that there is pressure along the lines of force, and a tension across them, the diagram may be taken to represent a double star, whose members attract one another gravitationally.

91. Diagrams of homogeneous fields. In a uniform field the lines of force are all straight and parallel, and distributed throughout with the same density. If we intend to apply to this case the same principle of construction that was used for systems having an axis of symmetry, we must choose as axis some line parallel to the direction of the field, and divide the space surrounding it into cylindrical shells, each of such cross-sectional area that the flux of force through it is unity. In the plane of the diagram, the limits of these cylindrical shells appear as straight lines parallel to the axis. The distances r1, r, r. . . . of these lines from the axis must satisfy the simple relation

When the diagram has been prepared in accordance with these conditions, it may be combined with the diagram for a single pole by drawing the diagonals of the small quadrilateral figures produced by the crossing of the two systems of lines. With the resultant lines we may then use the formula

=

1 2πrb

In fig. 30 a uniform field is represented, having the absolute strength = 0·00771 cm gr1 sec1. The radii of the successive cylindrical surfaces must accordingly be

The positive direction of the lines of force is from right to left. We must suppose, therefore, that there are two strong magnet-poles at distances far beyond the limits of the diagram; a north pole to the right and a south pole on the left.

Combined with this field is that of a north-seeking pole
If we

10

of strength + m = + = 0·7958 cm. gr.1 sec. 1.

4π

suppose a positive unit pole placed at a point where lines of the two systems intersect one another, it will be urged towards the left in the homogeneous field, and at the same time repelled by the pole N. This consideration shows us along which diagonals the resultant lines of force are to be drawn. The 10 units of flux of force which proceed from the pole N are so deflected by the influence of the uniform field, that they are ultimately all passing towards the left. The innermost conical surface has become narrowed to the tubular form, 1, 1, and all the remaining surfaces are correspondingly distorted from their original form. The shells numbered seven to ten, which start from the pole towards the right hand of the diagram, are seen to be entirely bent round, and all the ten shells have so completely acquired the direction of the field that further to the left the uniformity is completely restored.

The originally cylindrical shells of the uniform field spread out as they approach N, and bend round it as if it were an obstacle in their path, or more strictly, as if the uniform field were a uniform flow of fluid, and the pole N a source from which fluid was emanating. The surfaces more remote from N maintain their course with but little deviation. The present example shows very clearly the insight to be obtained from the construction of such diagrams.

If we consider the figure from the point of view of the tensions and pressures accompanying the lines of force, it is clear that N must experience a force urging it through the field towards the left. This is in accordance with the tendency of a north pole to move along the positive direction

of the lines of force (compare § 28). The reverse would be the case if we replaced the north pole by a south pole, which behaves as a sink towards the lines of force.

92. Combination of more than two fields.-A resultant field mapped out by this method may in turn be combined with another field, and so on; so that by successive applications of our construction we may obtain the diagram for even a very complicated case. The separate diagrams may be conveniently drawn on tracing paper, so that when two are superposed they are both easily visible. They must of course be drawn to the same scale. A very instructive case is that of the bipolar field of a bar magnet, combined with the uniform field of the earth, but this is left as an exercise for the reader.

CHAPTER VI

CONSTITUTION OF MAGNETS AND MAGNETIC FIELDS

So far we have confined our attention to the space surrounding magnetised bodies-that is, to the lines of force themselves. We have seen how the presence of these and their general character may be recognised from certain qualitative properties, and we have shown how to measure the quantities which determine their disposition and relations, and how to construct them graphically from numerical data. We must now attempt to obtain some insight into the constitution of the magnet itself; and we shall find that there are certain peculiarities of structure which must be assumed for all bodies through which magnetic lines of force are passing.

A. The magnetisation

93. Magnetism as a molecular property.-Experiment 41. Dip the whole length of a well-magnetised steel knittingneedle in iron filings. Considerable tufts of filings will adhere to the ends, while at the middle, in the indifferent region, there are no filings. Now break the needle at the middle and repeat the experiment with the two halves. In each case filings will adhere to the two ends, even to those which previously constituted the indifferent region. If each half of the needle is broken up into shorter pieces, each of these will be found to be a complete magnet, with two magnetic ends and an intermediate non-magnetic region.

Since the same result is obtained, however far we continue the subdivision, we are led to the conclusion that