a

b

For the production of the following line-of-force figures, we may make use of a board about 2 or 3 cm. thick, 20 cm. long, and 15 cm. wide, protected against warping by cross-ribs. In this grooves are to be cut, of such breadth and depth that the magnets to be examined, when fitted into them, may lie flush with the upper face of the board. The grooves are arranged as in fig. 9. In the central longitudinal groove a a, the two

b2

FIG. 9

a

bar magnets lie coaxally; while in the two grooves b, and b2 they can lie parallel, and in the groove c perpendicular to one another. Over all the sheet of paper is laid.

For the purpose of comparison it will be well once more to form the line-of-force diagram (fig. 4, § 21) corresponding to one only of the two magnets (which are supposed to be as nearly equal in strength as possible). On forming subsequently the line-of-force figures for the field surrounding the two magnets, the extent to which the lines of force diverge in issuing from each of the poles should be compared with what is observed in the case of a single isolated pole.

(a) Like poles turned towards one another (fig. 10).-The lines of force proceeding from a pole n, of the magnet m

(fig. 4). There is one place, J, in the field which is free from lines of force, and here consequently the resultant force vanishes, the effect due to one pole being neutralised by that due to the other; a short magnetic needle placed in this part of the field would thus be subject to no directing influence, and would behave quite independently of the neighbouring magnetised bodies. The point J is called an indifferent point or zero point.'

6

Sometimes the directing influence of a magnet at a place occupied by a magnetic needle may need to be greatly diminished. This is accomplished, as in the case just discussed, by bringing near the like pole of an auxiliary magnet, which causes a greater divergence of the lines of force. The needle is then said to be astaticised, a plan often adopted in magnetic measuring instruments, in order to increase their sensitiveness.

The deformation of the field common to the two magnets, taken in conjunction with the fact that these magnets repel one another (as indicated in the figure by the arrows), leads us to the conclusion that the lines of force repel one another perpendicularly to their own direction.

The significance of the lines of force is chiefly directional, but they also express a certain condition of the medium through which they pass. It may be mentioned here that the condition in question is one in which there is a pressure exerted perpendicularly to the direction of the lines of force. This was the conclusion at which Faraday arrived. (Compare Maxwell's memoir On physical lines of force.')

If we assume, therefore, that in the medium transmitting magnetic actions there is a pressure perpendicular to the magnetic lines of force, the line-of-force diagram shows that the two poles n, and n, will repel one another. Hence the mechanical force observed in experiment 25.

According to the older conception of magnetic phenomena, the seat of the effects was to be sought in the poles, where certain hypothetical fluids, or so-called magnetic masses, were considered to exist. These were supposed to exert upon one another a direct

'action at a distance,' without any intervention of a continuous connecting medium. The medium, however, plays a fundamental part in the phenomena, a fact which experiment 27 helps to illustrate. The most important distinction between the new conception and the old lies in the transference of the seat of magnetic phenomena from the poles to the fields which surround them.

(b) Unlike poles turned towards one another (fig. 11).The lines of force proceeding from a pole n, of a magnet

FIG. 11

m, bend round and

unite with the lines which terminate at the neighbouring pole s of the other magnet m2. In the neighbourhood of the axis of the diagram, the lines are only slightly curved, but in the more outlying parts of the field they are

more and more spread apart, and pass in wide curves from one pole to the other. Accordingly the lines of force passing from the first pole n, to the second pole s are especially closely crowded together. They are less spread out from one another, and much less curved than if either magnet were present alone, and uninfluenced by the other (compare fig. 4). There is a mechanical force urging the two magnets together, as indicated by the arrows. It follows then, that, in addition to the pressure across the lines of force, there must be a tension along them. If the lines of force passing from n, to s, have a tendency to shorten in their own direction, like stretched rubber cords whose ends are attached to these poles, there will result a mutual attraction, such as we actually observe. The cross-pressure which the separate lines of force exert upon one another keeps these lines from shrinking up, and passing across by the shortest path from n, to s2.

On the older hypothesis we should simply say that the two poles, endowed with different magnetic fluids, attracted one another at a distance. Faraday did not believe in such centres of attraction-at-a-distance. His description of the phenomenon in terms of the lines of force was much more complete.

We prefer to avoid the terms attraction' and 'repulsion' of magnetic poles, directing our attention rather to the state of stress in the medium, the pressure across the lines of force, and the tension along them; for herein lies the essential basis of all our subsequent conceptions.

By supposing all magnetic processes to have their seat in the field, we get rid of a difficulty of conception inherent in the older theory, that effects were produced by something at places where it was not. Action at a distance is now replaced by a continuous transmission of stress through a medium. All media are capable of transmitting magnetic influences, as Faraday proved; that is, they can take up and propagate that type of stress which constitutes the field. We can even avoid, then, introducing into our conceptions another hypothetical substance the so-called ether. It can be shown that all regions which we are able to investigate are filled with matter. For example, a Torricellian vacuum, above the mercury in a good barometer which has been well boiled out, still contains so much vapour of mercury and glass, that even here we do not need to invoke the aid of any special medium for the transmission of the stresses which constitute the magnetic field.

[But as the transmission of magnetic effects does not become perceptibly less as the number of molecules per unit volume is reduced, we must suppose that the principal transmissive agent is something other than the molecules.]

35. Mutual action of two long bar magnets placed side by side; lines of force in bipolar magnetic fields.—We proceed to experiments with two long bar magnets fixed side by side. in a vertical position. The action of their extreme ends can be fully examined, and when the bars are long enough we shall be dealing with a magnetic field which is determined wholly by two poles occupying a limited portion of space, and is called a bipolar' field.

For the production of figs. 12 and 13 two bar magnets were used, 50 cm. long, 1 cm. thick, and magnetised to the same extent. These could be fixed in a vertical position at different distances from one another in a wooden stand 50 cm. in height and having a base and a cover; the two poles which were turned uppermost being like or unlike as desired.

(a) Field due to two unlike poles (fig. 12). The lines of force issuing from the one pole n will be absorbed by the unlike pole s of the other magnet, as is seen on comparison with the radially spreading lines in a unipolar field (fig. 5). Even the more outlying lines pass round finally to the south pole.

The heaping up of iron filings around n and s, and the existence of neighbouring bare patches, is due to causes already explained in § 21.

(b) Field due to two like poles (fig. 13).-The lines of force proceeding from a pole n curve back on encountering those which issue from the corresponding pole n of the other magnet. The figure clearly shows how this repulsive force affects the whole system of lines; the chains of filings run everywhere outwards. Between the two poles there is a place J, entirely free from lines of force-a so-called 'zero point.'

Since there is a tension along the lines of force, it follows that the unlike poles of fig. 12 must tend to approach one another; they thus appear to attract one another in a direction perpendicular to the axes of the bars. On the