222 M A G N E T I Held. Lines of magnetic force. representation of the most general case, and what the exact law of the forces ought to be, we are not yet in a position to decide. One thing, however, is clear, that the action between two poles must diminish when the distance between them increases ; otherwise we should not have been able to make the action of N or S upon N prevail, by bringing the one or the other nearer. It was perhaps the complexity of this analysis (along with the fact that the action of the magnet upon soft iron, which was the earliest discovered magnetic pheno menon, is not a pure case of this action, but involves also another phenomenon, viz., magnetic induction) that prevented for so long the discovery of the elementary law we are now discussing. At all events, it seems to have been a new discovery in the 16th century, if we may judge from a passage in the letter of Hartmann above alluded to. He was certainly aware of the existence of magnetic repul sion in some form or other. It is somewhat difficult to gather from his description what it was exactly that he observed, and he nowhere states the law fully and explicitly. In Norman s Newe Attractive l we find it clearly stated, and demonstrated by means of a needle floating on water or suspended by a thread; 2 yet he does not appear to claim the fact as his discovery. If, therefore, Hartmann was not the actual discoverer, we may at least conclude that the law became familiar to magnetic philosophers during the thirty years that separated him from Norman. Mapping The Magnetic Field. We next introduce a method of out the conceiving and describing magnetic actions which was invented and much used by Faraday. Since a magnet acts upon a magnetic needle placed anywhere in the surround ing space, 3 we call that space the magnetic field of the magnet. Neglecting the earth s magnetism, we may map out this field as follows. Conceive any plane drawn through the axis of the magnet, and place it so that this plane shall be horizontal. Then at any point in this plane place a very small magnetic needle, and note the direction which its axis assumes under the action of the magnet ; then proceed to move the centre of the needle in the direction in which its north pole points, and con tinue the motion so that at each point the centre is following the direction indicated by the north pole. The line thus traced will at last cut the surface of the magnet at some point lying towards its south pole ; and if we continue the line backwards, by following the direction continually indicated by the south pole of the needle, it will cut the surface of the magnet at some point lying towards the north pole. Such a line is called a line of magnetic force ; and, since one such line can be drawn through every point of the plane, and any number of planes can be taken through the axis of the magnet, we can conceive the whole magnetic field filled with such lines. Fig. 4, taken from Faraday, gives an idea of the distribu tion of the lines of force in the field of a bar magnet ; fig. 5 represents the lines in the field due to two neighbouring like poles. These diagrams were not obtained by the method we have just described, but by a much simpler process which we shall describe by and by. Their use, so far as we have gone, is to tell us how a small needle, free to move about its centre in any direction, will place itself at any part of the field, viz., it will place its axis along the tangent to the line of force which passes through its centre, its north pole pointing in that direction which ultimately leads to the south pole of the magnet producing the field. Suppose we apply these ideas to a spherical magnet (a or ideal terella, or earthkin, as Gilbert calls it). The lines of force earth. ! 1 1 Chap. i. 2 See also Gilbert, De Magnete, lib. i. cap. v. 3 Gilbert uses the phrase orbis virtutis in- a somewhat similar sense. in any plane through its axis would be found to run some thing like the curves in fig. 6. If, therefore, we carried a small needle (suspended from a silk fibre so as to be perfectly free to move in all directions) round the magnet in a meridian plane, its axis would constantly remain in the meridian plane, its north pole always point towards the south pole of the spherical magnet, but dip more and more Terella below the tangent plane to the sphere as the centre recedes from the equator, and end by pointing straight towards the south pole when the centre reaches the magnetic axis (see fig. 6). When we reflect that in all. our experiments the pro perties of magnets, whether native, such as the loadstone, or artificial, such as the needles magnetized by rubbing
with the loadstone, have proved alike, and that every