bonic acid, ethylene, and cyanogen are diamagnetic; nitrogen and hydrogen seem to be neutral. In order to demonstrate this phenomenon, a glass globe is suspended to the beam of a delicate balance over the pole of a powerful magnet. After the globe has been exhausted, it is counterpoised, and is then filled with the gas to be tested. In the case of oxygen, there is a very perceptible attraction, which is four or five times as strong as that exerted on air at the same pressure and temperature. 212. Relative Magnetisation.-A body of small dimensions and of permeability μ, placed in a liquid or gas of permeability p', behaves like a body whose permeability is μ1 = μ 5, or, what FIG. 181. This result leads to consequences analogous to those which are deduced from the principle of Archimedes for floating bodies. Three cases may present themselves: First, k>k', the body behaves like a magnetic body; second, k = k', the body appears neutral; and third, k < k', the body behaves like a diamagnetic body. It is possible that diamagnetism might be explained by a cause of this kind. CHAPTER XX. PERMANENT MAGNETS. 213. Permanent Magnets.-Permanent magnets are usually made in the form of straight prismatic bars, but they are also sometimes bent in the form of a horse-shoe. It is important that the metal of which they are made should have considerable coercive force. Highly tempered steel, especially such as contains tungsten, is found to answer best. As the bars are usually short, the effect of the ends is considerable. Further, it is impossible to obtain uniform magnetisation in a prismatic or cylindrical bar. The effective magnetising force is less near the ends of the bar than it is at the middle; consequently the intensity of magnetisation diminishes towards each end, producing an apparent distribution of north magnetism throughout a greater or less portion of the bar near one end, and of south magnetism throughout a corresponding region near the other end. It has been pointed out already in § 185 that, if a cylinder were uniformly and longitudinally magnetised, there would be no apparent magnetism except on the end-faces. Consider the state of things on each side of one of the end-faces of a uniformly magnetised bar: the magnetic intensity has the uniform value A everywhere on the inner side, within the bar, and the uniform value o everywhere on the outside; but there is no magnetism either inside or outside the surface, only on the surface itself. The numerical value of the surface-density of magnetisation on the end of the bar is equal to A, the intensity of magnetisation of the bar. The condition which we express by speaking of a layer of magnetism on the end of a bar is the phenomenon by which we recognise the change of intensity of magnetisation on passing from one side of the surface to the other. If the transition from a finite magnetisation A to zero magnetisation takes place abruptly, we say that the magnetism is merely superficial; if the transition takes place gradually through a measurable distance, we say that magnetism is distributed through a corresponding portion of the mass of the magnet, the (volume-) density of magnetism being numerically equal, at any given point, to the rate of variation of magnetic intensity at that point. The result of this, in its application to an actual bar magnet, is that the poles, or centres of mass of the north and south magnetisms respectively, are within the bar at some distance from the ends. Moreover, if the bars are thick, the metal is not homogeneous throughout; the hardening more particularly affects the superficial parts, and the magnetism seems to reside to a greater or less depth in this layer. If a bar is magnetised alternately in different directions, magnetic layers are formed which seem to superpose themselves. This fact can be shown by removing the surface layer either mechanically as by grinding, or chemically by dissolving the surface away with weak acid. 214. Distribution of Magnetism. We have already spoken of the impossibility of ascertaining the internal constitution of a magnet from its external effects. The investigation of these effects, speaking generally, does not even determine the distribution of the surface layer by which the internal magnetism might be supposed to be replaced. This layer, in fact, is not in equilibrium according to the law of inverse squares, and consequently Coulomb's theorem cannot be applied; therefore, even if we knew the value of the normal component at each point, we could not deduce from it that of the density. Thus most discussions as to the distribution of magnetism in magnets are of little value. Coulomb caused a very small magnetic needle to oscillate in front of various parts of the bar to be examined (Fig. 182). The needle, NS, was suspended by a cocoon fibre, and in order to make the oscillations slower it was fixed at right angles to a stout copper wire. The needle was first made to oscillate under the action of the earth alone, and then under the action of the earth and of the bar placed at a fixed distance in the plane of the meriIdian of the needle. Having regard to the smallness of the needle, we may treat it as though it were suspended in a uniform field, and apply to it the formula for the pendulum. If F is the force exerted by the earth on one of the poles, and ƒ that due to the bar, and if n and N respectively are the numbers of oscillations which the needle makes in the same time, when it oscillates under the action of the earth alone, and under that of the earth and magnet together, we have and therefore N2 n2 F+f If N' is the number of oscillations in the same time when the needle is opposite another point of the bar, we have The ratio may thus be regarded as being that of the two normal components of the magnetic force at the corresponding points of the bar. In order to make the number obtained for the end of the bar comparable with the others, Coulomb doubled it, a correction which is certainly somewhat arbitrary. In another series of observations Coulomb used the method of torsion. A long magnet, a knitting-needle for instance, was suspended horizontally by a metal wire, so that the wire was without torsion when the needle was in the magnetic meridian ; he then measured the torsion which had to be applied to keep the end of the needle at a small fixed distance opposite various points of a long magnetised bar placed vertically in the meridian of the needle. This torsion would give an approximate measure of the normal component, if it could be assumed that the magnetism of the needle remains the same and does not vary when it is placed opposite different parts of the bar. A third method consists in measuring the force needed to pull off a small sphere, or a small cylinder of soft iron placed in contact with different parts of the bar. To be able to assume, as is ordinarily done, that the effect measured is proportional to the square of the normal component, we must suppose that the coefficient of magnetisation of the test-sphere is independent of its magnetic intensity (§ 192), and that the presence of this sphere does not alter the magnetic state of the bar at the part which is being investigated. We shall afterwards learn a method which gives much more correctly the value of the normal component at each point of the bar. 215. If at each point of the bar we draw ordinates proportional to the numbers found, we obtain a curve which may be called the curve of the normal C α FIG. 183. В simple example will show this for a uniformly magnetised cylinder the method would still give a curve analogous to Fig. 183, which would fix the positions of the poles at a and ß, whereas the surface layer is A' A' nets, that is to say, those in which the length is more than 50 times the diameter, the base, BN, of the representative triangle is about 25 times the diameter of the bar (Fig. 184). The centres of figure are at a fixed distance from the ends equal to 7 or 8 times the diameter. Experiment confirms this result. For bars which differ only as to length, the effective B FIG. 185. P A length may be expressed by / x, where is the length of the bar and x a constant. For magnets whose length is less than about 50 times the diameter, the distribution is represented approximately by the sloping line A'B' (Fig. 185), which cuts the bar in the middle. S |