absolute value, the attraction for each unit of surface is 2πA2 (§ 44). For the total surface of contact S, the force in dynes is 2πA2S, and if P is the number of grammes whose weight would just pull off the keeper, we have (§ 187)— = If we take A 800 for steel, we get as the greatest value for P, 4 kilogrammes per square centimetre; this is, in fact, what is given by the best magnets. With soft iron raised to saturation, 10 or II kilogrammes per square centimetre is easily obtained. 225. Magnetisation by the Action of the Earth. It is very rarely that we find a piece of steel or iron, unless perhaps it is perfectly pure soft iron, which does not present magnetic polarity. Magnetisation is produced in it if it is struck, or undergoes any other mechanical disturbance while under the influence of the earth. A bar of soft iron which is placed parallel to the earth's field acquires a temporary magnetisation, which is reversed when the magnet is turned end for end. But if the bar is struck with a hammer, the magnetisation is raised to a maximum, and the iron at the same time acquires perceptible coercive force. A fresh blow on the bar, when placed transversely to the magnetic field, takes from it its magnetisation. A strand of soft wire twisted, while being held in the direction of the dipping-needle, also acquires permanent magnetisation. The value of k (§ 202) is about 40 for the intensity 0.47, which is that of the earth's field at London. A very long, thin, soft iron wire, for example, 1 millimetre in diameter, and 50 centimetres long, acquires a magnetic intensity of about 0.47 × 40 = 18.8; and, as its volume is nearly 0.40 cubic centimetre, its moment is 18.8 × .47.5 (§ 186). 226. Theory of Magnetisation. It is proved by experiment that magnetisation is a molecular phenomenon (§ 178). The simplest idea is to assume that the molecules of magnetic bodies are small magnets. In the neutral state these small magnets have no external action, either because they form closed chains, or because they are arranged indiscriminately in all directions. The process of magnetisation has the effect of arranging the molecular magnets in some predominating direction, and the maximum is reached when their axes are all parallel, and their similar poles in the same direction. It remains to establish the theory of the very complicated phenomenon of magnetism on this basis. Professor Ewing's experiments throw much light on this subject. He arranges a great number of very small magnetic needles movable on pivots, at small regular distances apart. Experiment shows that these small magnets may assume a great number of different stable configurations that do not exert external force. These configurations represent so many neutral states which are not identical with each other. If one part of the system is disturbed it falls into a different configuration; each single magnet takes up a position of stable equilibrium after oscillations of greater or less amplitude. These oscillations represent the loss of energy which the system experiences in passing from the first configuration to the second. The change in general is not reversible. Now, suppose the system exposed to the action of a uniform field gradually increasing from zero, the magnets are at first but slightly deflected, and if the directive force is removed, they revert to their first positions, and there is no permanent effect. As the field continues to increase, a point is reached at which the equilibrium is suddenly broken, and the system falls into a new configuration in which all the elements have approximately the same direction as the field. From this point the effect of an increase in the strength of the field is only to make the arrangement more complete. These three phases correspond to the three parts of the curve of magnetisation (§ 195). If now the strength of the field is decreased, the system does not pass through the same states; it tends towards whatever condition of stable equilibrium is nearest to the existing configuration. Thus without any hypothesis of a coercive force analogous to friction, we may explain the effects of hysteresis and of residual magnetism. Experiment shows that if the system is homogeneous, that is to say, if the small magnets are uniformly distributed, the transition to quasi-parallelism is made suddenly. This is what happens in the case of soft iron. If the system is not homogeneous, and the magnets are unevenly grouped, they do not equally and simultaneously obey the external action; the magnetisation curve becomes elongated, and does not so soon attain a maximum; on the other hand the residual magnetism is more stable. This is the case of steel. The effect of heat may be accounted for if we assign to it a double effect, that of increasing the distance of the elements, and of making them oscillate. Finally, in order to account for the disappearance of magnetic properties, Professor Ewing assumes that the oscillatory motion being gradually amplified changes into a continuous rotating one. This theory also accounts very satisfactorily without any fresh hypothesis for the complicated relations of magnetism with the mechanical actions of stretching and torsion. CHAPTER XXI. TERRESTRIAL MAGNETISM. 227. Terrestrial Field.—The field of force due to the earth, though practically uniform throughout any moderate space that is not affected by the presence of magnetic bodies, varies greatly both in intensity and direction from one place to another on the earth's surface; and even in one and the same place it changes in course of time. We know that its action on a magnet is that of a couple (§ 171). In order that a magnet may indicate the direction of the force at a given point, it must be acted upon by the earth's force independently of any other; the direction which the magnetic axis then takes is that of the field due to the earth. In this part of the world this direction is roughly north and south, but it makes a large angle with the horizon, the north pole pointing downwards. We may define this direction by means of two angles, the declination, and the inclination or dip. The magnetic meridian is the vertical plane which contains the direction of the earth's force. The declination is the angle which the magnetic meridian makes with the astronomical meridian. The inclination or dip is the angle which the direction of the earth's force makes with its projection on the horizontal plane. The declination, D, the inclination, I, and the intensity, T, of the field are three elements which characterise the earth's magnetism in a given time and place. 228. It is not practicable to construct an instrument in which a magnet is suspended freely by its centre of gravity. In practice, two instruments are employed, one in which the magnet is movable only about a vertical axis: this is called a declination compass ; the other, in which the needle moves only about a horizontal axis passing through its centre of gravity: this is the inclination compass or dip needle. A α YA M Suppose the magnet in any position (Fig. 191), and let a be the angle which the vertical plane, OA, containing the axis makes with the magnetic meridian, OM; the force, 7, which acts on each unit of magnetism of the pole at O, may be resolved into two components independent of the angle a ; the one, vertical, Z 7 sin I; the other, horizontal, H = T cos I ; this latter may be again resolved into two others, also horizontal, namely, X H cos a, situate in the plane of the magnet; the other, Y sin a perpendicular to this plane. We have thus- = = = X = T cos I cos a, Y = T cos I sin a, Ꭲ, Z FIG. 191. 229. Declination Compass.-If the needle is movable only about a vertical axis, it is only acted on by the horizontal component; its position of equilibrium is that in which its axis is in the magnetic meridian. When it is deflected through an angle a, the couple which acts on the needle and tends to bring it to its position of equilibrium is MH sin a; M being the magnetic moment of the needle. This couple is proportional to the sine of the deflection; consequently, the law of the motion of the needle when disturbed and left to itself is that of the pendulum (§ 216). In order to realise the fundamental condition of the apparatus, it is not needful for the vertical axis of rotation of the magnet to |