In order to compare magnets and to facili tate magnetic computations, certain methods of measurement have been devised. Only a brief sketch can be given here, as full details of these operations may be found in books devoted to this subject, some of which will be men tioned at the end of this article. When a bar magnet is placed at right angles to the lines of a uniform magnetic ,field it will experience a twist tending to place it along these lines. The amount of this twist will depend upon three things. First: The pole strength of the magnet in question. Second: The distance between the poles. Third: The strength of the field where it is placed. The product of the pole strength by distance between poles is called the mag netic moment of the magnet. When a magnet is suspended freely and slightly displaced from a position parallel to the lines of force it will vibrate about this position. The time required for a complete swing is found to depend upon the magnetic moment, the moment of inertia and the strength of the field where the magnet is placed. The vibration period may be directly observed and the moment of inertia computed from the dimensions and weight of the magnet. In this way the product of the magnetic mo ment by the field strength may be found. If the same magnet is held with the line joining its poles cast and west it will cause a small freely suspended magnet some distance to the east or west to turn slightly from its equilibrium posi tion. The amount of this deflection depends on the distance between the magnets and the ratio of magnetic moment to field strength. If we denote the magnetic moment by ml and the field strength by H, the product of in! times H is found from the time of vibration, and by means of the deflection of the small auxiliary m/ magnet Ti may be determined. When ml times H or ml divided by H is known either ml or H is readily computed. When the field at any point is known, a comparison of the time of vibration of a magnet at the known point with its period when vibrating at any other point enables us to compare the two fields without further measurement. The law of change being that if periodic time is doubled the field strength would be four times as great ; or the period varies inversely as the square foot of the field in which the magnet vibrates.
The facts mentioned above regarding tht ability of a magnet to cause pieces of neutral iron or steel to show magnetic properties is frequently spoken of as magnetic inducti,n, The general phenomena can be readily remem bered if we imagine that it is easier for lines of magnetic force to pass through iron than through air. Small pieces, as shown at P, Fig 2, would have lines entering at "S" and leaving at "N" and would behave as small magnets placed in corresponding positions. Owing to the tension of the lines force these small pieces would tend to set themselves nearly parallel the undisturbed direction of the lines. If a sheet of glass or other non-magnetic material is placed over a magnet and iron filings are sprinkled on its surface, a slight tapping, suffi cient to overcome friction, will enable the of force to arrange the small temporary mad nets parallel to the field. In this way maps magnetic fields may be readily found, and their study throws considerable light upon many de tails of these peculiar phenomena. Such fields are shown in Figs. 3 and 4. If a sphere of iron or cobalt is free to move in a magnetic field which is not uniform, a tendency is always served for the iron to place itself in the strong est part of the field, or so that as many of the magnetic lines pass through it as possible. Such a substance is called paramagnetic. Some sub stances, as for example a sphere of bismuth, will tend to move to the weaker portions of the field, indicating that it is more difficult for magnetic lines to pass through the material than through air. These are called diamagnetic bodies.
The importance of magnetic action in both theoretical and practical affairs is due largely to its intimate connection with the phenomena of the electric current. In fact it is absolutely impossible under any conditions to have an electric current flow in a conductor without pro ducing a magnetic field. In the case of a long straight wire carrying current the magnetic lines are circular in form, concentric with the wire, and their planes are perpendicular to its axis. If a wire is wound in a long, straight,
cylindrical coil, frequently called a solenoid, and a current he passed through it, the field pro duced will be nearly identical with that of a bar magnet, the difference being that the lines of force are entirely in air and are not modified by the peculiar properties of iron. By increas ing the strength of the current and the number of turns of wire, a comparatively strong mag netic field may be produced at the. centre. A piece of soft iron or steel inserted in the coil becomes a powerful temporary magnet, while strips or bars of 'hardened iron or steel would in the same way become permanent magnets. The requirements of modern electrical processes have led to very careful investigations of the magnetic behavior of iron in connection with the production and the measurement of electric energy. Only a brief sketch of the fundamental features can be given here. If we suppose an electric current flowing in a long solenoid, which does not contain an iron core, the strength of the magnetic field through the in side of the solenoid may be readily computed from a knowledge of the number of turns of wire and the strength of the current The sym bol H is generally used to indicate the field strength when iron is absent. If now a bar of iron be inserted it will be found that the mag netic field is greatly increased. The new field will depend partly on the original value of H and partly on the quality and previous magnetic history of the iron inserted. The symbol B is generally used to denote the intensity of the field when iron is present. It may then be stated that B equals Fi H, where 14 is a variable factor depending on the nature of the iron and the field strength; this factor is called the per meability. The original field H is frequently spoken of as the magnetizing field and the new one as the induction. Or H stands for the number of lines per square centimeter where iron is absent and B stands for the number of lines per square centimeter in the iron. If iron, in a neutral magnetic condition, is placed in a solenoid and the electric current is gradually increased from zero the iron will be subjected to a steadily increasing magnetizing field. A comparison of corresponding values of B and H in such a case leads to very important re sults. The relation between these values is best explained by reference to a curve drawn by using these quantities as co-ordinates. Such curves, usually called the curves of magnetiza tion, are shown in Fig. 5. It should be observed that when H is almost zero, the induction is very small, then B increases more and mote rapidly with a rising field until at point two the rate of increase of B with H begins to fall off rapidly, and shortly a value of B is reached which cannot be materially increased no matter how strong a magnetizing field is used. For example in the specimens shown it is useless to extend the value of H much above 70, and in actual practice this limit would be taken much lower. When as many lines as possible are car ried through the iron it is said to be saturated. The exact shape of the magnetization curve will depend upon the nature and previous magnetic history of the specimen, but the ratio B-H at any point gives the ability of the iron to mul tiply magnetic field strength for that particular field. If, however, any definite state of mag netization is attained as at the point M, Fig. 6, it will be found that upon reducing the field, H, the values of the induction, B, will not agree with those found for the same value of H when the field was increasing. In fact if H be changed to zero and then to negative values and hack again to the former condition the value of B will form a loop as indicated. This peculiar lag of the induction when the field is reduced is called hysteresis, and the hysteresis loop as shown is of practical importance be cause its area enables one to find the work con verted into heat when the magnetization is car ried through one complete cycle. The line ON measured the residual magnetism, which is semi-permanent, and will be greater in hard than in soft iron or steel. No matter where the process of magnetization is stopped a series of cyclic changes of the magnetic field always gives corresponding loops.