818. Kinetic and potential energy of the medium 820. The action of magnetism must depend on a real rotation about 821. Statement of the results of the analysis of the phenomenon 823. Variation of the vortices according to Helmholtz's law 827. The equations of motion 828. Velocity of a circularly-polarized ray 829. The magnetic rotation 830. Researches of Verdet 831. Note on a mechanical theory of molecular vortices .. ELECTRIC THEORY OF MAGNETISM. 836. Theory of a current in a perfectly conducting circuit 841. A medium containing perfectly conducting spherical molecules 423 842. Mechanical action of magnetic force on the current which it 848. Relative motion of four electric particles. Fechner's theory.. 427 849. Two new forms of Ampère's formula 850. Two different expressions for the force between two electric 854. Helmholtz's deductions from Weber's formula .. 855. Potential of two currents.. 856. Weber's theory of the induction of electric currents 857. Segregating force in a conductor 858. Case of moving conductors 859. The formula of Gauss leads to an erroneous result.. 860. That of Weber agrees with the phenomena PART III. MAGNETISM. CHAPTER I. ELEMENTARY THEORY OF MAGNETISM. 371.] CERTAIN bodies, as, for instance, the iron ore called loadstone, the earth itself, and pieces of steel which have been subjected to certain treatment, are found to possess the following properties, and are called Magnets. If, near any part of the earth's surface except the Magnetic Poles, a magnet be suspended so as to turn freely about a vertical axis, it will in general tend to set itself in a certain azimuth, and if disturbed from this position it will oscillate about it. An unmagnetized body has no such tendency, but is in equilibrium in all azimuths alike. 372.] It is found that the force which acts on the body tends to cause a certain line in the body, called the Axis of the Magnet, to become parallel to a certain line in space, called the Direction of the Magnetic Force. Let us suppose the magnet suspended so as to be free to turn in all directions about a fixed point. To eliminate the action of its weight we may suppose this point to be its centre of gravity. Let it come to a position of equilibrium. Mark two points on the magnet, and note their positions in space. Then let the magnet be placed in a new position of equilibrium, and note the positions in space of the two marked points on the magnet. Since the axis of the magnet coincides with the direction of magnetic force in both positions, we have to find that line in the magnet which occupies the same position in space before and after the motion. It appears, from the theory of the motion of bodies of invariable form, that such a line always exists, and that a motion equivalent to the actual motion might have taken place by simple rotation round this line. To find the line, join the first and last positions of each of the marked points, and draw planes bisecting these lines at right angles. The intersection of these planes will be the line required, which indicates the direction of the axis of the magnet and the direction of the magnetic force in space. The method just described is not convenient for the practical determination of these directions. We shall return to this subject when we treat of Magnetic Measurements. The direction of the magnetic force is found to be different at different parts of the earth's surface. If the end of the axis of the magnet which points in a northerly direction be marked, it has been found that the direction in which it sets itself in general deviates from the true meridian to a considerable extent, and that the marked end points on the whole downwards in the northern hemisphere and upwards in the southern. The azimuth of the direction of the magnetic force, measured from the true north in a westerly direction, is called the Variation, or the Magnetic Declination. The angle between the direction of the magnetic force and the horizontal plane is called the Magnetic Dip. These two angles determine the direction of the magnetic force, and, when the magnetic intensity is also known, the magnetic force is completely determined. The determination of the values of these three elements at different parts of the earth's surface, the discussion of the manner in which they vary according to the place and time of observation, and the investigation of the causes of the magnetic force and its variations, constitute the science of Terrestrial Magnetism. 373.] Let us now suppose that the axes of several magnets have been determined, and the end of each which points north marked. Then, if one of these be freely suspended and another brought near it, it is found that two marked ends repel each other, that a marked and an unmarked end attract each other, and that two unmarked ends repel each other. If the magnets are in the form of long rods or wires, uniformly and longitudinally magnetized, see below, Art. 384, it is found that the greatest manifestation of force occurs when the end of one magnet is held near the end of the other, and that the |