270 MAGNETISM Mo j e . In a very important class of modern theories, the f unda- cular mental assumption is that the molecules, or at all events magnet a certain proportion of the molecules, of magnetic sub- theory. s t ances are sm all permanent magnets. In a body which is to outward appearance unmagnetized, the axes of these molecular magnets are turned indifferently in all directions ; in a body which is magnetized in a certain direction a larger proportion than usual of the molecular magnets have their axes more or less in that direction. Magnetic induction is supposed to consist, not in any alteration of the molecular magnets themselves, but in the orientation of their axes under the action of the inducing force. The reader may figure to himself the nature of the action by imagining a line of small magnetic needles with their axes all horizontal, but all pointing in different directions ; the whole system thus arranged will have no determinate magnetic moment, and will represent an unmagnetized body. Next, suppose a magnetizing force to act parallel to the line joining the centres of the needles, they will then arrange themselves in that line, and the magnetic moment of the system will be the sum of the moment of the different parts ; we have thus an image of a body magnet ized by induction. Weber s The notion of molecular magnets seems to have been suggested form. by Kirwan; but it was not until a definite form was given to it by Weber that it acquired any importance. The mathematical problem presented is one of great complexity. In the position of equilibrium any molecule is acted on by the magnetizing force, by a magnetic force due to the combined action of the other molecules, and possibly by a force arising from the displacement as veil. Weber assumes that the couple tending to restore the mole cule to its original position is that due to a constant magnetic force D, parallel to the original direction of its axis. If m be the magnetic moment of a molecule, and there be n molecules in a unit of volume, then the magnetic intensity |j due to the magnetizing force |j is given by $ = 2m?i!/3D, if |j<D; and by | = m(l - D 2 /3$ 2 ), if P > D. In other words, the curve (|, $JS) is straight till it reaches the point ($mn, D), it then becomes concave towards the axis of |jj, and rises towards an asymptote parallel to the axis of D ; the maximum value of 3 is mn. The theory does, therefore, give a general explana tion of the phenomena of magnetic induction. The reader will be able by comparison with the experimental data given above to see how far it falls short of a complete explanation. If the magnetic substance be devoid of coercive force, we must suppose that the molecules return to their original positions when the magnetizing force is removed. In substances capable of being permanently magnetized, ave must imagine something of the nature of a frictional resistance to the motion of the magnetic molecules ; so that, when they are deflected through more than a certain angle, they retain a permanent set after removal of the magnetizing force. Max- Maxwell has worked out the particular hypothesis that each mole- well s cule which is deflected through an angle less than /3 returns when form. the magnetizing force ceases to act, but that a molecule deflected through an angle #>;8 retains the deflexion /8-/3 . Denoting I)sin/3 by L, he finds as the result of the above supposition that the curve of temporary magnetization is a straight line from US = to $ = L ; after that it is concave to the axis of |, and rises to an asymptote, the maximum value of $ being mn as before. The curve of residual magnetization begins when ji) = L ; it is concave to the axis of H, and rises to an asymptote corresponding to the maximum g = mn { 1 + VI - L 2 /D 2 } 2 . It results from the hypothesis that, when a bar is permanently magnetized by a positive force U 1} its magnetism cannot be increased by a positive force < X^, but may be diminished by a negative force <% l ; and, when the bar is exactly demagnetized by a negative force $ 2 , it cannot be mag netized in the opposite direction without the application of a force >|) 2 ; but a positive force <$ 2 is sufficient to begin to remagnetize the bar in the original direction. Ampere s Behind the molecular magnet theory there arises the hypo- question, What is the nature of the magnetic molecule 1 ? IS1S> One answer to this question is given by the hypothesis of Ampere, that around each such molecule a current circulates in planes perpendicular to the axis of the molecule. That such an arrangement will be equivalent to an infinitely small magnet in the axis of the molecule, so far as external action is concerned, we know from the laws of electrodynamics. It remains only to inquire what the nature and properties of these molecular currents must be, to trace the full logical consequences of the assumption, and to compare them with experience. This was first done by Weber, and afterwards more completely by Clerk Maxwell. It is obvious in the first place that the circuits in which the molecular currents flow must be perfectly conducting ; for other wise the electrokinetic energy of the molecular currents would be continually transformed into heat, and a constant supply of energy from without would be necessary to support the magnetism of a permanent magnet, which is contrary to experience. Let A be the effective area of a molecular circuit, L its coefficient of self- induction, 6 the inclination of its axis to the inducing force ^, y the primitive current, and 7 the current after the inducing force is in action. Then 7=-=7o~ l)Acos0/L ; and the component of the moment parallel to ^ will be A(7 - |)Acose/L)cos0. There are three different cases to consider. 1. Let either y be so great, or $A/L be so small, that the effect due to the electromagnetic induction may be neglected in compari son with the effect due to the deflexion of the molecule ; putting m = Ay , we have thus merely the theory of molecular maguets already explained. 2. Let the force resisting the turning of the molecules be in- Weber finitely great, we then find for the magnetic susceptibility the value theory K = - 4?iA 2 /L. This is the theory originally proposed by Weber to diamaj explain diamagnetism. netism 3. If the effects due to deflexion of the molecules and to electro magnetic induction in the molecular circuits be both considered, we have a theory intermediate to (1) and (2), inclining to the one or the other according to the assumptions made as to the relative values of y , A, and L. The reader will find a full discussion of the different cases in Maxwell s Electricity and Magnetism, vol. ii. chap. xxii. The most important attempt that has yet been made to Max- realize a mechanism affording a dynamical explanation of well s magnetic phenomena is the theory of molecular vortices, "^f published by Clerk Maxwell in the Philosophical Magazine V0 rtex for 1861 and 1862 (4th ser., vols. 21 and 23). The general theory results, stripped of all particular assumptions, will be found embodied in his great treatise on Electricity and Magnetism; but the following summary, taken from the original paper, may be of some interest. 1. Magnetoelectric phenomena are due to the existence of matter under certain conditions of motion or of pressure in every part of the magnetic field. The substance producing these effects may bo a certain part of ordinary matter, or it may be an aether associated with matter. 2. The condition of any part of the field through which lines of magnetic force pass is one of unequal pressure in different directions, the pressure being least along the lines of force, so that they may be considered as lines of tension. 3. This inequality of pressure is due to vortices coaxial with the lines of force. The density of the revolving matter is propor tional to the magnetic permeability of the medium. The direction of rotation is related to the direction of the line of force ; and the velocity at the circumference of the vortex is proportional to the resultant magnetic force. 4. The vortices are separated from each other by a single layer of round particles ; so that a system of cells is formed, the partitions being layers of these particles, and the substance of each cell being capable of rotating as a vortex. 5. The particles forming the layer are in rolling contact with both the vortices which they separate, but do not rub against each other. They are perfectly free to roll between the vortices and so to change their place, provided they keep within one complete molecule of the substance ; but in passing from one molecule to another they experience resistance and generate irregular motions which constitute heat. These particles play the part of electricity. Their motion of translation constitutes an electric current ; their rotation serves to transmit the motion of the vortices from one part of the field to another ; the tangential pressures thus called into play constitute electromotive force ; and the elastic yielding of the connecting particles constitutes electric displacement. Maxwell deduces without difficulty all the principal electrical and magnetic phenomena from this theory ; and he points out that its general conclusions have a value which does not depend upon the somewhat intricate kinematical arrangements supposed to exist in the magnetic medium. The theory certainly affords us a most instruc- tiv3 dynamical picture of the phenomena of electricity and magnetism ; and it remains, so far as we know, the only
successful attempt of its kind. (G. CH.)