Theories of Terrestrial Magnetism

A possible source of maintenance of internal currents has been suggested by Lamor"), chiefly in reference to an explanation of the magnetic field of the sun. If there is any internal circulation of matter in meridional planes and if we start with an initial mag netic flux parallel to the polar axis, the flow will set up induced currents in circles parallel to the equator. If the initial mag netic flux is in the right direction in relation to the circulation, the induced currents set up will increase the original field, so that a finite field may become produced in this manner from in finitesimal beginnings, as in the case of a self exciting dynamo, the energy coming, of course, from the internal circulation. On such a view, the secular variation would have to seek its origin in a secular periodicity in the internal circulatory motion.

The enormous amount of positive and negative electricity in the earth tempts us to seek in strange places for possibilities as re gards a residual current which might result from a slight differ ence in their velocities. Thus, if the free electrons in the earth were absolutely free, and if the remainder of the substance of the earth were dying down in velocity, for example as a result of total friction, and if the causes responsible for the decay of motion operated only on the part of the matter other than the free elec trons, the latter would continue to revolve with undiminishing velocity, and as time went on a large current would result from the relative motion of these electrons and the remainder of the earth's substance. In practice, the relative motion would only grow until the drag due to friction—in this case, electrical resist ance—which resulted from the relative velocity was sufficient to bring about the continual destruction of momentum of the elec trons as a result of their continual loss of velocity. On submit ting the matter to calculation we find that, for the specific resist ance of the earth's core as calculated from diurnal variation con siderations, it would be necessary for the earth to lose practically the whole of its angular velocity in a very small fraction of a second in order that the electric current set up as a result of the drag should be sufficient to account for the earth's field.

The argument for the foregoing consideration is as follows: Suppose o is the specific resistance of the material of the earth, e the electronic charge, and m the mass. Then, if i is the electric current density sought, and if v is the tangential velocity of the earth at the point in Question and it would have been necessary for the earth to lose practically the whole of its velocity in less than a day in order to give rise to a magnetic field comparable with that of the earth.

Quite apart from considerations invoking a finite rate of decay in the earth's rotation, it is not out of the realm of possibility that the mere rotation itself may bring about a condition in which there is a relative motion between the free electrons and the re mainder of the matter. It may not even be necessary to provide a

source of power to maintain the relative motion in opposition to electrical resistance ; for, such a state of relative motion may be the state of equilibrium which must be attained in order that there shall be no dissipation of energy. The elements which enter in this connection are those associated with the mechanism by which electrical conductivity arises in a metal and there are cer tain not unreasonable hypotheses which would provide for con ditions of this kind"). However, any attempt to account for the earth's magnetism along these lines must necessarily be highly speculative.

Magnetization of Rotation.

If we believe that the atoms of which the substance of the earth is composed are magnetic, and that this magnetic condition arises from the rotation of electrons in the atom, we should expect the atoms to act like gyroscopes and tend to turn with their axes parallel to the axis of the earth's rotation, this effect in favour of organized orientation being op posed by the temperature agitation of the molecules. However, a phenomenon of this kind makes the intensity of magnetization independent of the size of the sphere for a given angular velo city"), so that if it were a potent factor in the case of the earth's magnetism, the effect would be very readily observable in the case of small bodies set into rotation in the laboratory. The magnetiz ation produced by rotation has been experimentally measured by S. J. Barnett, and both calculation and experiment alike show that even in the most favourable case, that of an earth with an iron core, we could not expect to realize a magnetic field more than about 1 for the earth's magnetic field.

It has sometimes been suggested that a very weak magnetizing intensity, either of the nature of a magnetic field of unknown origin or of a dynamical nature such as the gyroscopic action just discussed might, in the presence of an abnormally large perme ability, result in an intensity of magnetization comparable with that of the earth. Such might indeed be the case for a long cylin drical body; but, in the case of a sphere magnetized to an intensity I, there is within the sphere a demagnetizing field equal to 1/3, resulting from the so-called fictitious distribution of positive and negative magnetism on the two hemispheres (this fictitious dis tribution being of course, as regards its action, the representative of all the molecular magnets of which the sphere is composed).