THEORIES OF TERRESTRIAL MAGNETISM Theories Involving Permanent Magnetization.—While it is true that a complete theory of terrestrial magnetism must take account of the variations of the earth's magnetism with time, and of the non-coincidence of the geographic and magnetic axes we should feel that we had made a reasonably satisfactory advance if we could see some way in which to account for any sort of a magnetic field of the right order of magnitude even though our theory should require that field to be symmetrical with respect to the axis of rotation and to show in its simplest form no secular variation.
The first idea which suggests itself is that the earth's interior may be of magnetizable substance, and that somehow or other, at some time or other it became magnetized. We cannot escape so easily the responsibilities of an explanation, however, for our ideas as to the temperature of the earth's interior place grave difficulties in the way of an assumption of a state of magnetization in the earth's interior; since, under ordinary conditions, iron, for example, would lose its capacity for magnetization at temperatures which would be reached at a depth of about 20 kilometers, and magnetite ceases to be magnetic at even lower temperatures than iron. Thus, unless we invoke some unknown effect of pressure to increase the temperature at which a substance loses its capacity for magnetization we must confine the possibilities as regards permanent magnetization to a relatively thin shell of the earth.
A uniformly magnetized sphere of radius a, magnetized to an intensity I, acts at external points like a doublet of moment M and a shell of thickness ba acts like the difference of two such spheres of radii a and a-3a. It acts in fact like a doublet of moment SM =.47ragoa. In order that S1iI should correspond to the effective moment of the earth it is necessary to assume a value of about 5o for I if Sa is to be as small as 15 or 20 kilometers. While this value of the intensity is not large beyond all reason its existence seems highly improbable.
Theories Involving Rotation of Charge Distributions.— It is difficult to resist the temptation to believe that the earth's magnetism may arise as a result of its rotation. As a guide in such
considerations we have the experimental fact, as revealed by study of the Zeeman effect, that the sun possesses a magnetic field whose intensity at its pole is about 5o gauss. Further, the magnetic field which could arise from the rotation, at attainable speeds, of bodies of laboratory size must necessarily be small, as otherwise such magnetic fields would have revealed themselves long ago. Any theory which attempts to explain terrestrial magnetism as a result of rotation must lead to a formula consistent with the above facts.
The fact that a rotating charged body produces a magnetic field, leads one to inquire as to whether the earth's charge (see ELEC TRICITY, ATMOSPHERIC) may, by its rotation with the earth, pro duce a magnetic field comparable with that of the earth. Calcula tion shows, however, that the field so produced would be a hundred million times too small. The magnetic potential S2 at a point with polar co-ordinates r and 0 is given by where Q is the total charge in electrostatic units, c the velocity of light, w the angular velocity and a the radius of the sphere. The field outside the sphere is, in fact, similar to that of a doublet of moment Q w 3c. Its general form would be approximately cor rect as corresponding to the part of the field symmetrical about the axis of rotation, but only as viewed by an observer who did not participate in the rotation. Whenever we have to deal with a magnetic field produced by the rotation of a system which also has an electric field, we are faced with a difference between the magnetic field as it appears to an observer stationed on the rotat ing body and to an observer who does not participate in the In the case of the rotation of a charged earth cited above, the effect would, for an observer on the earth, cause a reversal of the horizontal intensity as seen by a stationary ob server, while leaving the vertical intensity unchanged. The effect of this is to produce over the surface of the sphere a distribution of field quite inconsistent with the facts.