The generalized equations lead, very approximately, to the same expressions for the fields as are given by the classical theory, except that the and of classical theory are replaced by S and Thus, in the case of a rotating neutral earth there is a fictitious current density aP±(3Q and a fictitious charge density aP The value of a chosen as above is too small to make appreciable contribution to the fictitious current density. The fictitious current density is provided for by 0Q, and the choice of j3 necessary to result in a magnetic field equal to that of the earth is such that, as regards any fictitious charge density of importance in its power to give rise to the earth's electric field, the term (30:2 t is negligible, as is also the term aP The electric field is provided for otherwise, as outlined above.
The forms of the invariants a and are chosen so that the theory gives the correct ratio for the magnetic field of the earth to that of the sun, and predicts for a small sphere of laboratory size, rotating at the highest attainable speed, a magnetic field and a rate of death of charge which would be immeasurable, or meas urable only with considerable difficulty.
Gravitation is provided for by a replacement of the force equa tion by two equations, for the motions of positive and negative electrons respectively, the modification implying, primarily, a difference in the forces between equal like charges and equal unlike charges.
Magnetic Field of the Sun.—The magnetic field of the sun is of particular interest in relation to theories of terrestrial mag netism ; for, in the sun and earth we are presented with bodies of entirely different size, angular velocity, and physical condition. In addition to strong magnetic fields of the order of 2,000 gauss which are to be found in sunspots, the sun possesses a general magnetic field similar in some respects to that of the earth, but with very important differences.
The Zeeman effect affords a means of measuring the magnetic intensity at different levels in the sun's atmosphere. Measure ments extend from altitudes of 250 kilometres to 450 kilometres above the sun's disc, and show a remarkably sharp decline in value from 5o gauss for the former altitude to i o gauss for the latter. If the magnetic field of the sun were anything like that of a uni formly magnetized sphere, the field would vary as the inverse cube of the distance from the sun's centre, and would change by only about 0.1 per cent between the altitudes cited.
The direction of the sun's magnetic field at a point bears the