The attempt to integrate the equations of motion of an electrified particle in the field due to. a magnet of infinitesimal dimensions was called forth by Birkeland's discovery of the attraction ("suction") of cathode rays towards a magnetic pole. Considering the field due to a single pole, M. Poincar• had integrated the equations of motion, his integrals, however, failing to explain the existence of certain rings observed in the Crookes tubes during the experiments. These =ings can be accounted

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... for by substituting an elementary magnet for the single pole. The force acting on the particle bein, g perpendicular to the magnetic force and also to the path, the velocity remains constant. St•rmer's two first integrals suffice to enable him to portion off space into regions, first, where the particles recede to infinite distance from the magnet, secondly, regions where the particles approach the magnet indefinitely, and, finally, regions into which none of the paths of the particles can penetrate. The latter regions are bounded by surfaces of revolution of the third order, about the axis of the magnet. The shape of these surfaces depends upon an integration constant, but in most cases at least a portion forms an anchor-ring with an opening so narrow, that it touches the magn•et. Singular solutions--e. g., Weyr's "electromagnetic curve"--exist in the plane perpendicular to the magnet. Birkeland's theory that auroras are the result of suction of a cathodic ernanation from the Sun by the Earth's magnetic poles, agrees well with the above analysis. The author shows that, taking the Earth as a small magnet in the above sense, any particle emanating from the Sun must strike the Earth, if at all, in the polar regions. Furthermore, the aurora would be mainly due to rays on that side of the Earth which recedes from the Sun, and each of its constituent particles would revolve continually about the Earth's magnetic axis from E. to W. until it reaches a certain surface depending on the altitude of the Sun above the horizon at the magnetic pole. P.W. x S•r•M•, C. Sur le mouver-ent d'un point mat•riel potant une charge d'•leetricit6 sous l'action d'un aimant 61•mentaire. Christiania •9o4, 32 pp., • chart.