The problem of the orbits of electrons in FOUNVATION. the earth's magnetic field has been treated co,mmcation No.o. extensively by St6rmer i from the theoretical side, and by Birkeland 2 from the experimental side, chiefly in relation to the theory of the aurora. In connection with that problem, the orbit of an electron in the equatorial plane did not assume a role of primary importance, as the main point of interest concerned the possibility of explaining how electron orbits could penetrate to sufficiently low latitudes to coincide with the auroral latitudes. In view, however, of the recent recognition of the possibilities of electron energies much higher than would have seemed reasonable a few years ago, and particularly of the recent experiments by Prof. A. H. Compton on the variation of cosmic-ray intensity with latitude, the problem of electronic motion in the magnetic equatorial plane at zero latitude becomes of importance. The formula for this case is, of course, deducible immediately from the more general case. Since, however, it can be deduced from particularly elementary considerations for motion in the magnetic equatorial plane, it may be of interest to record here a derivation, particularly as the derivation serves to emphasize certain important features.
If r is the radius vector to a point P on a curve, o the radius of curvature at P, p the perpendicular distance from the origin to the tangent at P, and r0 the length of the tangent