On the Allowed Cone of Cosmic Radiation

Abstract

Further results of an extensive study of trajectories asymptotic to a known family of unstable periodic orbits in the earth's dipolar magnetic field, carried out by means of Bush's differential analyzer, are presented in this paper. A detailed discussion is given of our methods of determining asymptotic trajectories by means of the differential analyzer and by numerical integration of a whole family at a time; comparison of the results obtained shows the absence of systematic errors of any consequence in the mechanical integrations and exhibits the precision attained with the differential analyzer. The families of asymptotic trajectories are then analyzed systematically in order to determine the main cones for latitudes up to 30°. This leads to the theory of the azimuthal effect and a study of the region in the vicinity of the zenith.