Review of the evidence indicates that a magnetic field of the order of 10~5 gauss probably lies along a spiral arm of the galaxy. If so, any anisotropy observed in high-energy cosmic radiation must be associated with this field. Anisotropy might be due to: (a) acceleration by Fermi's mechanism, either by his longitudinal collisions or by betatron effects; (b) diffusion along field lines toward a region where the cosmic rays escape from the galaxy; (c) inhomogeneities in cosmic-ray density normal to the field lines. From symmetry considerations theoretical expressions are developed for the cosmic-ray flux as a function of direction and for the resulting sidereal time dependence of extensive showers as a function of latitude and the orientation of the detecting apparatus. If atmospheric effects can be corrected for, the main harmonics predicted are the first and second, the second being mainly due to anisotropy produced by acceleration. In the absence of detailed calculations based on a specific theory of the origin of cosmic rays and on the way the extensive showers are detected, the amplitude of the harmonics must be determined from experiment. Preliminary reports of measurements by Cranshaw and Galbraith and by Farley and Storey seem to indicate tentatively that the magnetic field is as described above and that cosmic rays are accelerated by Fermi's mechanism; the measurements of Daudin and Daudin require some other explanation.