The origin and behavior of cosmic rays in the Galaxy depend crucially upon whether the galactic magnetic field has a closed topology, as does the field of earth, or whether a major fraction of the lines of force connect into extragalactic space. This paper examines the structure of a galactic field that opens initially into intergalactic space and, with the inclusion of turbulent diffusion, finds no possibility for maintaining a significant magnetic connection with an extragalactic field. Unless some mechanism can be found, we are forced to the conclusion that the field is closed, that cosmic rays are of galactic origin, and that cosmic rays escape from the Galaxy only by pushing their way out.