The most recent (September 1–2, 1971) of the rare ground level events signaling the arrival at the earth of relativistic solar cosmic rays arising from a flare on the sun's invisible hemisphere displayed marked anisotropy for several hours. Application of newly developed analytical procedures has made it possible to study in detail the evolution of the anisotropic pitch angle distribution. Throughout the anisotropic phase the solar particle flux is proportional to the cosine of the angle between the weighted mean asymptotic direction of viewing and an axis of symmetry corresponding to the spiral interplanetary magnetic field line that connects the sun to the earth. Furthermore, the degree of anisotropy deduced from the ratio of the fluxes in the garden hose direction toward and away from the sun decays exponentially. The results of this analysis and the reexamination of the three previously observed invisible hemisphere ground level events have demonstrated that propagation along the spiral interplanetary field line connecting the sun to the earth occurs even when the source lies far beyond the limb of the sun. In one case (January 28, 1967) the anisotropy near onset was 100% (i.e., no particles traveling toward the sun), a situation that had only been reported twice previously and then in association with visible flares that occurred within 10° of the foot of the nominal garden hose field line. These results bespeak the operation of an efficient transport mechanism in the solar corona that enables relativistic protons to travel over distances at least as great as 70° in heliolongitude in about 15 min.