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Grain boundary penetrations of radioactive silver into copper bicrystals having a common cubic direction have been measured using an autoradiographic technique. Diffusion occurred along directions forming an angle φ=0°, 45°, and 90° with the common cubic direction. For very low angles of disorientation Θ, no preferential intergranular penetration was observed; for low and intermediate relative orientations, grain boundary diffusion was found to be most rapid along the common direction (φ=0°); for high angles of misfit, little anisotropy of boundary diffusion was detected. The observed asymmetry about Θ=45° of the curves of grain boundary penetration versus Θ is in agreement with the known dependence of the density of boundary dislocations on the angle between grains and on grain boundary direction. The anisotropy measurements may be qualitatively explained in terms of the distribution and relative amounts of elongated areas of ``fit'' and ``misfit'' in the grain boundary, and they confirm the earlier proposed model of grain boundaries in the region of angles where the simple dislocation model does not apply.