The propagation of energetic solar protons of ≲1 MeV into the magnetosheath is investigated through three-dimensional pitch angle distributions measured on Vela-satellites. Distortions are observed in the magnetosheath as compared with isotropic or unidirectional distributions normally expected in interplanetary space. Two types of distortions are observed which are characterized by breaks in the distributions at &mgr;oO, where &mgr; is the cosine of the pitch angle. The distributions in the magnetosheath are explained by a Liouville transformation, if particle motion across the bow shock and through the magnetosheath is assumed to be adiabatic. Whether &mgr;o is positive or negative is determined by whether the satellite in the magnetosheath lies beyond or in front of the region of maximum magnetic field compression (or neck) in the magnetosheath, relative to the direction of the net flow of particles. The magnitude of &mgr;o is a measure of the field ratio between neck and satellite. Scattering effects, which must occur at the bow shock and in the magnetosheath, only perturb the adiabatic propagation of the particles. The results show that one must be cautious in inferring the true interplanetary anisotropy from the measured in the magnetosheath. While the maxima and minima of the corresponding pitch angle distributions will be the same, the distributions can be vastly different, and both anisotropy and omnidirectional intensities significantly different, too. By corollary, the pitch angle distribution and anisotropy measured in the solar wind on field line that intercepts the bow shock sunward of the earth will in general be different from that which would be measured in interplanetary space on a field line not connected to the bow shock; to first order the effect of the bow shock can be computed by treating the motion as adiabatic.