Strong evidence is presented for escape of magnetospheric particles along reconnected field lines into the magnetosheath, using observations of ~30- to ~120-keV/charge protons and alpha particles made by the Max-Planck-Institut/University of Maryland instrument on Isee 1. During three magnetopause crossings, which have been identified from tangential stress balance analysas is reconnection events, the magnetospheric particle distribution extends well into the magnetosheath, and the particles in the magnetosheath show a strong anisotropy along the magnetic field. The proton to alpha particle ratio in this layer as well as in distinct bursts within the magnetohseath is the same as this ratio within the magnetosphere (at equal energy per charge). We conclude that the most likely explanation for these observations is that magnetospheric particles are escaping along reconnected field lines into the magnetosheath. It is argued that magnetospheric particles are seen in the magnetosheath up to the reconnection separatrix, and the magnetosheath bursts are interpreted as multiple encounters of this magnetosheath layer by the satellite due to boundary motions.