Two cylindrical multiwire proportional chambers (ePC1, ePC2) outside the hydrogen vessel determine the direction vector of the electron/positron from muon decay. Their resolution is chosen so that the physical resolution dominated by multiple scattering in the hydrogen vessel is not deteriorated. The read-out of the chamber system is non-standard, as all wire hits are recorded avoiding the deadtime introduced by standard decoder circuits. These chambers are followed by a hodoscope consisting of a barrel of 2x16 slabs of scintillators made of two coincident timing elements (eSC). The electron detector package is instrumented sufficiently, so that the scintillator array can be analyzed alone or in coincidence with wire chamber tracks. The first analysis is particularly simple, albeit with larger accidental contributions. The second method employs the full tracking information, thus allowing higher rates and less accidentals. In both cases the scintillators are used in coincidence to provide a fast and stable timing signal and to suppress potential spurious afterpulses in the chambers.