The characteristics of 33 diffuse particle events in the energy range from ~30 to ~130 keV/Q observed upstream of the earth's bow shock have been determined. The measurements were made with the Ultra Low Energy Charge Analyzer (ULECA) sensor of the Max-Planck-Institut/University of Maryland instrument of ISEE-1. The energy spectra of these events are clearly steeper than power low and are generally well described by either an expotential or Maxwellian in energy per charge, with average e folding values of ~20 keV/Q and ~15 keV/Q, respectively. The composition in these events is remarkably constant as a function of energy per change and is similar (within a factor of ~2) to that of the solar wind. The particle flux is found to decay expotentially with distance from the bow shock, with an e folding distance of ~7 REE for H and He at 30 keV/Q. Inverse velocity dispersion was observed in each event, with an average delay time of ~40 min between the 30 keV and 130 keV proton equilibrium intensity levels. Our measurements are consistent with a Fermi acceleration mechanism and the presence of a free escape boundary upstream of the bow shock. Although existing Fermi-escape boundary models differ somewhat in detail, our present analysis is unable to differentiate among them.