The fluxes of trapped and precipitating particles are often near equal at the trapping boundary in the radiation belts at low satellite altitudes. Near midnight this isotropy phenomenon was previously discovered frequently to occur only above an energy threshold which decreases rapidly with increasing L value. Now, much finer energy resolution measurements of the phenomenon for electrons have been performed with much lower backgrounds and higher sampling rates, and hence better statistical accuracies in the energy spectra. Here we present details on the strong dependence of the measured ratios of precipitating to trapped electrons on the gyroradius of the particles. Published theoretical calculations for the L dependences of the magnetic rigidity of the onset of isotropy for both electrons and protons near midnight are compared with the present measurements under both very quiet and very disturbed magnetic activity conditions. The measured curves are generally steeper than the theoretical ones except for a few at very disturbed times when reasonable agreement is achieved. The frequency of occurrence of an energy selective threshold for isotropy at the trapping boundary is presented as a function of magnetic local time; it was observed on 34% of the passes near midnight and seldom near noon. ¿ American Geophysical Union 1988