Near the trapping boundary at local midnight the ratio of precipitating to trapped fluxes of electrons (0.16–2.4 MeV) and of protons (0.04–0.95 MeV) observed at low satellite altitudes (∼750 km) is a strong function of both particle energy and L value. On a particular L shell, isotropy is often observed for particles above a given energy, whereas below that energy the precipitating fluxes are much lower than the trapped fluxes. The onset of isotropy typically occurs at a sharply defined energy threshold which decreases rapidly with increasing L value. The occurrences of isotropy for electrons and protons together show a consistent variation with L when they are considered in terms of magnetic rigidity. For the onset of isotropy the equivalent gyroradius at the equator of particles with the same energy and a 90° pitch angle spans the range ∼5 km to ∼500 km and varies approximately as (LL0 — 0.1)1.8, where L0 is the L shell at which isotropy occurs for electrons with an equatorial gyroradius of 10 km. The observed magnetic rigidity thresholds for isotropy may provide a measure of the effective scale length of the inhomogeneities of the geomagnetic field.