The Lockheed high-energy particle spectrometer on the SCATHA satellite, P78-2, occasionally measures energetic electron fluxes near synchronous altitude that exceed the commonly cited Kennel and Petschek trapping limit. Twelve cases have been analyzed in detail, including several from relatively quiet times and from times when the spectrum became very hard. These were compared with an energy-dependent formulation of the trapping limit (Schulz and Davidson, this issue), which predicts a steeply descending spectrum above the minimum resonant energy for wave growth, and a 1/E spectrum at high energies. The spectrometer permits pitch angle resolution fine enough to resolve the loss cone and to derive the anisotropies that were needed to make the comparisons with the theory. In all the cases examined, over a wider range of conditions, there is a region of the spectrum, often less than a decade wide in energy, that matches the theoretical spectrum. The plasma densities derived from the fitting of ideal theoretical spectra to the measured spectra were compared with ion densities determined from the University of California, San Diego, ion spectrometer aboard the SCATHA satellite. The agreement between the two independent determinations of the plasma density supports an interpretation of the energetic electron spectra based on the occurrence of flux limiting during the events analyzed. It is concluded that flux limiting may be active much of the time over some portion of the electron spectrum, and that the overall spectrum exhibits greater variability than can be simply explained by steady state flux limiting alone. The results are consistent with a model in which the limiting process takes place in sporadic precipitation events, punctuated by intervals of weak diffusion. Numerical estimates of the energy-integrated flux above the minimum resonant energy agree well with the Kennel and Petschek prediction. A new empirical energy-integrated flux limit of I*≈2¿1011/L4 electrons cm-2 s-1 is suggested.