The precipitation of energetic electrons which are commonly observed in the drift loss cone east of 60¿ east longitude between L~1.6 and L~1.8 can be accounted for by a Doppler-shifted cyclotron resonance between the electrons and nonducted whistler mode waves from high-power, ground-based VLF transmitters. A ray-tracing analysis using a diffusive-equilibrium model shows that 17.1-kHz waves starting with vertical wave normals between 23¿ and 31¿ magnetic latitude cross the magnetic equator between L~1.6 and f L~1.8 with wave normals of approximately 63¿. A relativistic cyclotron-resonance analysis for the same model plasmasphere using the ray-tracing results gives an energy versus L shell dependence for the precipitated ray electron which is in excellent agreement with the observed dependence. The primary VLF transmitter is most probably the UMS transmitter located near Gorki, USSR. It transmits on 17.1 kHz. VLF records covering this frequency band were available for only three of the time periods when electrons were observed. In two cases UMS was transmitting at the time required to account for the observations. In the third case a higher frequency is required to fit the data. At the time, the NWC transmitter at North West Cape, Australia was operating at 22.3 kHz. These data are consistent with a model in which weak pitch angle scattering by whistler mode waves from NWC does not completely fill the drift loss cone at the longitude of NWC.