Gyroresonance and Landau resonance interactions between unducted low-frequency whistler waves and trapped electrons in the earth's plasmasphere have been studied. Ray paths for waves launched near the plasmapause have been traced. In agreement with recent findings by Thorne et al. (1979), we have found waves which return through the equatorial zone with field-aligned wave normal angles. However, when the growth along the ray path is calculated for such waves, assuming an electron distribution function of the form E-n sinm &agr;, we find that for all the waves considered, the local growth rate becomes negative before plasmapause reflection, limiting the total gain to small values. Most waves reach zero gain before reflection. This is the result of Landau damping at oblique propagating angles, which necessarily occurs before reflection can take place. We conclude that the concept of cyclic ray paths does not provide an explanation for the generation of unguided plasmaspheric hiss.