New Measurements from the energetic ion composition spectrometer on the Dynamics Explorer 1 satellite reveal the existence of hybrid conical distributions which are interpreted as the first direct observation of a two-stage acceleration of ionospheric ions. The ions display characteristics of having experienced both transverse and parallel acceleration in the process of being injected into the magnetosphere. This signature consists of field alignment of the ions at energies just above a lower energy cutoff below which no fluxes are measured. At increasing energy the field-aligned distribution gradually becomes a conical one whose apex angle widens with increasing energy. The lower energy cutoff gradually increases and then decreases as the satellite moves in latitude in a manner like that found in ion inverted V's. In one case analyzed in detail transversely accelerated oxygen ions having energies to 5 keV were observed while the lower energy ions were primarily field-aligned between 430 and 870 eV. It is concluded that ions were accelerated from the ionospheic plasma by a mechanism acting primarily transverse to the geomagnetic field at an altitude near 18,000 km and additionally accelerated through a parallel potential that exceeded 300 volts in the core of the inverted V. The heating mechanism produced a bi-Maxwellian distribution of oxygen ions with transverse and parallel temperatures of ~1.2 keV and ~260 eV, respectively. The deduced O+ density was on the order of 0.5 cm-3 in the source.