  We have measured the cosmic ray spectrum at energies above $10^{17}$ eV using
the two air fluorescence detectors of the High Resolution Fly's Eye experiment
operating in monocular mode. We describe the detector, PMT and atmospheric
calibrations, and the analysis techniques for the two detectors. We fit the
spectrum to models describing galactic and extragalactic sources. Our measured
spectrum gives an observation of a feature known as the ``ankle'' near $3\times
10^{18}$ eV, and strong evidence for a suppression near $6\times 10^{19}$ eV.
