A measurement of the primary spectrum of the cosmic radiation in the energy range of 5·1011 eV to ∼5·1015 eV has been made, employing the detection of atmospheric Cerenkov-light pulses produced in extensive air showers. Through the use of an all linear system and an extensive series of calibration, the uncertainties of previous measurements have been removed. The relation between the Cerenkov pulseheight spectrum and the primary cosmic-ray spectrum was investigated through the use of Monte Carlo air shower simulations designed specifically for interpretation of the results of this experiment, covering primary energies from 1011 eV to 1013 eV. These indicate that, due to large fluctuations in shower development, the technique is relatively insensitive to the spectrum of primaries at energies of 1011 eV to 1013 eV. The simulations also indicate a decrease in the importance of fluctuations with increasing primary energy. The measured spectral index shows an increase at ∼1.5·1015 eV. The physical implications of this bending are discussed.