  We use the high energy predictions of a QCD-inspired parameterization of all
accelerator data on forward proton-proton and antiproton-proton scattering
amplitudes, along with Glauber theory, to predict proton-air cross sections at
energies near \sqrt s \approx 30 TeV. The parameterization of the proton-proton
cross section incorporates analyticity and unitarity, and demands that the
asymptotic proton is a black disk of soft partons. By comparing with the p-air
cosmic ray measurements, our analysis results in a constraint on the inclusive
particle production cross section.
