  Old models of the scattering of composite systems based on the Glauber model
of multiple diffraction are applied to hadron-nucleus scattering. We obtain an
excellent fit with only two free parameters to the highest energy
hadron-nucleus data available. Because of the quality of the fit and the
simplicity of the model it is argued that it should continue to be reliable up
to the highest cosmic ray energies. Logarithmic extrapolations of proton-proton
and proton-antiproton data are used to calculate the proton-air cross sections
at very high energy. Finally, it is observed that if the exponential behavior
of the proton-antiproton diffraction peak continues into the few TeV energy
range it will violate partial wave unitarity. We propose a simple modification
that will guarantee unitarity throughout the cosmic ray energy region.
