End to the Cosmic-Ray Spectrum?

The primary cosmic-ray spectrum has been measured up to an energy of $10^{20}$ eV, and several groups have described projects under development or in mind to investigate the spectrum further, into the energy range $10^{21}-10^{22}$ eV. This note predicts that above $10^{20}$ eV the primary spectrum will steepen abruptly, and the experiments in preparation will at last observe it to have a cosmologically meaningful termination.