We discuss the atmospheric showers initiated by 1--${10}^{4}$-TeV photons emitted by cosmic accelerators such as Cygnus X-3. The direction and characteristic time structure of the radiation from such sources can be used to tag a beam of known composition (\ensuremath{\gamma} rays) with well-understood interactions (QED) with the target atmosphere. An experiment using a cosmic beam, therefore, overcomes the classic hurdles in interpreting cosmic-ray data. Tagged photon experiments covering a ${(10}^{2}$--${10}^{3}$-m${)}^{2}$ area can conceivably achieve the statistics and signal-to-noise ratio to probe the anticipated new structure in particle physics at a scale of (\ensuremath{\surd}2 ${G}_{F}$${)}^{\mathrm{\ensuremath{-}}1/2}$\ensuremath{\simeq}0.25 TeV. They would at the same time constitute a new generation of telescopes at the highest energies of the emission spectrum. We also extend our discussion of muons to underground experiments in the corresponding energy region.