An experiment to measure the cross section for high-energy cosmic-ray protons and neutrons to interact with the Fe nucleus has been carried out at 3250 m elevation. The detector had a relatively good energy resolution, and was designed to select nucleons in the vicinity of 50 Bev. The purpose was to obtain a single interaction cross section with good accuracy in order to compare it with results obtained with accelerators in the 1- to 5-Bev region. This comparison yields a value for the elementary meson-production cross section [the average of σ(pp) and σ(np)] near 50 Bev. The Fe results are: neutrons, σFe=0.61+/-0.03 barn; protons, σFe=0.61+/-0.04 barn. The corresponding average nucleon-nucleon "inelastic" (presumably meson production) cross section is σnucleon=21+/-4 millibarns.