Cosmic rays are mainly protons. Their energy spectrum decreases with increasing energy. Their interactions with the atmospheric nuclei produce mesons, which give rise, by decaying, to v_μ and v_e. In a sample of N_v =106 v_μs with 1 GeV energy, how many interact in crossing the Earth along its diameter? [Note: σ 7 fb, ρ≈ 5 x10³ kg m^-3, R≈ 6000 km.]