The interaction of high-energy muon neutrinos produced in the atmosphere by primary cosmic rays has been observed deep underground (8.74×${10}^5$ g ${\mathrm{cm}}^{-2\mathrm{}}$ std. rock) in the rock surrounding a large-area (160 ${\mathrm{m}}^2$) liquid-scintillation-detector hodoscope. A series of arguments is given to separate the residual atmospheric muons which reached the detector from those produced by neutrino interactions in the surrounding rock. These arguments are based on the widely differing angular distributions and mean energies of the two sources. The observation of four events arising from the decay of muons stopping in the detector suggests that the energy of neutrino-induced muons is ∼½ GeV. Operation of the system over a three-year period yielded a total of 39 which we identify as neutrino-produced muons. Of these, 35 were in the aperture chosen for the observation of neutrino-induced muons, yielding a total rate of (6.5±1.1)×${10}^{-7\mathrm{}}$ ${\sec }^{-1\mathrm{}}$. In a companion paper, this result is compared with rates predicted using various theoretical models of the neutrino-nucleon interaction. This comparison selects the most appropriate model and leads to an underground neutrino-induced muon flux. In the present paper the simplifying approximation of an isotropic neutrino distribution leads directly to a flux of (3.7±0.6)×${10}^{-13\mathrm{}}$ ${\mathrm{cm}}^{-2\mathrm{}}$ ${\sec }^{-1\mathrm{}}$ ${\mathrm{sr}}^{-1\mathrm{}}$.

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