Muon neutrinos produced as a result of cosmic-ray interactions with the atmosphere are used to search for ${\nu }_{\mathrm{\mu }}$ oscillations into ${\nu }_{\mathrm{\tau }}$ by comparing the measured rate of upward-going muons in the Irvine-Michigan-Brookhaven detector with the expected rate. In addition, the ratio of upward-going muons which stop in the detector to those which exist is used to search for deviations from the expected energy spectrum. This latter technique is free of flux and cross-section normalization uncertainties. No evidence for oscillations is found. 90% C.L. limits on δ${\mathit{m}}^2$ are derived in the range (1–2)×${10}^{\mathrm{-}4}$ ${\mathrm{eV}}^2$ for ${\sin }^2$2θ>0.5.

• Received 23 March 1992

DOI:https://doi.org/10.1103/PhysRevLett.69.1010