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The atmospheric neutrino flux is measured using a 3.4-ktyr exposure of the IMB-3 detector. Singlering events are classified as showering or nonshowering using the geometry of the Cerenkov pattern. A simulation of neutrino interactions and three models of atmospheric neutrino production are used to predict the composition of the sample. Showering-nonshowering character is strongly correlated with the flavor of the neutrino parent. In the lepton momentum range p < 1500 MeV/c, we find that nonshowering events comprise [41 ± 3(stat) ± 2(syst)]% of the total. The fraction expected is [51 ± 5(syst)]%.PACS numbers: 96.40.Tv, 95.85.Qx Cosmic-ray interactions in the atmosphere produce broad and nearly isotropic spectra of v e and v M which may be observed by massive detectors. The flight paths of these neutrinos range from roughly 20 to 12000 km; using this long base line, atmospheric neutrino propagation may be studied over much greater distances than neutrinos produced in the laboratory. Using the ringimaging ability of the IMB-3 detector to separate events induced by v e and v M , the neutrino flavor content at the detector can be compared to calculated production rates in the atmosphere. Any discrepancy may point to new physics of flavor oscillation or decay in a region inaccessible to present accelerator and reactor experiments, but hinted at by our earlier data' and strongly suggested by a similar experiment. 2 The IMB-3 detector, 3 " 7 with a 3.3-kt fiducial mass and 2048 8-in. photomultiplier tubes (PMTs) augmented with wavelength-shifting plates, has operated since May 1986. Relativistic-charged-particle tracks are detected via Cerenkov radiation, and reconstructed using timing and pulse-height information from the PMTs. A 7.5-jus time scale after the primary trigger allows detection of muon decays with 70% efficiency. The pulse-height measurements, corrected for light attenuation in water, are also used to determine the "visible energy" of each event. Visible ^nergy is defined to be proportional to the number of Cerenkov photons radiated, and equal to the primary particle energy for e -and y. Visible-energy resolution is 3% LEvisCGeV)] 1/2 , with an additional systematic uncertainty of ± 7%.A live time of 376 d has been analyzed to find events originating within the fiducial volume, characteristic of either nucleon decay or neutrino interaction. Triggers resulting from prompt firing of 70-900 PMTs, corresponding to visible energies of 50 MeV to 2.5 GeV, form the initial sample for this search. Data and calibrations are independently analyzed by two groups, and the results are merged into a combined data set. The combined efficiency for extracting events starting in the fiducial volume is approximately 85% for events with over 100-MeV visible energy. A total of 422 contained events were identified. The spatial distribution of these events is roughly uniform over the fiducial volume, as expected for nucleon decays or atmospheric-neutrino-induced events. The distribution of events with identified muon decays is ...