A new measurement of the momentum spectra of both positive and negative muons as function of atmospheric depth was made by the balloon-borne experiment CAPRICE94. The data were collected during ground runs in Lynn Lake on the 19-20th of July 1994 and during the balloon flight on the 8-9th of August 1994. We present results that cover the momentum intervals 0.3-40 GeV/c for negative muons and 0.3-2 GeV/c for positive muons, for atmospheric depths from 3.3 to 1000 g/cm**2, respectively. Good agreement is found with previous measurements for high momenta, while at momenta below 1 GeV/c we find latitude dependent geomagnetic effects. These measurements are important cross-checks for the simulations carried out to calculate the atmospheric neutrino fluxes and to understand the observed atmospheric neutrino anomaly.
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