  We present the measurement of two event samples induced by atmospheric
$\nu_\mu$ of average energy $ \bar {E}_\nu \sim 4 GeV$. In the first sample,
the neutrino interacts inside the MACRO detector producing an upward-going muon
leaving the apparatus. The ratio of the number of observed to expected events
is $ 0.57 \pm0.05_{stat} \pm0.06_{syst} \pm0.14_{theor}$ with an angular
distribution similar to that expected from the Bartol atmospheric neutrino
flux. The second is a mixed sample of internally produced downward-going muons
and externally produced upward-going muons stopping inside the detector. These
two subsamples are selected by topological criteria; the lack of timing
information makes it impossible to distinguish stopping from downgoing muons.
The ratio of the number of observed to expected events is $0.71 \pm 0.05_{stat}
\pm0.07_{syst} \pm0.18_{theor}$ . Using the ratio of the two subsamples (for
which most theoretical uncertainties cancel) we can test the pathlength
dependence of the oscillation hypothesis. The probability of agreement with the
no-oscillation hypothesis is 5% .
  The deviations of our observations from the expectations has a preferred
interpretation in terms of $\nu_\mu$ oscillations with maximal mixing and
$\Delta m^2 \sim 10^{-3} \div 10^{-2} eV^2$. These parameters are in agreement
with our results from upward throughgoing muons, induced by $\nu_\mu$ of much
higher energies.
