  The neutrino mass hierarchy, presently unknown, is a powerful discriminator
among various classes of unification theories. We show that the $\nu_{\mu} +
\bar{\nu}_\mu$ survival rate in atmospheric events can provide a novel method
of determining the hierarchy in megaton water Cerenkov detectors. For
pathlength and energy ranges relevant to atmospheric neutrinos,this rate
obtains significant matter sensitive variations not only from resonant matter
effects in $P_{\mu e}$ but also from those in $P_{\mu\tau}$. We calculate the
expected muon event rates in the case of matter oscillations with both natural
and inverted hierarchy.We identify the energy and pathlength ranges for which
resonant matter effects can lead to observable differences between the above
two cases. We also estimate the exposure time required to observe this
difference and determine the sign of $\Delta_{31}$ in a statistically
significant manner.
