  Recently a new method for determining the neutrino mass hierarchy by
comparing the effective values of the atmospheric \Delta m^2 measured in the
electron neutrino disappearance channel, \Delta m^2(ee), with the one measured
in the muon neutrino disappearance channel, \Delta m^2(\mu \mu), was proposed.
If \Delta m^2(ee) is larger (smaller) than \Delta m^2(\mu \mu) the hierarchy is
of the normal (inverted) type. We re-examine this proposition in the light of
two very high precision measurements: \Delta m^2(\mu \mu) that may be
accomplished by the phase II of the Tokai-to-Kamioka (T2K) experiment, for
example, and \Delta m^2(ee) that can be envisaged using the novel Mossbauer
enhanced resonant \bar\nu_e absorption technique. Under optimistic assumptions
for the systematic uncertainties of both measurements, we estimate the
parameter region of (\theta_13, \delta) in which the mass hierarchy can be
determined. If \theta_13 is relatively large, sin^2 2\theta_13 \gsim 0.05, and
both of \Delta m^2(ee) and \Delta m^2(\mu \mu) can be measured with the
precision of \sim 0.5 % it is possible to determine the neutrino mass hierarchy
at > 95% CL for 0.3 \pi \lsim \delta \lsim 1.7 \pi for the current best fit
values of all the other oscillation parameters.
