  Recently it is advocated that high intensity and low energy $(E_\nu \sim 2
GeV)$ neutrino beams should be built to probe the $(13)$ mixing angle $\phi$ to
a level of a few parts in $10^4$. Experiments using such beams will have better
signal to background ratio in searches for $\nu_\mu \to \nu_e$ oscillations. We
propose that such experiments can also determine the sign of $\Delta_{31}$ even
if the beam consists of {\it neutrinos} only. By measuring the $\nu_\mu \to
\nu_e$ transitions in two different energy ranges, the effects due to
propagation of neutrinos through earth's crust can be isolated and the sign of
$\Delta_{31}$ can be determined. If the sensitivity of an experiment to $\phi$
is $\epsilon$, then the same experiment is automatically sensitive to matter
effects and the sign of $\Delta_{31}$ for values of $\phi \geq 2 \epsilon$.
