  We show that matter effects change the ${\rm {\nu_\mu \to \nu_\tau}}$
oscillation probability by as much as 70% for certain ranges of energies and
pathlengths. Consequently, the ${\rm {\nu_\mu \to \nu_\mu}}$ survival
probability also undergoes large changes. A proper understanding of $\nu_\mu$
survival rates must consider matter effects in $P_{\mu \tau}$ as well as
$P_{\mu e}$. We comment on a) how these matter effects may be observed and the
sign of $\Delta_{31}$ determined in atmospheric neutrino measurements and at
neutrino factories and b) how they lead to heightened sensitivity for small
$\theta_{13}$.
