  We calculate matter effects on neutrino oscillations relevant for long
baseline neutrino oscillation experiments. In particular, we compare the
results obtained with simplifying approximations for the density profile in the
Earth versus results obtained with actual density profiles. We study the
dependence of the oscillation signals on both $E/\Delta m^2_{atm.}$ and on the
angles in the leptonic mixing matrix. The results show quantitatively how
matter effects can cause significant changes in the oscillation signals,
relative to vacuum oscillations and can be useful in amplifying these signals
and helping one to obtain measurements of mixing parameters and the magnitude
and sign of $\Delta m^2$.
