  We calculate matter effects on neutrino oscillations relevant for long
baseline experiments. In particular, we compare the results obtained with
constant density along the neutrino path versus results obtained by
incorporating the actual density profiles in the Earth. We study the dependence
of the oscillation signal on both $E/\Delta m^2_{atm}$ and on the angles in the
leptonic mixing matrix. We also comment on the influence of $\Delta m^2_{sol}$
on the oscillations. The results show quantitatively how, as a function of
these input parameters, matter effects can cause significant (25 %) changes in
the oscillation probabilities. An important conclusion is that matter effects
can be useful in amplifying certain neutrino oscillation signals and helping
one to obtain measurements of mixing parameters and the magnitude and sign of
$\Delta m^2_{atm}$.
