We calculate matter effects on neutrino oscillations relevant for long base
line experiments. In particular, we compare the results obtained with const
ant density along the neutrino path versus results obtained by incorporatin
g the actual density profiles in the Earth. We study the dependence of the
oscillation signal on both E/Delta m(atm)(2) and on the angles in the lepto
nic mixing matrix. We also comment on the influence of Delta m(sol)(2) and
CP violation 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 t
hat matter effects can be useful in amplifying certain neutrino oscillation
signals and helping one to obtain measurements of mixing parameters and th
e magnitude and sign of Delta m(atm)(2).