  We discuss the possibility for matter effects in the three-neutrino
oscillations of the atmospheric nu_e (bar{nu}_e) and nu_mu (bar{nu}_mu), driven
by one neutrino mass squared difference, |Delta m2_{31}| >> Delta m2_{21}, to
be observable under appropriate conditions. We derive predictions for the Nadir
angle (theta_n) dependence of the ratio N_mu/N_e of the rates of the mu-like
and e-like multi-GeV events which is particularly sensitive to the Earth matter
effects in the atmospheric neutrino oscillations, and thus to the values of
sin2{theta_{13}} and sin2{theta_{23}}, and also to the type of neutrino mass
spectrum.
