  The neutrinos of long baseline beams travel inside the Earth's crust where
the density is approximately rho = 2.8 g cm^-3. If electron neutrinos
participate in the oscillations, matter effects will modify the oscillation
probabilities with respect to the vacuum case. Depending on the sign of Delta
m^2 an MSW resonance will exist for neutrinos or anti-neutrinos with energy
approximately E_nu(res) = 4.7 |\Delta m^2|/(10^-3 eV^2) GeV. For Delta m^2 in
the interval indicated by the Super-Kamiokande experiment this energy range is
important for the proposed long baseline experiments.
  For positive Delta m^2 the most important effects of matter are a 9% (25%)
enhancement of the transition probability P(nu_mu -> nu_e) for the KEK to
Kamioka (Fermilab to Minos and CERN to Gran Sasso) beam(s) in the energy region
where the probability has its first maximum, and an approximately equal
suppression of P(antinu_mu -> antinu_e). For negative Delta m^2 the effects for
neutrinos and anti-neutrinos are interchanged. Producing beams of neutrinos and
antineutrinos and measuring the oscillation probabilities for both (nu_mu ->
nu_e) and (antinu_mu -> antinu_e) transitions can solve the sign ambiguity in
the determination of Delta m^2.
