  We present a formalism for the matter effects in the Earth on low energy
neutrino fluxes which is both accurate and has all advantages of a full
analytic treatment. The oscillation probabilities are calculated up to second
order term in $\epsilon(x) \equiv 2V(x)E/\Delta m^2$ where $V(x)$ is the
neutrino potential at position $x$. We show the absence of large undamped
phases which makes the expansion in $\epsilon$ well behaved. An improved
expansion is presented in terms of the variation of $V(x)$ around a suitable
mean value which allows to treat energies up to those relevant for Supernova
neutrinos. We discuss also the case of three-neutrino mixing.
