  We investigate the possible influence of the MSW effect on the expectations
for the solar neutrino experiments in the maximal mixing scenario suggested by
the atmospheric neutrino data. A direct numerical calculation of matter induced
effects in the Sun shows that the naive vacuum predictions are left completely
undisturbed in the particular case of maximal mixing, so that the MSW effect
turns out to be unobservable. We give a qualitative explanation of this result.
