  Assuming the seesaw mechanism for hierarchical neutrino masses, we calculate
the heavy neutrino masses under the hypotheses that the mixing in the Dirac
leptonic sector is similar to the quark mixing ($V_D \sim V_{CKM}$) and that
$M_{\nu} \sim M_u$ or $M_e$, where $M_{\nu}$ is the Dirac mass matrix of
neutrinos. As a result we find that for $M_{\nu} \sim M_u$ the vacuum
oscillation solution of the solar neutrino problem leads to a scale for the
heavy neutrino mass well above the unification scale, while for the MSW
solutions there is agreement with this scale. For $M_{\nu} \sim M_e$ the vacuum
solution is consistent with the unification scale, and the MSW solutions with
an intermediate scale. The mass of the lightest heavy neutrino can be as small
as $10^5$ GeV.
