  A first empirical extraction of the transversity distributions for the $u$-
and $d$-quarks has been done by Anselmino {\it et al.} based on the combined
global analysis of the measured azimuthal asymmetries in semi-inclusive deep
inelastic scatterings and those in $e^+ e^- \to h_1 h_2 X$ processes. Although
with large uncertainties, the determined transversity distributions already
appear to reveal a remarkable qualitative difference with the corresponding
longitudinally polarized distributions. We point out that this difference
contains very important information on internal spin structure of the nucleon.
