  The quark helicity measured in polarized deep inelastic scattering is
different from the quark spin in the rest frame of the nucleon. We point out
that the quark spin distributions $\Delta q_{RF}(x)$ are connected with the
quark helicity distributions $\Delta q(x)$ and the quark transversity
distributions $\delta q(x)$ by an approximate relation: $\Delta q_{RF}(x) +
\Delta q(x)=2 \delta q(x)$. This relation will be useful in order to measure
the rest frame (or quark model) spin distributions of the nucleon once the
quark helicity distributions and quark transversity distributions are
themselves measured. We also calculate the $x$-dependent quark transversity
distributions $\delta q(x)$ and quark spin distributions $\Delta q_{RF}(x)$ in
a light-cone SU(6) quark-spectator model, and present discussions on possible
effect from the sea quark-antiquark pairs.
