  Accounting for transverse momenta of the quarks, a longitudinal quark spin
asymmetry exists in a transversely polarized nucleon target. The relevant
leading quark distribution $g_{1T}(x,k_T^2)$ can be measured in the
semi-inclusive deep-inelastic scattering. The average $k_T^2$ weighted
distribution function $g^{(1)}_{1T}$ can be obtained directly from the
inclusive measurement of $g_2$.
