  Polarized neutron inelastic scattering experiments have been carried out in
the quasi-1D Ising-like antiferromagnet TlCoCl$_3$. We observed the
longitudinal magnetic fluctuation $S_{zz} (Q, \omega)$ for the spin-wave
excitation continuum, which has not been observed in the unpolarized neutron
inelastic scattering experiments of the quasi-1D Ising-like antiferromagnets
CsCoCl$_3$ and TlCoCl$_3$ so far, together with the transverse magnetic
fluctuation $S_{xx} (Q, \omega)$. We compared both obtained intensities of
$S_{xx} (Q, \omega)$ and $S_{zz} (Q, \omega)$ with the perturbation theory from
the pure Ising limit by Ishimura and Shiba, and a semi-quantitative agreement
was found.
