  A study of photofission of $^{232}$Th and $^{238}$U was performed using
quasi-monoenergetic, linearly-polarized $\gamma$-ray beams from the High
Intensity $\gamma$-ray Source at Triangle Universities Nuclear Laboratory. The
prompt photofission neutron polarization asymmetries, neutron multiplicities
and the photofission cross sections were measured in the near-barrier energy
range of 4.3-6.0 MeV. This data set constitutes the lowest energy measurements
of those observables to date using quasi-monoenergetic photons. Large
polarization asymmetries are observed in both nuclei, consistent with the E1
excitation as observed by another measurement of this kind made in a higher
energy range. Previous experimental evidence of a deep third minimum in the
$^{238}$U fission barrier has been identified as an accelerator-induced
background.
