We have measured the distribution in angle and velocity of the prompt neutrons from the bremsstrahlung-induced photofission of ${\mathrm{Th}}^{232}$ in the photon energy region near threshold. Using knowledge of the fission-fragment angular distribution, the data have been interpreted in terms of the neutron distribution relative to the fragment axis. The measurement allows a quantitative estimate of the fraction of neutrons which are not emitted by fully accelerated fragments. The result for this fraction is 0.07\ifmmode\pm\else\textpm\fi{}0.09. Assuming isotropic neutron emission in the fragment center-of-mass frame, the analysis also determines some characteristics of the neutron energy spectrum in this frame. The spectrum has an average energy $\overline{\ensuremath{\eta}}=1.14\ifmmode\pm\else\textpm\fi{}0.06$ MeV and a second central moment ${\ensuremath{\sigma}}^{2}(\ensuremath{\eta})=(0.77\ifmmode\pm\else\textpm\fi{}0.06){\overline{\ensuremath{\eta}}}^{2}$. If it is represented by an evaporation-type spectrum with some distribution of temperatures, there is no significant contribution from temperatures equal to or greater than $\overline{\ensuremath{\eta}}$. We have made a similar analysis of data on prompt neutrons from the spontaneous fission of ${\mathrm{Cf}}^{252}$ obtained by Bowman, Thompson, Milton, and Swiatecki, and compared the results with those for ${\mathrm{Th}}^{232}$ photofission.