Neutron emission in the fissioning<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Er</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>158</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>composite system

We have measured the spectra and angular distribution of neutrons emitted in coincidence with fission fragments in the following reactions: $^{16}$O${+\mathrm{}}^{142}$Nd (${E}_{\mathrm{beam}=207}$ MeV), $^{24}\mathrm{Ba}$ (180 MeV), $^{32}\mathrm{Te}$ (180 MeV), and $^{50}\mathrm{Pd}$ (216 MeV). We decompose neutron emission into components resulting from nonequilibrium emission, emission from the compound system, and emission from the fission fragments. We find that statistical model calculations tend to underestimate the number of neutrons evaporated prior to fission. Incorporating the effects of (1) the finite time until equilibrium fission probability is attained at the saddle point, (2) correction to the Bohr-Wheeler formalism due to nuclear viscosity, and (3) neutron emission during the descent from saddle to scission, improves the agreement with the experimental data. The value of the reduced nuclear dissipation coefficient \ensuremath{\beta} that is consistent with our data is approximately 6\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$, within the framework of the model we have used.