A one-group transport equation is derived from the general Boltzmann equation with the sole assumption that the neutron velocity spectrum is independent of position and direction. It is shown that with this assumption the correct way to define a diffusion constant is to form averages of the scattering crosssection, not the mean free path, over the neutron spectrum. Conclusions are also drawn regarding the equivalence between moderator systems studied with pulsed neutron sources and critical reactors and regarding possible systematic differences in diffusion constants derived from stationary and pulsed source experiments. An accurate equation for the neutron spectrum is derived, and finally other approaches to the problem are discussed briefly.