A method has been developed for calculating resonance effects in nuclear reactor lattices without the two widely used assumptions: 1) that the neutron flux is spatially independent within each region of the lattice cell; 2) that the flux recovers an asymptotic l/E form between resonances. The neutron slowing down problem is formulated in terms of a Boltzmann integral equation, and the correct transport kernel is derived for a Wigner-Seitz equivalent cell with isotropic scattering in the laboratory system. A new method of polynomial approximations is then used to reduce the transport problem to matrix form. The result is a set of integral equations in lethargy for the neutron flux at a number of discrete ordinates. These equations are numerically integrated to obtain the neutron flux as a function of position and energy. Resolved resonance integrals are calculated for a number of 238U-graphite lattices with both metal and oxide rods. Where comparisons are made, the results are in excellent agreement with accurate Monte Carlo calculations. Both the flat flux and flux recovery assumptions are found to cause significant overestimates of the resonance integrals, the errors increasing with the rod radii. The temperature coefficients, however, are less sensitive to these assumptions.