In the theory described in this paper, the lattice of a critical or subcritical system is represented by an array of finite cylindrical elements, arbitrarily distributed throughout a cylindrical volume of moderator. The flux in each element is determined from multigroup PN theory, whose asymptotic part in the moderator, i.e., that part of the flux which survives in the moderator at distances of a few mean-free-paths from the element, can readily be identified. The PN-corrected multigroup diffusion equation is solved in the moderator, taking full account of lattice geometry. It is then connected to the asymptotic part of the interior PN solution across each individual element-to-moderator interface. Thus the physical requirement that the angular neutron distribution be continuous across all interfaces is satisfied throughout the lattice. A similar approach is employed to make the distribution continuous across the moderator-to-reflector boundary. The theory yields, as do all heterogeneous theories, a neutron spectrum which changes continuously, both radially and azimuthally, across the lattice. The method is consistent in that it determines fuel characteristics in accordance with this changing spectrum without the need for defining cells or extrapolation lengths.