A method is developed for computing thermal neutron distributions in reactor lattices as functions of energy and a single spatial coordinate. The integral form of the transport equation is used and it is assumed that the scattering process is isotropic in the laboratory system. The energy exchange kernels are based on the free gas model of Brown and St. John. The resulting equations are solved by numerical techniques using the IBM 704. The iterative calculations are greatly accelerated by enforcing neutron conservation at each iteration.