A series of experiments has been performed to study the diffusion of thermal neutrons in Al-H2O plate lattices. Although diffusion perpendicular to the plates could be described by an exponential function, thus defining a diffusion length, such was not the case for diffusion parallel to the plates. Various ancillary experiments support the conclusion that a discrete eigenvalue does not exist for parallel diffusion in such systems. This conclusion is in agreement with the theoretical predictions of Clancy, Durance, and McCulloch, and of Williams.