With a view to a detailed study of heterogeneity effects in lattices, and in particular of the streaming effects introduced by the presence of channels, a project has been undertaken in France for studying graphite lattices by the pulsed source technique. The aim of the project is to obtain experimental data on clean simple systems for testing the methods used in lattice calculations. The project comprises three progressive stages: study of lattices of empty channels, followed by lattices of non-fissile material, and finally by multiplying lattices. This article presents the results obtained in the study of empty-channel lattices. Regarding the theoretical aspects of the project, the expressions involved are somewhat different, depending on whether one is dealing with stationary or with non-stationary systems. The point of view adopted in the theoretical studies presented in this article, as well as in a related article that has appeared in Nuclear Science and Engineering, has been to consider stationary systems as particular cases of non-stationary ones. In the present article, detailed expressions are obtained for non-multiplying lattices, and wherever it was possible without digressing too much from the context, multiplying lattices have also been discussed. In one of the Appendixes in particular, a method is presented for the direct calculation of decay constants in multiplying or non-multiplying lattices, a particular form of which can be used for the calculation of critical bucklings. The main part of the article deals with the axial and the transversal diffusion coefficients in empty-channel lattices. Experiments have been performed on lattices with a square pitch of 20-cm side, the channel radii studied being 1.5, 2.5, 3.5, 4.5, 5.5, and 7 cm. Since the object was to determine if the anisotropy effects introduced in the diffusion coefficients by the cell geometry could be properly interpreted, the theoretical calculations have been limited to one-velocity treatments, which should be adequate for empty-channel systems. The comparison between experiment and theory is quite satisfactory, though some discrepancy is observed with the axial diffusion coefficient in the case of the large channel radii. The experiments indicate, furthermore, that the diffusion cooling coefficients vary very rapidly with channel radius. The theoretical treatment of cooling coefficients in lattices is very complex, and has not been attempted. One section of the article has been devoted to the consideration of extrapolation lengths of empty-channel graphite systems. Approximate analytical calculations as well as a numerical calculation utilizing the TDC code have been presented. They indicate that it is reasonable to consider the extrapolation length as being equal to 0.71 times the cell mean-free-path associated with the direction considered. This expression has been utilized to define the bucklings of the blocks studied. However, a more detailed study of extrapolation lengths would be very useful. The theoretical studies presented are based on the classical approach of expressing the finite medium decay constant as a power series of the buckling. This approach is strictly valid only if the corresponding infinite lattice has an asymptotic decay constant. The conditions necessary for its existence are considered and it is seen that configurations of non-multiplying lattices can very easily be such that the required conditions are not satisfied. A satisfactory treatment of such “singular” cases would require a theoretical approach that treats the finite system directly without calling upon the corresponding infinite one.