The critical parameters of coupled, fissionable assemblies in close proximity to one another are studied by differential equations for the conservation of neutrons. The coupling between the assemblies is taken into account by the use of approximate boundary conditions derived from expressions for the average neutron flow between the assemblies. Critical equations are found from the one and two group diffusion theories and from the P3 approximation/The results are compared with existing experimental data. The present methods are especially suited to the study of arrays of prisms.