Properties of two-phase ``cell materials''

``Symmetric cell materials'' and ``asymmetric cell materials'' were defined by Miller in connection with the physical properties (such as the effective dielectric constant) of two-phase solid mixtures. It is shown here that while the ``symmetric cell material'' is self-consistent, the ``asymmetric cell material'' is not: The postulated three-point probabilities do not add up to the correct one-point probabilities. A self-consistent generalization of the ``symmetric cell material'', based on the requirement that a certain integral must reduce to an integral over a finite region, is developed, and one construction procedure for producing such a material is described.