Effective dielectic constant of arrays of elliptical cylinders

We apply the Rayleigh method to derive a formulation yielding the effective dielectric tensor of a periodic composite consisting of an array of elliptical cylinders placed in a matrix of unit dielectric constant. We consider two types of composites having this structure: dilute noncritical and dilute critical. For dilute noncritical composites we comment on our result in relation to the competing forms of the Maxwell-Garnett formula, which have been proposed previously