Did Maxwell know about the percolation threshold? (on the fiftieth anniversary of percolation theory)

A new approximation obtained in terms of the Maxwell approach is proposed for the effective conductivity of a macroscopically disordered medium. In contrast to the standard Maxwell approximation, this approximation is valid over a much wider concentration range and can qualitatively describe the presence of the percolation threshold. The relation of the proposed approximation to the Pade approximant of the standard Maxwell approximation is also discussed.