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The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transition operator are calculated in momentum representation. Numerical illustrations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-know quasicrystalline approximation. A comparison is made with measured loss tangent in dry snow.