We study the effective dielectric tensor for a composite of spheres with anisotropic dielectric tensor embedded in an isotropic uniform medium. We also study the effective conductivity tensor for a suspension of conducting spheres, where both the spheres and the conducting background medium are gyro- tropic due to an applied magnetic field. The anisotropy of the effective conductivity tensor leads to the Hall effect. In theory the two problems are rather similar. We derive expressions of the Clausius-Mossotti type for the effective tensors. Correlation corrections are evaluated for weak gyrotropy by computer simulation. We consider both uniform spheres and the dipole approximation.