The theory of propagation of light through a medium of molecules with induced multipole moments of arbitrary order is studied. Positional and orientational correlations between molecules are neglected. A central result is the generalization of Lorentz's expression for the average local field acting on a molecule to a medium with higher multipole densities of arbitrary spatial variation. This allows one to avoid the Ewald-Oseen extinction theorem in the description of the mutual interference of secondary waves. The theory of optical activity is reformulated with the aid of a local-field tensor.