A perturbation calculation of optical frequency polarization quadratic in the Maxwell field is made for a dielectric in which the electrons are localized on units of the crystal. The result is expressed in a power series in Kr∼10-3 where r is the size of the unit and K is the wave number of the field. The term of zeroth order is the electric-dipole term which vanishes in a crystal with a center of symmetry. The term first order in Kr is separated into electric-quadrupole and magnetic-dipole contributions by introducing a special gauge for the electromagnetic potentials. Higher power terms are neglected. © 1964 The American Physical Society.