On the averaging of induced multipoles in non-conductive linear media withweak spatial dispersion

Linear reciprocal and non-conductive media with weak spatial dispersion are considered. In the recent work the Maxwell Garnett model of averaging of m ultipolar polarizabilities has been developed. The model is based on the Lo renz-Lorentz like relations between the local and averaged fields which has been considered as static ones. In this work one proves the self-consisten cy of these relations with the weak spatial dispersion concept. simultaneou sly, it is proved that the corresponding relations for media with second-or der spatial dispersion depend in the general case on the external field. Th erefore for these media there is no general procedure of evaluation of the medium multipolar susceptibility via the polarizability of its particles (i ndependent on the wave vector).