Electromagnetic radiation recoil of a system of N-charged particles

We give the radiation of an N-charged particles system associated with the succeeding terms in the expansion in the inverse powers of the velocity of light of the four vector force on the material system in a slow motion. We investigate the conditions under which the N-charged particles system may recoil while emitting electromagnetic radiation. Furthermore, the lowest-order secular effects in the radiation arise from dipole and quadrupole exactly as it is expected from the classical theory. (orig.)