  We consider a classical model of matter--radiation interaction, in which the
matter is represented by a system of infinitely many dipoles on a
one--dimensional lattice, and the system is dealt with in the so--called dipole
(i.e. linearized) approximation. We prove that there exist normal--mode
solutions of the complete system, so that in particular the dipoles, though
performing accelerated motions, do not radiate energy away. This comes about in
virtue of an exact compensation which we prove to occur, for each dipole,
between the ``radiation reaction force'' and a part of the retarded forces due
to all the other dipoles. This fact corresponds to a certain identity which we
name after Oseen, since it occurs that this researcher did actually propose it,
already in the year 1916. We finally make a connection with a paper of Wheeler
and Feynman on the foundations of electrodynamics. It turns out indeed that the
Oseen identity, which we prove here in a particular model, is in fact a weak
form of a general identity that such authors were assuming as an independent
postulate.
