  We solve the linearized Einstein equations for a specific oscillating mass
distribution and discuss the usual counterarguments against the existence of
observable gravitational retardations in the "near zone", where d/r << 1 (d =
oscillation amplitude of the source, r = distance from the source). We show
that they do not apply in the region d/r \approx 1, and prove that
gravitational forces are retarded in the immediate vicinity of the source. An
experiment to measure this retardation is proposed, which may provide the first
direct experimental observation of propagating gravitational fields.
