  We prove that if the frame S is decaying surface non-radiating, in the sense
of Definition 1.1, then if the charge and current are analytic, either they
both vanish, or S is non-radiating, in the sense of a previous paper. In
particularly, by the result there, the charge and current satisfy certain wave
equations in all frames S', connected to S by a real velocity vector, whose
magnitude is less than the speed of light.
