Continuity equations for transverse multipole amplitudes for both the electromagnetic and the asymptotic gravitational field

Continuity equations are obtained for both kinds of transverse multipole amplitude of the electromagnetic field. The equations relate the time variation of any given transverse multipole amplitude to the outgoing flux of corresponding multipole amplitudes of both the electromagnetic field and the current. This completes a similar result, obtained in a previous paper, concerning the radial multipole amplitudes. The theory allows us to derive, in a straightforward way, the peeling-off theorem for the e.m. field and a set of absolutely conserved quantities, similar to those considered by Newman and Penrose. The results can be extended to the asymptotically linearized gravitational field, generated by an insular source embedded into an asymtotically flat space-time background