2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/87890In the previous paper we proved that the Evans-Vigier definitions of B^{(0)} and {\bf B}^{(3)} may be related {\it not} with magnetic fields but with a 4-vector field. In the present {\it Addendum} it is shown that the terms used in the {\bf B}- Cyclic theorem proposed by M. Evans and J.-P. Vigier may have various transformation properties with respect to Lorentz transformations. The fact whether the {\bf B}^{(3)} field is a part of a bi-vector (which is equivalent to antisymmetric second-rank tensor) or a part of a 4-vector, depends on the phase factors in the definition of positive- and negative- frequency solutions of the ({\bf B}, {\bf E}) transverse field. This is closely connected to our considerations of the Bargmann-Wightman-Wigner (Gelfand-Tsetlin-Sokolik) Constructs and with the Ahluwalia's recent consideration of the phase factor related to gravity. The physical relevance of proposed constructs is discussed.ReVTeX file, 5pp., no figures, see also physics/9611009Classical PhysicsGeneral Physicstext