  In this paper I shall construct, in a four-dimensional space, all
vector-tensor field theories that are conformally invariant, consistent with
conservation of charge, and flat space compatible. By the last assumption I
mean that the Lagrangian of the theory in question, is well defined and
differentiable, when evaluated for either a flat metric tensor (and) or
vanishing vector field. Under these assumptions there exists only two classes
of Lagrangians. One is represented by the Lagrangian which yields the Bach
tensor density multiplied by a constant, while the other is represented by a
constant multiple of the usual Lagrangian that yields Maxwell's equations. Thus
under the aforementioned assumptions, the field equation obtained by varying
the vector field, must be Maxwell's.
