  Using two new well defined 4-dimensional potential vectors, we formulate the
classical Maxwell's field theory in a form which has manifest Lorentz
covariance and SO(2) duality symmetry in the presence of magnetic sources. We
set up a consistent Lagrangian for the theory. Then from the action principle
we get both Maxwell's equation and the equation of motion of a dyon moving in
the electro-magnetic field.
