  New Lagrangians, depending on the field strengths and the electric and
magnetic sources are found, which lead to the Maxwell equations. One new
feature is that the equations of motion are obtained by varying the Lagrangian
with respect to both the field strengths and the sources. In this way,
conserved currents can be found for the field strengths and the electric or
magnetic sources. Furthermore, using the equations of motion, the electric or
magnetic sources can be eliminated, leading to conserved currents for the field
strengths only (in the presence of electric and magnetic sources). Another new
feature is the construction of a Lagrangian invariant under the duality
transformation for both field strengths and electric and magnetic sources. The
conserved current, after the elimination of electric and magnetic sources,
depends on the field strengths only. The conserved quantity is related to the
total helicity of the electromagnetic field.
