  A modified version of the double potential formalism for the electrodynamics
of dyons is constructed. Besides the two vector potentials, this manifestly
duality invariant formulation involves four additional potentials, scalar
potentials which appear as Lagrange multipliers for the electric and magnetic
Gauss constraints and potentials for the longitudinal electric and magnetic
fields. In this framework, a static dyon appears as a Coulomb-like solution
without string singularities. Dirac strings are needed only for the Lorentz
force law, not for Maxwell's equations. The magnetic charge no longer appears
as a topological conservation law but as a surface integral on a par with
electric charge. The theory is generalized to curved space. As in flat space,
the string singularities of dyonic black holes are resolved. As a consequence
all singularities are protected by the horizon and the thermodynamics is shown
to follow from standard arguments in the grand canonical ensemble.
