  In the framework of Einstein-Maxwell theory, we consider collinear arrays of
rotating electrically charged black holes connected by Misner-Dirac strings
carrying gravimagnetic and magnetic fluxes. The first law of mechanics for
these systems is derived. It involves as dynamical variables the areas, angular
momenta and electric charges of the various Killing horizons -- black holes and
Misner strings. When the gravimagnetic fluxes all vanish, the first law reduces
to a form where the dynamical variables associated with the strings are the
string tensions and magnetic fluxes. This form is not generically invariant
under electric-magnetic duality.
