  It has recently been predicted that certain magnetic materials contain mobile
magnetic charges or `monopoles'. Here we address the question of whether these
magnetic charges and their associated currents (`magnetricity') can be directly
measured in experiment, without recourse to any material-specific theory. By
mapping the problem onto Onsager's theory of weak electrolytes, we show that
this is possible, and devise an appropriate method. Then, using muon spin
rotation as a convenient local probe, we apply the method to a real material:
the spin ice Dy2Ti2O7. Our experimental measurements prove that magnetic
charges exist in this material, interact via a Coulomb interaction, and have
measurable currents. We further characterise deviations from Ohm's Law, and
determine the elementary unit of magnetic charge to be 5 muB per Angstrom,
which is equal to that predicted by Castelnovo, Moessner and Sondhi using the
microscopic theory of spin ice. Our demonstration of magnetic charge transport
has both conceptual and technological implications.
