  Temperature- and field-dependent measurements of the Hall effect of pure and
4 % Rh-doped URu$_{2}$Si$_{2}$ reveal low density (0.03 hole/U) high mobility
carriers to be unique to the `hidden order' phase and consistent with an
itinerant density-wave order parameter. The Fermi surface undergoes a series of
abrupt changes as the magnetic field is increased. When combined with existing
de Haas-van Alphen data, the Hall data expose a strong interplay between the
stability of the `hidden order,' the degree of polarization of the Fermi liquid
and the Fermi surface topology.
