We describe a theory of electrophoresis of ideally polarizable, charged spherical mercury drops in aqueous electrolyte, which is based on the work of Henry, Overbeek and Booth. This is compared with the theory of Frumkin and Levich, who make use of the Lippmann equation, and also of a boundary condition of charge conservation which involves a surface divergence of the tangential current density. It is shown that this conservation condition may be derived from three-dimensional continuity equations of ion flow in the theory of Overbeek and Booth, provided κa ⪢ 1, where a is the drop radius and 1 κ the diffuse layer thickness. Our electrical terms in the conditions of continuity in tangential and normal stresses across the mercury-aqueous solution interface differ from those of Frumkin and Levich. In place of the Lippmann equation, we adopt Booth's use of the Maxwell electrostatic stress tensor. A key step in our theory is the introduction of a polarization term in the potential distribution, which is analogous to the relaxation term for dielectric particles. It is shown that this term implies a significant departure from superposition of the equilibrium electric field and applied field, resulting in a considerable displacement in the surface charge density on the mercury drop. A consequence is a large electrical force acting on the mercury drop, which is the driving force responsible for an electrophoretic mobility, exceeding that on a dielectric particle by orders of magnitudes. Thus the polarization term dominates the magnitude of this mobility. Our theory becomes identical with that of Frumkin and Levich in the limiting case where κa ⪢ 1 and surface potentials are in the Debye-Huckel range.