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In this paper the Maxwell-Minkowski equations are used to find a general integral for the electromagnetic fields in an infinite moving medium. The medium is assumed to be homogeneous, isotropic, and to move with a constant velocity much less than the speed of light. Only time-harmonic fields are considered. A wave equation for the electric field is derived and is integrated by means of a Green's Identity and an appropriately defined Dyadic Green's Function. The result gives the electric field inside a volume of space in terms of known sources in the volume and the tangential components of the electric and magnetic fields over the enclosing surface. Finally, the fields radiated by a point dipole are found.