Acceleration is invariant under the Galilean transformations, which implies that a system moving at a nonzero constant velocity doesn't undergo acceleration it isn't already subject to when it is at rest. However a charged particle moving at a nonzero constant velocity in a static magnetic field undergoes acceleration it isn't subject to when it is at rest in that field (Faraday's Law or the Lorentz Force Law), and the needle of a magnetic compass moving at a nonzero constant velocity in a static electric field undergoes deflection it isn't subject to when it is at rest in that field (Maxwell's Law). The Galilean transformations therefore conflict with electrodynamics, and must be modified. Einstein obtained the modified Galilean transformations via postulating that the speed of light in empty space is fixed at the value c, which in fact is a consequence of electrodynamics rather than a postulate. Here we instead read off the space part of a modified constant-velocity Galilean transformation from the four-potential of a point charge moving at that constant velocity; its time part then follows from its space part plus either relativistic reciprocity (a fundamental property of the unmodified Galilean transformations) or the fixed speed c of light.