Which electromagnetic equations apply in rotating coordinates?

It was discovered some years ago by Schiff that the equations divE = 4πQ and curlB - (1/c) ∂E/∂t = (4π/c)J for fields in vacuum do not carry over without change from an inertial frame to a frame with rotating axes of space coordinates, even for a region with all velocities of orderv≪c. However, the belief that all four of the field equations are invariant under such conditions is still prevalent and causes misconceptions in physical applications, including astrophysical and geophysical ones. The purpose of the present paper is therefore to call attention to Schiff's discovery, discussing its basis and its extension to fields in material media, and to interpret the additional terms that must be added to the equations in order to obtain valid transformations to rotating axes of coordinates.