  Recently, Feigel has predicted a new effect in magnetoelectric media. The
theoretical evaluation of this effect requires a careful analysis of a dynamics
of the moving magnetoelectric medium and, in particular, the derivation of the
energy-momentum of the electromagnetic field in such a medium. Then, one can
proceed with the study of the wave propagation in this medium and derive the
mechanical quantities such as the energy, the momentum, and their fluxes and
the corresponding forces. In this paper, we develop a consistent
general-relativistic variational approach to the moving dielectric and magnetic
medium with and without magnetoelectric properties. The old experiments in
which the light pressure was measured in fluids are reanalysed in our new
framework.
