  We compare the known in literature, explicitly covariant 4-dimensional
formula for the symmetric energy-momentum tensor of electromagnetic field in a
medium and the energy-momentum tensor derived by Abraham in the 3-dimensional
vector form. It is shown that these two objects coincide only on the physical
configuration space $\overline\Gamma$, formed by the field vectors and the
velocity of the medium, which satisfy the Minkowski constitutive relations. It
should be emphasized that the 3-dimensional vector formulae for the components
of the energy-momentum tensor were obtained by Abraham only on
$\overline\Gamma$, and the task of their extension to the whole unconditional
configuration space $\Gamma$ was not posed. In order to accomplish the
comparison noted above we derive the covariant formula anew by another method,
namely, by generalizing the Abraham reasoning. The comparison conducted enables
one to treat the explicitly covariant formula as a unique consistent extension
of the Abraham formulae to the whole configuration space $\Gamma$. Thus the
question concerning the relativistic covariance of the original 3-dimensional
Abraham formulae defined on $\overline\Gamma$ is solved positively. We discuss
in detail the relativistic covariance of the 3-dimensional vector formulae for
individual components of the 4-dimensional tensors in electrodynamics which is
manifested in the form-invariance of these formulae under Lorentz
transformations.
