for deriving some explicit forms of the global conservation laws in general relativity. First, let us remark that the expressions based on surface integrals at infinity [@ll], [@wei], [@mtw] are of no real use within the post-Newtonian context because one loses a power $1/c^2$ in reading out a conserved quantity from the asymptotic behaviour of metric. Concerning approaches where the conserved quantities are given as three-dimensional integrals, we note the formulation of Fock [@fo], taken up by Brumberg [@bru], and that of Chandrasekhar and coworkers [@cha1], [@cha2], followed by the parametrized version of Will [@wi]. Neither approaches constitute useful starting points for us. Indeed, on the one hand, Fock and Brumberg restricted themselves to the (ill-defined) case of a “rigidly rotating” bodies and introduced some mass moments which are not compatible with the ones that enter naturally the DSX formalism, while, on the other hand, Chandrasekhar et al. restricted themselves to the special case of perfect fluids and chose basic variables which do not fit well within the DSX scheme.

A more convenient starting point for our purpose is the work of Blanchet, Damour and Iyer [@bd], [@di1] (see also [@di2]). These authors have defined global-frame post-Newtonian mass and spin 