\quad + {\cal O}(4) \; , \label{nineteen}\end{aligned}$$ where the second row applies to the case of standard worldline data. Eq. (\[nineteen\]) agrees with previous results [@ll], [@mtw]. In the case of the pole-dipole truncated model the expression for the mass dipole reads $$m^i_{PD} = m^i_{LD-EIH} + {1 \over c^2} \sum_A v^j_A s^{ij}_A +
 {\cal O}(4) \; , \label{twenty}$$ a result previously derived by Damour and Schäfer [@ds] from the spin dependent Lagrangian of Ref. [@dam].

Let us remark, as an aside, that defining some “Fock” local mass dipole moments for instance by $c^2 M^A_{a F} =
\int_A d^3X_A\, X_A^a(1+W/2c^2){\bf T}^{00}$ does not simplify at all the writing of our result (\[eighteen\]). In fact, this definition introduces several bad algebraic structures (notably the moments $N^A_L$; see [@dam1; @dam2; @dam3]) which do not enter the final dynamical results of the DSX formalism. This is one of the reasons why Fock, in his book [@fo], did not succeed in getting a good definition of the mass centers of the individual bodies (in spite of the fact that, in the case of the mass center of the entire isolated system, the Blanchet-Damour and Fock definitions, written in the global coordinate system, give the same 