the form $$s_i(t) = \sum_A \left[ \Psi^A_i\left(M_L,S_L,G_L,H_L;P_L,N_L\right)
 + \theta_{1 i}^A + \theta_{2 i}^A\right] \; , \label{twentysix}$$ where $\Psi^A_i$ is a function of both the good DSX moments $(M_L,S_L,G_L,H_L)$ and the bad ones $(P_L,N_L)$, and where the remaining two terms (which follow from the last term in Eq. (\[twentyfive\])) read $$\begin{aligned}
 c^2 \theta_{1 i}^A =& \epsilon_{ijk} z_A^j V_A^a R^k_{A b}
  \int_A d^3X_A \left[{\bf T}^{ab} - \delta_{ab} {\bf T}^{cc}\right]
  \; , \\
  c^2 \theta_{2 i}^A =& \epsilon_{ijk} R^j_{A a} V_A^b R^k_{A c}
  \int_A d^3X_A \,X^a\left[{\bf T}^{bc} - \delta_{bc} {\bf T}^{dd}
  \right] \; .\end{aligned}$$ Note that if we augment our list of “bad” moments by including $Q^A_{ab} = \int_A d^3X_A\, {\bf T}^{ab}$ and $Q^A_{ab;c} =
\int_A d^3X_A\, {\bf T}^{ab}X_A^c$, we can express the total spin $s_i(t)$ in terms of some individual moments of the $N$-bodies. We tried to get rid of the non-dynamical moments $(P^A_L,N^A_L,Q^A_L)$ by using the local conservation of energy-momentum $(\nabla_\alpha
{\bf T}^{\alpha
\beta}=0)$ to connect them to the dynamical moments $(M^A_L,S^A_L)$ and the tidal ones $(G^A_L,H^A_L)$. We did not succeed in doing so. \[In fact, such transformations introduced an undesirable dependence upon the internal part $W^{\alpha +}_A(X)$ of the local gravitational potential\]. We thus hypothesize that the total spin $s_i$ 