\quad - {1 \over c^2} {d \over dt} \int
  d^3x \,\sigma^j \left(x^i x^j - {1 \over 2} \delta_{ij} x^2\right)
  + {\cal O}(4)  \; . \nonumber\end{aligned}$$ It satisfies the following conservation law [@bd] $${d^2 m_i(t) \over dt^2} = 0 \; . \label{sixteen}$$ In fact, the first derivative of $m_i(t)$ is nothing but the conserved total linear momentum of the system $$p_i \equiv {d m_i(t) \over dt} = {\rm const.}   \; .
 \label{seventeen}$$

Employing the results of Sec. II.A and definition (\[fifteen\]) we obtain after tedious but straightforward calculations the following form of the total mass dipole moment $m_i(t)$ of the system $$\begin{aligned}
 m_i(t) &=& \sum_A\biggl\{ M^A z_A^i \left[1+{1 \over c^2}\left(
  {1 \over 2}v_A^2+G_{A}^{\prime\prime} \right)\right] + {1 \over c^2}
  v_A^j s_A^{ij} - {3 \over c^2} a_A^j m_A^{ij} \nonumber \\
 & & \qquad\; - {1 \over c^2} \left(z_A^i z_A^j - {1 \over 2}
  \delta_{ij}
  z_A^2 \right) R^j_{A a} \sum_l {1 \over l!} M_L^A G_{aL}^{A\prime}
  - {2 \over c^2} z_A^j R^i_{A [a} R^j_{A b]} \sum_l
  {1 \over l!} M_{aL}^A  G_{bL}^{A\prime} \biggr\} \nonumber \\
 & & +  \sum_A \biggl\{m^i_A \left[1+{1 \over c^2}\left(
  {1 \over 2}v_A^2+G_{A}^{\prime\prime} \right)\right]
  + {1 \over c^2} z_A^i \left[M^{A (1)}_a V_A^a + 2 M^A_a
  G_a^{A\prime\prime} \right]\biggr\} \nonumber \\
 & & + {\cal 