\begin{table}%t4
\caption{\label{t1}Matrix ${\bf G}_2$ is a symmetric matrix of inner products  of the velocity components $\langle V_0~V_i~ V_j~...,\; V_0 ~V_p~ V_q~... \rangle$, according to Latin indices, with $V_0\equiv 1$ and the other indices sorted as $1 \leq i\leq j\leq \ldots \leq 3$ and $1 \leq p\leq q\leq \ldots \leq 3$\tablefootmark{\dag}.}
$$
\begin{array}{r|ccccccccccccccc}
       &  0  &    1    &    2   &    3    &    1 1     &    1 2     & 1 3    &  2 2   &  2 3   &    3 3         &    1 1 1         &    1 1 2         &\cdots  &    3 3 3   &\cdots\\\hline 
0      &  1  & m_{1}   & m_{2}  & m_{3}   & m_{1 1}    & m_{1 2}    &m_{1 3} & m_{22} & m_{23} & m_{3 3}        & m_{1 1 1}        & m_{1 1 2}        &\cdots  & m_{3 3 3}        & \cdots\\
1      &     & m_{1 1} & m_{1 2}& m_{1 3} & m_{1 1 1}  & m_{1 1 2}  &m_{113} & m_{122}& m_{123}& m_{1 3 3}      & m_{1 1 1 1}      & m_{1 1 1 2}      &\cdots  & m_{1 3 3 3}      & \cdots\\
2      &     &         & m_{2 2}& m_{2 3} & m_{1 1 2}  & m_{1 2 2}  &m_{123} & m_{222}& m_{223}& m_{2 3 3}      & m_{1 1 1 2}      & m_{1 1 2 2}      &\cdots  & m_{2 3 3 3}      & \cdots\\ 
3      &     &         &        & m_{3 3} & m_{1 1 3}  & m_{1 2 3}  &m_{133} & m_{223}& m_{233} & m_{3 3 3}     & m_{1 1 1 3}      & m_{1 1 2 3}      &\cdots  & m_{3 3 3 3}      & \cdots\\
11     &     &         &        &         & m_{1 1 1 1}& m_{1 1 1 2}&m_{1113}&m_{1122}&m_{1123}& m_{1 1 3 3}    & m_{1 1 1 1 1}    & m_{1 1 1 1 2}    &\cdots  & m_{1 1 3 3 3}    & \cdots\\ 
12     &     &         &        &         &            & m_{1 1 2 2}&m_{1123}&m_{1222}&m_{1223}& m_{1 2 3 3}    & m_{1 1 1 1 2}    & m_{1 1 1 2 2}    &\cdots  & m_{1 2 3 3 3}    & \cdots\\ 
13     &     &         &        &         &            &            &m_{1133}&m_{1223}&m_{1233}& m_{ 1333}      & m_{11113}        & m_{11123}        &\cdots  & m_{13333}        & \cdots\\
22     &     &         &        &         &            &            &        &m_{2222}&m_{2223}& m_{ 2233}      & m_{11122}        & m_{11222}        &\cdots  & m_{22333}        & \cdots\\
23     &     &         &        &         &            &            &        &        &m_{2233}& m_{ 2333}      & m_{11123}        & m_{11223}        &\cdots  & m_{23333}        & \cdots\\
33     &     &         &        &         &            &            &        &        &        & m_{3 3 3 3}    & m_{1 1 1 3 3}    & m_{1 1 2 3 3}    &\cdots  & m_{3 3 3 3 3}    & \cdots\\
111    &     &         &        &         &            &            &        &        &        &                & m_{1 1 1 1 1 1}  & m_{1 1 1 1 1 2}  &\cdots  & m_{1 1 1 3 3 3}  & \cdots\\
112    &     &         &        &         &            &            &        &        &        &                &                  & m_{1 1 1 1 2 2}  &\cdots  & m_{1 1 2 3 3 3}  & \cdots\\ 
\vdots &     &         &        &         &            &            &        &        &        &                &                  &                  &\vdots  &\vdots            & \vdots\\
333    &     &         &        &         &            &            &        &        &        &                &                  &                  &        & m_{3 3 3 3 3 3}  & \cdots\\
\vdots &     &         &        &         &            &            &        &        &        &                &                  &                  &        &                  & \vdots\\
\end{array}
$$

\tablefoot {\tablefoottext{\dag}{{The external  first row and first column refer to the velocity indices.} Since the matrix is symmetric, only the diagonal and upper triangular part are written.}}

\end{table}