  We give a definition of an integer-valued function $\sum_i \alpha_i x ^*_i$
derived from arrow diagrams for the ambient isotopy classes of oriented
spherical curves. Then, we introduce certain elements of the free
$\mathbb{Z}$-module generated by the arrow diagrams with at most $l $ arrows,
called relators of Type~($\check{\rm{I}}$) (($\check{\rm{SI\!I} }$),
($\check{\rm{WI\!I}}$), ($\check{\rm{SI\!I\!I}}$), or ($\check{\rm{
WI\!I\!I}}$), resp.), and introduce another function $\sum_i \alpha_i
\tilde{x}^*_i$ to obtain $\sum_i \alpha_i x^*_i$. One of the main results shows
that if $\sum_i \alpha_i \tilde{x}^*_i$ vanishes on finitely many relators of
Type~($\check{\rm{I}}$) (($\check{\rm{SI\!I}}$) , ($\check{\rm{WI\!I}}$),
($\check{\rm{SI\!I\!I}}$), or ($\check{\rm{WI\! I\!I}}$), resp.), then $\sum_i
\alpha_i \tilde{x}$ is invariant under the deformation of type $\rm{RI}$
(strong$\rm{RI\!I}$, weak$\rm{RI\!I}$, strong$\rm{RI\!I\!I}$, or
weak$\rm{RI\!I\!I}$, resp.). The other main result is that we obtain functions
of arrow diagrams with up to six arrows. This computation is done with the aid
of computers.
