  In general coordinate invariant gravity theories whose Lagrangians contain
arbitrarily high order derivative fields, the Noether currents for the global
translation and for the Nakanishi's IOSp(8|8) choral symmetry containing the
BRS symmetry as its member, are constructed. We generally show that for each of
those Noether currents a suitable linear combination of equations of motion can
be brought into the form of Maxwell-type field equation possessing the Noether
current as its source term.
