  We prove that the knot invariant induced by a $\Bbb Z$-homology 3-sphere
invariant of order $\leq k$ in Ohtsuki's sense, where $k\geq 4$, is of order
$\leq k-2$. The method developed in our computation shows that there is no
$\Bbb Z$-homology 3-sphere invariant of order 5. This result agrees with a
conjecture of Rozansky based on physical predictions about the asymptotic
behavior of Witten's Chern-Simons path integral.
