  We show that for an $n$-component, $n$-bridge link and a positive integer
$m$, the following is true: If the longitudes of $L$ lie in the $(m+2)$-th term
of the lower central series of the link group then all the finite type
invariants of orders $\leq m$ for $L$ are the same as these of the
$n$-component unlink.
