  Given a homomorphism from a link group to a group, we introduce a $K_1$-class
in another way, which is a generalization of the 1-variable Alexander
polynomial. We compare the $K_1$-class with $K_1$-classes in \cite{Nos} and
with Reidemeister torsions. As a corollary, we show a relation to Reidemeister
torsions of finite cyclic covering spaces, and show reciprocity in some senses.
