  J.P. Levine showed that the Conway polynomial of a link is a product of two
factors: one is the Conway polynomial of a knot which is obtained from the link
by banding together the components; and the other is determined by the
$\bar{\mu}$-invariants of a string link with the link as its closure. We give
another description of the latter factor: the determinant of a matrix whose
entries are linking pairings in the infinite cyclic covering space of the knot
complement, which take values in the quotient field of ${\Bbb Z}[t,t^{-1}]$. In
addition, we give a relation between the Taylor expansion of a linking pairing
around $t=1$ and derivation on links which is invented by T.D. Cochran. In
fact, the coefficients of the powers of $t-1$ will be the linking numbers of
certain derived links in $S^3$. Therefore, the first non-vanishing coefficient
of the Conway polynomial is determined by the linking numbers in $S^3$. This
generalizes a result of J. Hoste.
