  It is well-known that self-linking is the only Z valued Vassiliev invariant
of framed knots in S^3. However for most 3-manifolds, in particular for the
total spaces of S^1-bundles over an orientable surface F not S^2, the space of
Z-valued order one invariants is infinite dimensional. We give an explicit
formula for the order one invariant I of framed knots in orientable total
spaces of S^1-bundles over an orientable not necessarily compact surface F not
S^2. We show that if F is not S^2 or S^1 X S^1, then I is the universal order
one invariant, i.e. it distinguishes every two framed knots that can be
distinguished by order one invariants with values in an Abelian group.
