  We show that the integration of a 1-cocycle I(X) of the space of long knots
in R^3 over the Fox-Hatcher 1-cycles gives rise to a Vassiliev invariant of
order exactly three. This result can be seen as a continuation of the previous
work of the second named author, proving that the integration of I(X) over the
Gramain 1-cycles is the Casson invariant, the unique nontrivial Vassiliev
invariant of order two (up to scalar multiplications). The result in the
present paper is also analogous to part of Mortier's result. Our result differs
from, but is motivated by, Mortier's one in that the 1-cocycle I(X) is given by
the configuration space integrals associated with graphs while Mortier's
cocycle is obtained in a combinatorial way.
