  This work makes a parallel construction for curves on threefolds to a
``current-theoretic'' proof of Abel's theorem giving the rational equivalence
of divisors P and Q on a Riemann surface when Q - P is (equivalent to) zero in
the Jacobian variety of the Riemann surface. The parallel construction is made
for homologous ''sub-canonical'' curves P and Q on a general class of
threefolds. If P and Q are algebraically equivalent and Q - P is zero in the
(intermediate) Jacobian of a threefold, the construction ''almost'' gives
rational equivalence.
