The author generalizes B. Harris’ definition of harmonic volume to the algebraic cycle
W
k
−
W
k
−
{W_k} - W_k^-
for
k
>
1
k > 1
in the Jacobian of a nonsingular algebraic curve
X
X
. We define harmonic volume, determine its domain, and show that it is related to the image
ν
\nu
of
W
k
−
W
k
−
{W_k} - W_k^-
in the Griffiths intermediate Jacobian. We derive a formula expressing harmonic volume as a sum of integrals over a nested sequence of submanifolds of the
k
k
-fold symmetric product of
X
X
. We show that
ν
\nu
, when applied to a certain class of forms, takes values in a discrete subgroup of
R
/
Z
{\mathbf {R}}/{\mathbf {Z}}
and hence, when suitably extended to complexvalued forms, is identically zero modulo periods on primitive forms if
k
≥
2
k \geq 2
. This implies that the image of
W
k
−
W
k
−
{W_k} - W_k^-
is identically zero in the Griffiths intermediate Jacobian if
k
≥
2
k \geq 2
. We introduce a new type of intermediate Jacobian which, like the Griffiths intermediate Jacobian, varies holomorphically with moduli, and we consider a holomorphic torus bundle on Torelli space with this fiber. We use the relationship mentioned above between
ν
\nu
and harmonic volume to compute the variation of
ν
\nu
when considered as a section of this bundle. This variational formula allows us to show that the image of
W
k
−
W
k
−
{W_k} - W_k^-
in this intermediate Jacobian is nondegenerate.