  We develop a method to calculate the N\'eron-Tate height of tautological
integral cycles on jacobians of curves defined over number fields. As examples
we obtain closed expressions for the N\'eron-Tate height of the difference
surface, the Abel-Jacobi images of the square of the curve, and of any
symmetric theta divisor. As applications we obtain a new effective positive
lower bound for the essential minimum of any Abel-Jacobi image of the curve and
a proof, in the case of jacobians, of a formula proposed by Autissier relating
the Faltings height of a principally polarized abelian variety with the
N\'eron-Tate height of a symmetric theta divisor.
