  In this paper normal functions (in the sense of Griffiths) are used to solve
and refine geometric questions about moduli spaces of curves. The first
application is to a problem posed by Eliashberg: compute the class in the
cohomology of M_{g,n}^c of the pullback of the zero section of the universal
jacobian along the section that takes [C;x_1,...,x_n] to Sum d_j x_j in Jac
(C), where d_1 + ... + d_n = 0. The second application is to slope inequalities
of the type discovered by Moriwaki. There is also a discussion of height
jumping and its relevance to slope inequalilties.
