  We compute the second variation of the \lambda-invariant, recently introduced
by S. Zhang, on the complex moduli space M_g of curves of genus g>1, using work
of N. Kawazumi. As a result we prove that (8g+4)\lambda is equal, up to a
constant, to the \beta-invariant introduced some time ago by R. Hain and D.
Reed. We deduce some consequences; for example we calculate the
\lambda-invariant for each hyperelliptic curve, expressing it in terms of the
Petersson norm of the discriminant modular form.
