  Using a simple geometric argument, we obtain an infinite family of nontrivial
relations in the tautological ring of $M_g$ (and in fact that of $M_{g,2}$).
One immediate consequence of these relations is that the classes
$\kappa_1,...,\kappa_{[g/3]}$ generate the tautological ring of $M_g$, which
has been conjectured by Faber, and recently proven at the level of {\em
cohomology} by Morita.
