  A new codimension 2 relation among descendent strata in the moduli space of
stable, 3-pointed, genus 2 curves is found. The space of pointed admissible
double covers is used in the calculation. The resulting differential equations
satisfied by the genus 2 gravitational potentials of varieties in Gromov-Witten
theory are described. These are analogous to the WDVV-equations in genus 0 and
Getzler's equations in genus 1. As an application, genus 2 descendent
invariants of the projective plane are determined, including the classical
genus 2 Severi degrees.
