  The WDVV equation is satisfied by the genus 0 correlation functions of any
topological field theory in two dimensions coupled to topological gravity, and
may be used to determine the genus 0 (rational) Gromov-Witten invariants of
many projective varieties (as was done for projective spaces by Kontsevich).
  In this paper, we present an equation of a similar universal nature for genus
1 (elliptic) Gromov-Witten invariants -- however, it is much more complicated
than the WDVV equation, and its geometric significance is unclear to us. (Our
prove is rather indirect.) Nevertheless, we show that this equation suffices to
determine the elliptic Gromov-Witten invariants of projective spaces.
  In a sequel to this paper, we will prove that this equation is the only one
other than the WDVV equation which relates elliptic and rational correlation
functions for two-dimensional topological field theories coupled to topological
gravity. It is unclear if there are any further equations of this type on the
small phase space in higher genus, but we think it unlikely. (The genus 0 and 1
cases are special, since the correlation functions on the small phase space
determine those on the large phase space.)
