  Four-graviton scattering in eleven-dimensional supergravity is considered at
one loop compactified on one, two and three-dimensional tori. The dependence on
the toroidal geometry determines the known perturbative and non-perturbative
terms in the corresponding processes in type II superstring theories in ten,
nine and eight dimensions. The ultra-violet divergence must be regularized so
that it has a precisely determined finite value that is consistent both with
T-duality in nine dimensions and with eleven-dimensional supersymmetry.
