  This is a revised version of our previous paper by the same name and preprint
number. It contains various changes, two figures and new results in sect.5. We
propose a new approach to four-dimensional Planckian-energy scattering in which
the phase of the ${\cal S}$-matrix is written---to leading order in $\hbar$ and
to all orders in $R/b =Gs/J$---in terms of the surface term of the gravity
action and of a boundary term for the colliding quanta. The proposal is checked
at the leading order in $R/b$ and also against some known examples of
scattering in strong gravitational fields.
