  We demonstrate that the use of on-shell methods involving calculation of the
discontinuity across the t-channel cut associated with the exchange of a pair
of massless particles can be used to evaluate loop contributions to the
electromagnetic and gravitational scattering of both massive and massless
particles. In the gravitational case the use of factorization permits a
straightforward and algebraic calculation of higher order scattering results,
which were obtained previously by considerably more arduous Feynman diagram
techniques.
