  We demonstrate that the use of analytical on-shell methods involving
calculation of the discontinuity across the t-channel cut associated with the
exchange of a pair of massless particles (photons or gravitons) can be used to
evaluate one-loop contributions to electromagnetic and gravitational
scattering, with and without polarizability, reproducing via simple algebraic
manipulations, results obtained previously, generally using Feynman diagram
techniques. In the gravitational case the use of factorization permits a
straightforward and algebraic calculation of higher order scattering without
consideration of ghost contributions or of triple-graviton couplings, which
made previous evaluations considerably more arduous.
