The relation between elastic amplitudes for polarized proton collisions and spindependent scattering observables is studied near the forward direction with a view to providing information on particular amplitudes at low values of momentum transfer. Such information has been singularly successful, for instance, in evaluating the amount of beam polarization achieved by the RHIC facility for its spin programme. A more extensive deployment of polarized facilities at a number of accelerators would permit a much deeper analysis of spin physics in a range of kinematic domains.