The Jefferson Lab Hall A experiment E99-114 comprised a series of measurements to explore proton Compton scattering at high momentum transfer. For the first time, the polarisation transfer observables in the p (~ 0 ~ p) reaction were measured in the GeV energy range, where it is believed that quark-gluon degrees of freedom begin to dominate. The experiment utilised a circularly polarised photon beam incident on a liquid hydrogen target, with the scattered photon and recoil proton detected in a lead-glass calorimeter and a magnetic spectrometer, respectively.