Pure QCD is studied on a large Euclidean lattice consisting of 324 points at values of the coupling beta equal to 6.29, 6.585 and 6.88. Results are presented for the lowest-order spin-dependent corrections to the non-relativistic potential between a quark and an antiquark. Working within a Bethe-Salpeter formalism, it is concluded that the linear term in the non-relativistic potential is consistent with having arisen from scalar exchange; the Coulomb-like term similarly arises from a purely vector exchange. As part of the above study, calculations of the A1u hybrid potential in quarkonium are made, showing it to be similar in behaviour to the Eu potential.