  We provide numerical results for the running coupling in $SU(3)$ Yang-Mills
theory as determined from an analysis of lattice two and three-point gluon
correlation functions. The coupling is evaluated directly, from first
principles, by defining suitable renormalisation constants from the lattice
triple gluon vertex and gluon propagator. For momenta larger than 2 GeV, the
coupling is found to run according to the 2-loop asymptotic formula. The
influence of lattice artifacts on the results appears negligible within the
precision of our measurements, although further work on this point is in
progress.
