  We describe a new method for determining proper motions of extended objects,
and a pipeline developed for the application of this method. We then apply this
method to an analysis of four epochs of [S~II] HST images of the HH~1 jet
(covering a period of $\sim 20$~yr).
  We determine the proper motions of the knots along the jet, and make a
reconstruction of the past ejection velocity time-variability (assuming
ballistic knot motions). This reconstruction shows an "acceleration" of the
ejection velocities of the jet knots, with higher velocities at more recent
times. This acceleration will result in an eventual merging of the knots in
$\sim 450$~yr and at a distance of $\sim 80"$ from the outflow source, close to
the present-day position of HH~1.
