  We prove that a rank one transformation satisfying a condition called
restricted growth is a mixing transformation if and only if the spacer sequence
for the transformation is uniformly ergodic. Uniform ergodicity is a
generalization of the notion of ergodicity for sequences in the sense that the
mean ergodic theorem holds for what we call dynamical sequences. In particular,
Adams' class of staircase transformations and Ornstein's class constructed
using ``random spacers'' have both restricted growth and uniformly ergodic
spacer sequences.
