  A well-known result of Bill Parry shows that a topologically transitive
continuous piecewise monotone mapping with positive topological entropy is
conjugate to a uniformly piecewise linear mapping with slope determined by the
entropy. In this note we generalise Parry's result somewhat to what we call the
class of essentially transitive mappings. This generalisation is of some
interest in as much as for mappings with one turning point the converse also
holds, i.e., a uniformly piecewise linear mapping with one turning point and
with slope greater than 1 is essentially transitive.
