Charles Lyell, Historian of Time's Cycle - Time's Arrow, Time's Cycle: Myth and Metaphor in the Discovery of Geological Time - page 164

Oligocene, and Pleistocene-to express the finer divisions permitted by
increasing knowledge.) Lyell writes, citing a metaphor strictly comparable
with our beanbag:
This increase of existing species, and gradual disappearance of the extinct, as
we trace the series of formations from the older to the newer, is strictly
analogous, as we before observed, to the fluctuations of a population such as
might be recorded at successive periods, from the time when the oldest of the
individuals now living was born to the present moment.
This simple description of Lyell's method cannot capture the brilliance and
radical character of his concept. Consider just three points:
First, Lyell proposed this numerical method based on a sophisticated model
of random processes at a time when such statistical thinking was in its
infancy. Most of us still need metaphors to grasp it today, after a century of
success for this powerful procedure.
Second, Lyell's method flies in the face of all paleontological convention
during his time. Most stratigraphers denied both substantive uniformities of
rate and state—and each denial led to a method abjured by Lyell. I have
already discussed how progressionism (nonuniformity of state) led most
stratigraphers to search for key fossils that might mark time by their
anatomical complexity—a method contrary to Lyell's statistical approach
toward entire faunas.
Lyell's opponents also rejected uniformity of rate by viewing the fossil record
as punctuated by mass extinctions and rapid subsequent radiations of new
species. This concept of life's history led to a different practice in dating—the
search for distinctive suites of species to mark each epoch of time. Such a
procedure makes no sense in Lyell's world. His species are independent
particles evenly spaced in time; they do not enter and leave the geological
scene in concert. Distinct epochs are an illusion of our imperfect record; we
can only capture moments with statistical measures of a smooth and
continuous flow: