248 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1949 
parts of the time scales are uncertain and the margin of error is often 
considerable. But an order of magnitude is gradually emerging and 
various portions of the time scales have been checked by independent 
methods and adjusted to each other. They have thus become useful 
instruments for the reconsideration of the time aspects of evolution. 
It is my intention to introduce you to this fascinating subject. 
Within the limited time available only a few interesting examples 
can be given. The treatment of facts and problems will inevi- 
tably be sketchy, which means that some of my remarks will over- 
state the case, while others, which might appear to be overstatements, 
are not overstatements. In order to show the applicability, or 
otherwise, of some of the apparent rules to different branches of the 
tree of life, examples have been selected from as great a variety of 
groups as possible. 
Let us first discuss the rate of changes in direct lines of descent, 
disregarding the phenomenon of splitting or branching of the phylo- 
genetic tree. What I mean is illustrated by the pedigree of man, in 
which the numerous branches leading to other groups have been 
omitted. In order to attack the problem of the time rate of evolution, 
such a generalized and tentative pedigree is of course useless. It is 
necessary to consider a group for which a close succession of abundant 
fossil material is available. Such a group is that of the horses, which 
has been well studied in the United States. In figure 1 the chrono- 
logical order and the range in time are shown for successive genera 
directly ancestral to Hquus, the modern horse. From this arrange- 
ment, Simpson has deduced the average duration of a horse genus as 
about 5% million years. In column III, the horse’s ancestors are 
spaced in accordance with the amount of structural modification 
between successive stages, and the amount is measured in arbitrary 
units. It is evident from the comparison of columns I, II, and III, 
that the morphological step, for instance, from EH’pihippus to Meso- 
hippus was great, though it did not take more time than the preceding 
one from Orohippus to Epihippus. Evolution appears to have been 
accelerated in this case, as also from Parahippus to Merychippus. 
The remainder of the diagram shows the kinds of morphological 
characters used in assessing the units of column III, and also the 
trend of evolution in the horses. 
This evidence supplies us with some interesting information, namely 
(a) that the rate of morphological change is not a simple function of 
time, and (b) that the average period of existence of a horse genus is 
of the order of a few million years. The horses have further provided 
an observation made by Stirton, which is worth mentioning. In 
studying the progressive increase in height (hypsodonty) of the 
cheek teeth, he noticed that at any one point of the lineage there is 
not enough individual difference in the height of the cheek teeth, 
