viation." In order to make
possible the comparison of the variabilities of characteristics
measured in unlike units, such as weight and stature, this index must
be converted into an equivalent abstract quantity. This is done by
reducing the index of variability to per cents of the group average,
giving what is called the _coefficient_ of variability. Thus, for
example, in stature the index of variability (standard deviation) of
certain classes of men is approximately 2.7 inches; that is, in a
large group of men the amount of individual variation from the average
height of 69 inches amounts to 2.7 inches. This gives an abstract
_coefficient_ of about 4.0 per cent, for 2.7 equals 3.9 per cent of
69. Similarly the index of variability of the weight of a group of
university students has been found to be about 16.5 pounds; the
average weight is about 153 pounds, and the coefficient of
variability is therefore about 10.8 per cent (16.5 equals 10.78 per
cent of 153). Although pounds and inches may not be compared, these
two abstract coefficients may be, and we may say that men are more
than twice as variable in weight as in stature.

Turning now to variation of the second type we find what are
ordinarily called _mutations_, or differences quite properly termed
_variations_, in a strict sense, as distinguished from the preceding
fluctuations or variability phenomena. Mutations or variations are
abrupt changes of the average or type condition to a new condition or
value which then becomes a new center of fluctuating variability. The
difference between variability and variation may be illustrated
through an analogy suggested by Galton (Fig. 5). A polygonal plinth,
or better a polyhedron, resting upon one face is easily tipped
slightly back and forth, but after slight disturbance it always
returns to its first position of stable equilibrium. Each face of the
plinth or polyhedron represents an organismal characteristic; these
slight backward and forward movements represent fluctuations, always
centering about the average condition. An unusually hard push sends
the plinth over upon another face in which it has a new position of
stability; this represents true variation or mutation. In this new
position it is again stable, may again be rocked back and forth
showing fluctuations about its new average position.

[Illustration: FIG. 5.--Plinth to illustrate the difference
between variability (fluctuation) and variation (mutati