se sub-groups has its own average and its own amount
and extent of variability (fluctuation) and it is only by adding them
together that we get the larger group. Each of these elementary groups
is called a "pure line," which is defined as a group of organisms, all
of which are the progeny of a single individual. The characteristics
of each pure line remain stable through successive generations, each
about its own average; and it is chiefly this fact that enables us to
identify the different lines. Transition from the condition of one
pure line to another occurs only as a mutation. At present the theory
of the pure line is strictly applicable only to organisms reproducing
asexually or to self-fertilizing forms where the group observed is
actually composed of the progeny of a single organism. It is hardly
possible to say as yet whether or not this extremely important theory
is essentially applicable to the human species or any species where
two organisms are involved in the establishment of a race or line, but
there are some indications of a circumstantial nature that it is thus
applicable in its essentials and so modified as to include this fact
of biparental inheritance.

[Illustration: FIG. 6.--Curves illustrating the relation
between the pure line and the species or other large group.
_A_, a "species" curve composed of three pure lines. _B_,
the separate elements of the larger curve each with its own
average and variability.]

With this bare skeleton of the subject of variation before us let us
see how facts of this kind may have any significance for the subject
of Eugenics, any bearing upon the possibility of racial improvement.
When any of the varying human traits, and they all vary, is measured
carefully and the results tabulated we find that they give us a curve
approximating the normal frequency curve, such as we have described
above and illustrated in Fig. 3. The coefficients of variability of a
great many human traits are known and a few representative
coefficients are given in Table I. This type of variability is given
then, by measurements of physical characteristics of all kinds, and,
what is of greater importance, physiological traits, including mental
and moral characteristics, so far as they can be measured by present
methods, vary in just the same way. Annual individual earnings give us
a curve closely similar to that of a normal frequency curve with an
approximate minimum limiting