ays of variates"; the middle rank gives the median height of the
population; the tallest array (5 ft., 8 in.) is the mode. If a line be
drawn connecting the upper ends of the rows, the resulting geometric
figure will be a "scheme of distribution of variates" or more briefly a
"variability curve," such as was shown in several preceding figures. The
arrangement of homogeneous objects of any kind in such form as this is
the first step in the study of variation by modern statistical methods,
and on such study much of the progress of genetics depends.]

[Illustration: FIG. 15.--Height is one of the stock examples of
a continuous character--one of which all grades can be found. As will be
seen from the above diagram, every height from considerably under five
feet to considerably over six feet can be found in the army, but extreme
deviations are relatively rare in proportion to the amount of deviation.
The vertical columns represent the total number of individuals of a
given height in inches. From Davenport.]

If a group of soldiers be measured as the children were measured for
arithmetical ability, their height will be distributed in this same
curve of probability. Fig. 14 shows the cadets of Connecticut
Agricultural College; it is obvious that a line drawn along the tops
of the files would again make the step-pyramid shown in Figures 10, 11
and 13. If a larger number were taken, the steps would disappear and
give place to a smooth curve; the fact is well shown in a graph for the
heights of recruits to the American Army (Fig. 15).

The investigation in this direction need not be pursued any farther. For
the purpose of eugenics, it is sufficient to recognize that great
differences exist between men, and women, not only in respect of
physical traits, but equally in respect of mental ability.

This conclusion might easily have been reached from a study of the facts
in Chapter I, but it seemed worth while to take time to present the fact
in a more concrete form as the result of actual measurements. The
evidence allows no doubt about the existence of considerable mental and
physical differences between men.

The question naturally arises, "What is the cause of these differences?"

The study of twins showed that the differences could not be due to
differences in training or home surroundings. If the reader will think
back over the facts set forth in the first chapter, he will see clearly
that the fundamental differences in men