laborious methods of statistical analysis that the laws according to which
differences occur are the same where-ever the facts have been examined. A
single illustration will suffice to indicate the general nature of this
result. If the men of a large assemblage should group themselves according
to their different heights in inches, we would find that perhaps one half
of them would agree in being between five feet eight inches and five feet
nine inches tall. The next largest groups would be those just below and
above this average class,--namely, the classes of five feet seven to eight
inches and five feet nine to ten inches. Fewer individuals would be in the
groups of five feet five to six inches and five feet ten to eleven inches,
and still smaller numbers would constitute the more extreme groups on
opposite sides of these. If the whole assemblage comprised a sufficient
number of men, it would be found that a class with a given deviation from
the average in one direction would contain about the same number of
individuals as the class at the same distance from the average in the
opposite direction. Taking into account the relative numbers in the
several classes and the various degrees to which they depart from the
average, the mathematician describes the whole phenomenon of variation in
human stature by a concise formula which outlines the so-called "curve of
error." From his study of a thousand men, he can tell how many there would
be in the various classes if he had the measurements of ten thousand
individuals, and how many there would be in the still more extreme classes
of very short and very tall men which might not be represented among one
thousand people.

It is not possible to explain why variation should follow this or any
other mathematical law without entering into an unduly extensive
discussion of the laws of error. The mathematicians themselves tell us in
general terms that the observations they describe so simply by their
formulæ follow as the result of so-called chance, by which they mean that