The two terms _continuous_ and _discontinuous variation_ refer to the
succession or inheritance of the variations rather than to the actual
conditions amongst a group of individuals living at the same time; but
this distinction has only a subordinate value. The term _fluctuating_,
or _individual variation_, expresses more nearly the conditions of the
individuals of a species at any one time, and the continuation of this
sort of difference is the continuous variation spoken of above. The
discontinuous variations are probably of the same nature as those that
have been called mutations, and what Darwin sometimes called sports, or
single variations, or definite variations.
Continuous Variation
If we examine a number of individuals of the same species, we find that
no two of them are exactly alike in all particulars. If, however, we
arrange them according to some one character, for example, according to
the height, we find that there is a gradation more or less perfect from
one end of the series to the other. Thus, if we were to take at random a
hundred men, and stand them in line arranged according to their height,
the tops of their heads, if joined, would form a nearly continuous line;
the line will, of course, incline downward from the tallest to the
shortest man. This illustrates individual variation. An arrangement of
this kind fails to bring out one of the most important facts connected
with individual differences. If the line is more carefully examined, it
will be found that somewhere near the middle the men are much more
nearly of the same height, or rather there are more men having about the
same height than there are near the ends of the line. Another
arrangement will bring this out better. If we stand in a line all the
men from 60 to 61.9 inches, and in another parallel line all those
between 62 and 63.9, then those between 64 and 65.9, then between 66 and
67.9 inches in__ height, etc., it will be found that there are more men
in some of these lines than in others. The longest line will be that
containing the men of about 65 inches; the two lines formed out of men
on each side of this one will contain somewhat fewer men, and the next
ones fewer still, and so on. If we looked at our new group of men from
above, we should have a figure triangular in outline, the so-called
frequency polygon, Figure 3 B. With a larger amount of data of this sort
it is possible to construct a curve, the curve of frequency, Figure 3 A.
In order to obtain this curve of frequency, it is of course not
necessary to actually put the individuals in line, but the curve can be
drawn on paper from the measurements. We sort out the measurements into
classes as in the case given above. The classes are laid off at regular
intervals along a base-line by placing points at definite intervals.
Perpendiculars are then erected at each point, the height of each being
proportional to the frequency with which each class occurs. If now we
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