l curve
describes only a 'homogeneous class' of measurements; that is, a class
no portion of which is much influenced by conditions peculiar to itself.
If the class is not homogeneous, because some portion of it is subject
to _peculiar_ conditions, the curve will show a hump on one side or the
other. Suppose we are tabulating the ages at which Englishmen die who
have reached the age of 20, we may find that the greatest number die at
39 (19 years being the average expectation of life at 20) and that as
far as that age the curve upwards is regular, and that beyond the age of
39 it begins to descend regularly, but that on approaching 45 it bulges
out some way before resuming its regular descent--thus:

[Illustration: FIG. 12.]

Such a hump in the curve might be due to the presence of a considerable
body of teetotalers, whose longevity was increased by the peculiar
condition of abstaining from alcohol, and whose average age was 45, 6
years more than the average for common men.

Again, if the group we are measuring be subject to selection (such as
British soldiers, for which profession all volunteers below a certain
height--say, 5 ft. 5 in.--are rejected), the curve will fall steeply on
one side, thus:

[Illustration: FIG. 13.]

If, above a certain height, volunteers are also rejected, the curve will
fall abruptly on both sides. The average is supposed to be 5 ft. 8 in.

The distribution of events is described by 'some such curve' as that
given in Fig. 11; but different groups of events may present figures or
surfaces in which the slopes of the curves are very different, namely,
more or less steep; and if the curve is very steep, the figure runs into
a peak; whereas, if the curve is gradual, the figure is comparatively
flat. In the latter case, where the figure is flat, fewer events will
closely cluster about the average, and the deviations will be greater.

Suppose that we know nothing of a given event except that it belongs to
a certain class or series, what can we venture to infer of it from our
knowledge of the series? Let the event be the cephalic index of an
Englishman. The cephalic index is the breadth of a skull x 100 and
divided by the length of it; e.g. if a skull is 8 in. long and 6 in.
broad, (6x100)/8=75. We know that the average English skull has an index
of 78. The skull of the given individual, therefore, is more likely to
have that index than any other. Still, many skulls deviate from the
average, an