s4 THE SHADOW OF THE WORLD’S FUTURE
reproductive impulse of constant intensity; but at
every moment the effectiveness of the impulse is being
reduced in the ratio that the further population-
possibility of the region, at that moment, bears to the
total number which can live therein. Recently Prof.
Raymond Pearl and Dr Reed in the United States,
Mr Udny Yule in England, and others have system-
atically examined this supposition; have—following
Verhulst—called the curve representing it a “logistic
curve,” ! and have developed formule for its applica-
tion. In character the curve is similar to the * cross-
over ”” from one railway line to another line parallel
thereto. Initially it is concave upwards; its middle
is sensibly linear; after that it becomes convex upwards,
and approaches a limiting value asymptotically. That
is to say, as time goes on the population-numbers
increase more and more rapidly, per unit of time;
attain to a maximum rate of increase; then increase
more and more slowly as the numbers approach the
limiting number of the population.
The plausibility of this view is such that it cannot
be passed without comment. The underlying assump-
tion, viz., that human beings can be regarded as
organisms, exhibiting essentially constant qualities,
living in an environment which also is essentially
constant, is certainly not true to a sufficient degree of
approximation to warrant its being accepted as repre-
senting the facts. The instantaneous rates of increase
for the United States for the 10-year periods, which
are § years on either side of the middle of the years
shown in the table hereunder, were actually as indicated
t The axis of abscisse represents time, and the axis of ordinates
represents population-numbers. The curve will undoubtedly repre-
sent very approximately the growth of, say, micro-organisms, developing
in a limited region, where they are exhausting their pabulum by
developing. It was found also to represent the mode of increase of
the fly Drosoplila melanogaster, similarly circumstanced.
