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ON THE ANALYSIS OF LIBRARY GROWTH

75


The following paragraphs will argue that piecewise exponential
approximation to growth curves provides the most convenient and
informative tool for understanding the underlying processes. We
will argue that the nature of civilization is such that when influ-
ences which tend to retard growth are encountered, the
exponent
of the exponential growth curve is changed to relieve that retard-
ing pressure; in general, the
form of the function is not changed.
This is the same as saying that the growth exponent of the ex-
ponential is a function of time, and, with a sufficiently complex vari-
ation of this exponent with time, any growth curve can be traced
out. But it appears from a study of various important classes of
growth curves that the variation of the exponent with time is of
a particularly simple nature. It is constant most of the time but,
in reaction to external retarding influences, it makes a transition
from its original constant value to another constant value which
is compatible with the external circumstances.

Consider, for instance, the population growth of the United
States, shown in Figure 9, for the period 1610 to date. Until
1690, growth was extremely rapid and exponential; from 1700
until 1880 growth was again exponential with a remarkable degree
of accuracy and consistency. After 1880 a more complex pattern
occurs (to be discussed in Section 4). The departure from exponen-
tial growth which shows up for the first time in the 1880 census
corresponds to what historians call “Turner’s thesis,” concerned
with the closing of the Western Frontier. It is evident that the
270-year period from 1610 until 1880 can be accurately described
by two exponentials, thus four parameters.

Population statistics are unusually complete for the United
States ; most other nations have only recently begun to accumulate
accurate population estimates based on census data. Nevertheless,
it will be useful to look at the population growth of one other na-
tion. Figure 10 displays the growth of Japanese population since
1872. It can be accurately represented by two exponentials, from
1872 until 1900, and from 1900 to date. There is a sharp popula-
tion decline, shown by the 1945 census, due to manpower losses in
World War II, but this was completely made up by the time of the
1950 census. The long-term trend rate of Japanese population
growth has returned approximately to that level it has held since
1900. In the popular press as well as in demographic literature there
has been concern for the rapid growth of the Japanese population
since the war, and some relief that it appears to be coming back
under control at last. This is misleading ; in fact, having retrieved



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