ON THE ANALYSIS OF LIBRARY GROWTH
77
the population lost in the war, the growth rate is now returning to
its traditional value. This shows a danger inherent in looking at
short sections of time series. The local fluctuations may obscure the
general picture and lead to gross misestimates of what is happen-
ing. Further examples of this type of problem will come up in what
follows.
Returning to Figure 2, the Widener Shelf List Volume 7 imprint
date distribution, observe its essential exponentiality. Figure 11
displays the same information for the Stanford Undergraduate
Library. This collection is restricted to recent imprints because
of its small size and limited purpose. Nevertheless the usual ex-
ponential trend is clearly evident. It appears to make no difference
whether a subcollection of a large library or an entire small library
is examined. In Reference 3 it was shown that similar growth
occurred in a random sample from a university library of some
300,000 items, exclusive of periodicals.
Figure 12, taken from Reference 2, shows that the number of
scientific periodicals and also the number of scientific abstract
journals have been growing exponentially, the former for approxi-
mately 300 years.
Turning to quite a different type of growth statistic, in recent
years the Basic Oxygen Process has been increasingly used for the
production of steel in the United States. Growth in the output of
BOP raw steel is shown in Figure 13. It consists of two parallel
lines on the Semilogarithmic graph paper, separated by about a
year. Thus, apart from this fluctuation (which will be discussed in
Section 4), this statistic also follows the exponential growth law.3
4. Local Fluctuations in Growth
All of the graphs that have been discussed show consistent
exponential trends for most of their duration, but there are
deviations of several types.
I. There are minor fluctuations which appear to have an
average value of zero with respect to the underlying exponen-
tial trend. These probably correspond to random influences
that are of no long-range importance, and which cannot be
subjected to a deterministic analysis. There is not much that
has to be said about them other than that they always exist
in natural time series and that there is little that can be done
to analyze them. Figure 14 illustrates the residuals of the
Widener Shelf List data used for Figure 2 with respect to
exponential trend lines. Trends were obtained using least