ON THE ANALYSIS OF LIBRARY GROWTH
81
squares methods on the logarithms of the data for two distinct
samples: the period 1830-1876, and the period 1876-1965.
The residuals are the deviations of the logarithms of the data
from the logarithms of the fitted exponentials. From 1870
to 1914 it appears that the residuals are essentially random;
this represents Type-I fluctuation. The three largest residuals
occur in 1965, 1945, and 1918. The first is due to the incom-
pleteness of the collection in the most recent years; plotting
by imprint date invariably introduces a bias in the most
recent figures because items published in any given year are
acquired over a span of years following. Technically, this bias
extends over the entire collection; however, it is most notice-
able in the most recent five to ten years. It would be of inter-
est to determine the distribution of imprint dates for a given
year’s acquisitions to determine the effect of the bias more
precisely. The other two large residuals occur in the final
years of the world wars, and are both negative, as might be
anticipated. These fluctuations are clearly not Type-I. The
large residuals that occur in early portions of the sample
(e.g., that in 1840) are of questionable significance because
of the small sample sizes for those early years.
II. There are departures from exponential growth which
last for a short period relative to the duration of the ex-
ponential part, followed by a longer period of stable exponential
growth proceeding at a different growth rate. This type of
departure from exponential regularity appears to correspond
to a change in the underlying environment which requires a
readjustment of the growth rate. The readjustment is ef-
fected by passing in some (possibly irregular) manner from
the initial constant growth rate to the new constant rate by
means of a transition period of relatively short duration.
Two examples of this type of process are shown in Figure 9
(U. S. Population), one in Figure 10 (Japanese Population),
and two in Figure 1 (LC holdings).
III. The third type of fluctuation is perhaps the most inter-
esting. It is represented by a period of regular exponential
growth which is followed by a transition period of relatively
short duration. The transition period precedes another period
of stable exponential growth (as in Type-II above) which
proceeds at the same rate of growth as the exponential pre-
ceding the transition. Thus, on Semilogarithmic graph paper,