56 RICE UNIVERSITY STUDIES
of exponential growth. This important observation referred to the
number of holdings arranged by date of imprint', it did not refer
to growth in holdings arranged by date of accession. Although
these two types of growth are related, they behave in significantly
different ways. Even libraries that are much younger than the
invention of printing show the exponential behavior of their col-
lections as a function of imprint date, but they also usually show a
much more complex behavior of holdings as a function of accession
date. For example, the holdings of the Library of Congress as a
function of accession year are displayed in Figure 1 (on semi-
logarithmic graph paper, see also Table I). It is evident from
Figure 1 that there are several distinct periods of growth, each of
which is approximately exponential, but with varying growth rates.
In effect, the Library’s growth rate was greatest when it was small ;
as it developed, a lesser rate of growth appeared. This pattern is
easy to interpret, and occurs in many situations unrelated to
library problems. Of more significance is the fact that this growth
is essentially piecewise exponential, that is, it consists of consecu-
tive growth periods, each of which is exponential (see Section 3).
In Figure 2 the growth of the Widener Library subcollection
represented in Volume 7 (bibliography) of the Widener Shelf List
(Ref. 15) is shown as a function of date of imprint. This distribu-
tion, which covers a period of more than 400 years, is exponential
for almost 300 of these years with but minor deviations. It should
be contrasted with Figure 1.
The significant conclusion which is suggested by these two
figures, and confirmed by further studies, is that there are two
kinds of library growth. Some care must be taken to distinguish
them from each other. What we have called the imprint growth
rate is related to the total amount and nature of all published
materials; the other kind of growth is particular to the life cycle
of each library : it can reasonably be called accession growth. It is
obvious that accession growth must be influenced by the more
fundamental growth of imprints but, except possibly in special
situations that do not currently exist, the converse is not true.
Accession growth does not influence imprint growth.
The management problems of a specific library will be composed
of a complex combination of subproblems stemming from both
types of growth (as well as from other variables). It is necessary
to be able to separate these two kinds of subproblems to be able to
analyze their relative importance and to be able to provide reliable
projections of future requirements.