Offprint of: M.K. Buckland (1972).
Are Obsolescence and Scattering related? Journal of
Documentation, 28(3), pp. 242-246.
et la diffusion sont-elles liées?, French translation by Pinar Cytheree,
освесенство и разбирање поврзани?, Macedonian translation by
Katerina Nestiv, May 2019.
obsolescencja i rozproszenie są powiązane ze sobą?, Polish
translation completed by Jodi Williams, TheWordPoint, May 2023.
obsolescência e a disposição relacionadas?,
Portuguese translation by Artur Weber and Adelina Domingos, Nov 2017.
uzura morală şi împrăştierea legate?, Romanian
translation by eWorldSports,
Связаны ли устаревание и рассеяние?,
Russian translation by Angelina Baeva, Feb 2019.
relacionadas la obsolescencia y la dispersión?, Spanish translation
by Chema Bescos, Agencia de
traducción Ibidem Group, Feb 2023.
застарівання і розсіювання пов'язано?, Ukrainian translation by
ARE OBSOLESCENCE AND SCATTERING RELATED?
Michael K. Buckland.
Considerable attention has been paid, in this journal and elsewhere, to each
of two aspects of the use of literature. One of these is the relative decrease
in use of material as it ages ('obsolescence') which has been discussed by Brookes
 and many others . The other aspect
is the extent to which the use of material tends to be concentrated in a few
titles ('Bradford's Law of scattering'), which has been treated by Bradford
, Leimkuhler , Brookes ,
and Fairthorne .
Cole  perceived that these two 'laws', especially when
examined in conjunction, had significant implications for deciding how large
library collections should be. This area has been analysed in more depth by
Buckland and Woodburn  and by Brookes .
In brief, these analyses give some insight into the economics of library stock
policies with respect to the number of journal titles held and the length of
time they are retained. They are also relevant to the management of indexing
and abstracting services in that they indicate the loss of coverage which could
be expected to resulti from the exclusion of older and more marginal literature.
In each case it is assumed that there is an ascertainable pattern of obsolescence
which is known to vary from subject to subject. It is also assumed that the
scattering effect can be estimated and that this will also vary from one subject
The possibility that there might be some relationship between
these two variations
appears to have been neglected. Are they related? It would be of considerable
theoretical interest if a relationship could be established and much data collection
could be avoided if one could be deduced from the other. At the University of
Lancaster Library Research Unit, when the implications of scattering and obsolescence
were being explored during 1967 and 1968, an attempt was made to see if there
was any evidence of a relationship. The results were indicative but not conclusive.
Other research interests have taken priority and the purpose of this note is
to describe what was done in the hope that researchers engaged in bibliometric
analysis may be able to pursue this topic further.
It is convenient to discuss scattering and obsolescence in terms
of the compactness
of literatures. A highly obsolescent literature such as physics is more compact
with respect to time than the literature of geology. Similarly, some literatures
are more compact with respect to scattering than others. The initial
hypothesis had been that scattering and obsolescence tend to vary inversely.
For example, some literatures might tend to be wide and short (widely scattered
over a broad front of journals, but obsolescent in a short time) whereas others
might be narrow and long (narrowly concentrated in a few journals but long-lived,
i.e. obsolescing only slowly). This is represented graphically in Fig. 1a.
An alternative hypothesis was that scattering and obsolescence tend to vary
directly. For example, some literatures tend to be compact (narrowly
concentrated in a few journals and obsolescent in a short time) whereas others
are diffuse (widely scattered over a broad front of journals and long-lived,
i.e. obsolescing only slowly). This is depicted in Fig. 1b.
In order to get
comparable data for different subjects, reference was made to Brown's Scientific
serials . This contains analyses of citations at the
ends of articles published during a period of about eighteen months in each
of eight scientific subjects: Mathematics, Physics, Chemistry, Geology, Physiology,
Botany, Zoology, and Entomology. The citations from journals in each subject
were sorted by journal to give scatter and by age to give obsolescence. The
data is presented raw and no attempt was made to fit curves to the results.
In fact, Brown's commentary mixes absolute measures and proportions. For example,
his Table 16 gives the proportion of each sample covered by the most
productive 100 journals, even though the sample sizes vary enormously. It would
have been more appropriate to have examined the proportion of each sample covered
by a given proportion of the journals.
Brown's data were analysed and obsolescence was plotted against scattering
for each of the eight subjects. The results, which are presented in Fig. 2,
are clearly at variance with the original hypothesis that scattering and obsolescence
vary inversely. Instead they show a tendency for them to vary directly. The
data clearly imply that compactness with respect to time is associated with
concentration with respect to scattering.
Fig. 2. Compactness of Literatures
The scattering coefficient k is taken from Cole's formulation
of Bradford's law of scattering 
A note of caution should be made concerning this finding.
In some subjects
the source journals chosen contributed more citations than in others. For example
the leading chemistry journals contributed 10,052 citations whereas the leading
zoology journals contributed 1,819. There is, in fact, a correlation between
the sample size and the two kinds of compactness. The 'compact' subjects are
those with the larger number of citations in their samples. The implications
of this are not clear. Scattering and obsolescence patterns would appear to
be 'non-dimensional', in the sense that one would expect a random sample from
either distribution to form a distribution of the same shape. Nevertheless,
Professor E. T. O'Neill has suggested* that there may be an
element of dimensionality in that small sample sizes lead to the computation
of scattering coefficients which over-estimate the true amount of scattering.
Such a bias could explain, at least partially, the correlation between sample
size and literary compactness with respect to scattering. An alternative explanation
of the correlation with sample size is that a highly concentrated literature
needs to have relatively bulky journals in the nuclear zone and that this bulk
determines the size of samples picked by Brown's method.
Rn=RN(1 + k log n/N)
where Rn is the number of references in the most productive
n journals in a literature wherein N journals
references. The values of k which are given are based in each case on
the value of Rn which constitutes 90% of RN.
Data from Brown.
Assuming that some literatures are more compact than others,
one wonders why
this should be. Dr A. Hindle has suggested that the compactness of literatures
might be related to a subject's 'hardness' or 'softness'; that is to say, the
extent to which the terminology and hypotheses are clearly definable and the
problems are highly structured. In this respect physics is generally regarded
as more 'hard' than biology. The rankings of the subjects with respect to compactness
in Fig. 2 do seem to agree roughly with subjective impressions of the relative
hardness and softness of the subjects concerned. Quite independently, Professor
de Solla Price has advanced the theory that obsolescence is related to hardness
and softness and can be used as a hardness index .
1. BROOKES, B. C. The growth, utility, and obsolescence of
scientific periodical literature. Journal of Documentation, vol. 26,
1970, pp. 283-94.
2. For a convenient review see : JAIN, A. K Report on a
statistical study of book use, Ph.D. thesis. Purdue University, Lafayette,
Ind. (PB 176 525).
3. BRADFORD, S. C. Documentation. London, Crosley Lockwood.
4. LEIMKUHLER, F. F. The Bradford distribution. Journal
of Docurnentation, vol. 23, 1967, pp. 197-207.
5. BROOKES, B. C. The derivation and application of the
Journal of Documentation, vol. 24, 1968, pp. 247-65. (See also the note
by Mr Brookes in Journal of Documentation, vol. 25, 1969, pp. 58-60.)
6. FAIRTHORNE, R. A. Empirical hyperbolic distributions (Bradford-Zipf-Mandelbrot)
for bibliometric description and prediction. Journal of Documentation
, vol. 25, 1969, pp. 319-43.
7. COLE, P. F. Journal usage versus age of journal. Journal of Documentation,
vol. 19, 1963, pp. 1-11.
8. BUCKLAND, M. K. and WOODBURN, I. Some implications for library management
of scattering and obsolescence. (University of Lancaster Library Occasional
Papers, 1). Lancaster. 1968. (ERIC report ED 022 502.)
9. BROOKES, B. C. Optimum P% library of scientific periodicals. Nature
232(5311), 13 Aug. 1971, pp. 458-61.
10. BROWN, C. H. Scientific serials. (ACRL monograph, 16). Chicago, ACRL, 1956.
11. PRICE, D. J. de S. Citation measures of hard science, soft science,
technology, and non-science. In: NELSON, C. E. and POLLOCK, D. K.
Communication amongst scientists and technologists. Lexington,
Heath, 1970, pp. 3-22.
* Private communication, July 1971. Professor O'Neill was using Leimkuhler's formulation of the Bradford Distribution.