The distribution of references in a collection of pertinent source documents can be described and predicted by the relation where the parameter β is related to the subject field and the completeness of the collection. The model is used to predict the reference yield of ab stracting journals in a search for thermophysical property data. It is used also to explain differences among various literature studies of the past in terms of differences in subject and comprehensiveness of search. The model is derived from S. C. Bradford's 'law of scattering' and is called the Bradford Distribution.

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A comprehensive engineering approach to the analysis and functional design of library systems is described in terms of the fundamental space-time relationships which characterize university libraries. Longrun trends in acquisitions and circulation are related to the relative obsolescence of stored materials, and the uncertainty of short-run de-. mand patterns is related to the need for excess service capability. The spatial dispersion of library resources among specialized information centers and central depositories is considered with respect to availability, retrieval, duplication, and efficient storage.T ms PAPER attempts to outline a fairly comprehensive, engineering approach to the functional design of a university library system. It is comprehensive in the sense that it considers both long-run and short-run patterns in library operations in an integrated manner. It is an engineering approach in that it attempts to isolate the fundamental space-time relationships that characterize a library and to treat them in an analytic manner.Although a library is essentially a social institution steeped in human values of all kinds, it can be viewed as a complex communication system charged with the task of transferring information through space and time, and as such, it is particularly amenable to engineering analysis. The mathematical models which emerge from such an analysis may seem far removed from the librarian's view of the library, but they are almost certain to provide a much better basis for the design and operation of library systems than is now available.The models developed below are the result of several years of discussions and joint research efforts by librarians and industrial engineers at Purdue University. There is no attempt here to make forced applications of industrial techniques, although the general methodology of operations research is readily applicable in the library environment. The • appropriate goal is neither the advent of total library automation nor the complete mathematical description of a library system. Rather, it is a search for reliable methods of measurement and analysis which are compatible with the established objectives of library administration.In the remainder of the paper, models are developed to help to, explain how acquisition, circulation, storage, loan period, and duplication policies and patterns interact over the long run. Circulation, as a measure of library activity, becomes the one factor related to all of 1935 1940 1945 1950 1955 1960 19fi5 Systems Analysis in University Libraries I 15 first involves a time-series analysis of acquisitions, holdings, and circulation. The second part considers several aspects of book storage in a manner that is analogous to modern inventory theory. The third part treats the library as a stochastic service system and applies some elementary queueing models to determine the availability and circulation of single and duplicate copies at central or branch libraries. ACQUISITIONS, CIRCULATION' AND OBSOLESCENCEThe twentieth-centu...

An exact, discrete formulation of Bradford's law describing the distribution of articles in journals is derived by showing that Bradford's law is a special case of the Zipf‐Mandelbrot ‘rank frequency’ law. A relatively simple method is presented for fitting the model to empirical data and estimating the number of journals and articles in a subject collection. This method is demonstrated with an example application.