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We present a model of the relation between the circulation at a large library, the collection at that library, and the size of the user population. Based on analysis of data at Academic Research libraries in the United States we find a "square root law" which describes this relation quite well. We explore the theoretical foundations for such a law, in a geometric analogy, and speculate on bibliometric implications.

This work was performed at the Alexandria Project Laboratory, School of Communication, Information and Library Stidues, Rutgers University.  The resarch was supported in part by a Grant from the Council on Library and Information Resources(CLIR).