The dual of Bradford's law

Abstract

In this article, we examine the classical law of Bradford. This law yields groups with an equal number of articles, but where the number of journals increases geometrically. Within each group, and starting with the last ones (the least productive journals) we examine the maximal productivity of the journals. We describe, using only ym, the maximal productivity (of the journal of rank one), all the possible productivities of the journals in every Bradford group. The same method shows that the most productive journal in every group p (starting with the last group) produces a number of articles mp, where:[FORMULA] where k is the Bradford multiplicator and E is the number of Euler. Hence, the maximal journal productivity in each group forms an approximate Bradford law with fixed universal constant e−E ≈ 0.56. We can say that the dual law of a Bradford law is an approximate Bradford law. This approach is not a pure rank method (as is Bradford's law), nor a pure frequency method (as is Lotka's law), but a frequency method within a rank method. The formula for mp gives a theoretical formula (and hence an explanation) for k, the Bradford multiplier, which is easily applied in practical data. It also sheds more light on the Yablonsky-Goffman-Warren formula for k, which has only been established experimentally. © 1986 John Wiley & Sons, Inc.