A key law in the field of bibliometrics which describes and predicts the productivity of publishing by scientific researchers. This inverse square law expresses the observation that in a given scientific field, a small number of researchers make a large contribution in the form of publications, a larger number make fewer contributions, and many more make a small number of contributions, or only one. This is quantified as the number of authors making n contributions is 1/n2 of the total number of contributing authors. Thus, those authors making 2 contributions are 1/4 of the total number of authors, those making 3 are 1/9 of the total, those making 4 are 1/16 of the total, etc.

Lotka’s law was first expressed by Alfred Lotka in a 1926 article called "The Frequency Distribution of Scientific Productivity." (Journal of the Washington Academy of Sciences. June 19, 1926: 317-323.) Lotka analyzed the work of 8216 authors taken from two indexes, the Decennial Index to Chemical Abstracts 1907-16 and Auerbach’s Geschichtstafeln der Physik, covering historical contributions up to 1900.

Probably because bibliometrics is a relatively new field, Lotka’s work was not cited in another journal article until 1941, and it was not called "Lotka’s Law" until 1949. It was not applied to other fields than science until 1973. How accurate of a predictor Lotka’s Law is and whether or not it is applicable to non-scientific fields is a matter of debate. Attempts to conduct large scale studies to prove or disprove its validity have been relatively few compared to the number of times it has been cited in the literature. Keeping in mind that this is not a mathematical formula, but a broad rule of thumb, it seems to hold true for large sample sizes.

Potter, William Gray. "Lotka's Law Revisited." Library Trends. Summer 1981: 21-39.
Rubin, Richard E. Foundations of Library and Information Science. 2000.

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