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Russell C. Coile
(papers) was proportional to the logarithm of the corresponding number of
sources. Unfortunately, he restated in one sentence his law of distribution
of papers on a given subject in scientifi c periodicals using the words `the
number of periodicals' instead of writing explicitly `the running total of
numbers of periodicals.' Vickery (7), Leimkuhler (8), and Wilkinson (9),
(10), have taken this one sentence and developed a different interpretation
of Bradford's law from that of Brookes (11).
Davis
Harold T. Davis (12), Appendix D, examined Dresden's (13) data on
scientifi c productivity of mathematicians and Lotka's (2) data on chemists
and physicists in an effort to fi nd statistical support for a `Pareto law'
version of a general law of inequality. He fi tted a curve (equation 3) where
y is the number of persons contributing at least x contributions, to Arnold
Dresden's data on 278 mathematicians who wrote 1,102 papers during a
25-year period in Chicago. However, the slope of -2.11 is larger than the
usual -1.5 associated with the Pareto law.
Williams
C. B. Williams (14), Appendix E, of the Rothamsted Experimental
Station proposed a geometric series to estimate the number of biologists
publishing one paper, two papers, etc. This series is equation 4. If N is the
total number of papers and S is the total number of authors, nl and x are
determined from the expressions in equations 5 and 6.
Fisher
C. B. Williams (14), Appendix F, also examined the logarithmic series
fi rst suggested by Sir Ronald A. Fisher (15) in biological research on the
frequency of butterfl y species on the Malayan peninsula. The series is
equation 7, where n
1
is the number of authors publishing one paper and
x is a constant less than unity. If the total number of authors is S and
the total number of papers is N, then n
1
and x can be determined from
equations 8 and 9.
Simon
Herbert A. Simon (16), Appendix G, proposed a distribution function
for scientifi c publications which he called the `Yule' function because of
prior research by G. Udny Yule (17). Yule had developed a Beta-function