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).
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.
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.
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
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
and x can be determined from
equations 8 and 9.
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