Application of Bradford's Law of Scattering to the Literature of Library & Information Science: A Study of Doctoral Theses Citations Submitted to the Universities of Maharashtra, India
Vijay G. Wardikar
Librarian
Mahila Mahavidyalaya,
Amravati, Maharashtra.
Email: vijaywardikar123@ rediffmail.com
&
Dr. Vaishali P. Gudadhe (Choukhande)
Associate Professor & Head
Department of Library& Information Science
Sant Gadgebaba Amravati University, Amravati.
vgudadhe020@gmail.com

Introduction
The scientific information comes through number of publications such as periodicals, journals, thesis etc. Among various sources, journal is one of the valuable primary source of information. Importance of journal literature as a source of nascent information, which covers new researchable information and ideas Information contained in the journal is usually published therefore it is an published primary source which provides new ideas, concept formula and new research results. Journal may cover the depth information on micro thoughts, comparison of subjects, depth study of subjects or new developments in subjects etc.
In the subject of any disciplines there are some journals which are frequently referred by the researchers because of the close relation between the subject of the journals and the areas of the research work. These highly cited journals are listed as core journals of the particular subject. The rising prices of periodicals, declining credit of Indian currency abroad and waning funds of the libraries have posed a great threat to the librarian to procure all the published materials in the field which has become possible with the help of bibliometrics.
The concept of core journals was first coined by S.C. Bradford in 1934 which is popularly known by Bradford Law of Scattering. Bradford law of scattering describes how the literature on a particular subject is scattered or distributed in the journals. The law is based on an investigation performed in 1933 by L. Jones in the Science Museum Library, London. It was first reported in 1934 in the Journal ''Engineering'' by Bradford and subsequently in book entitled ''Documentation'' by the same author in 1948. Bradford formulated his law as follows.
''If scientific journals are arranged in order of decreasing productivity of articles on a given subject, they may be divided into a nucleus of periodicals more particularly devoted to the subject and several groups or zones containing the same articles as the nucleus, when the number of periodicals in the nucleus and succeeding zones will be as
1: n: [n.sup.2], where 'n' is a multiplier."

Objectives of the Study
The main objectives of the study were:
(i) To prepare a rank list of most cited journals by the doctoral researchers in Library and Information Science of Maharashtra.
(ii) To study the phenomenon of scattering for citation data.
(iii)To test the appropriateness of verbal and graphical formulation of Bradford's Law of Scattering.

Methodology
A total of 798 journals containing 5467 references collected from 138 doctoral theses submitted to Universities in Maharashtra State, India were arranged in descending order of productivity. the study treated references as items and journals as sources. The verbal formulation was tested by three separate parameters for carrying the different number of periodicals, while for testing the appropriateness of graphical formulation, the natural log value of the cumulative number of journals was calculated for plotting the graph.
3.1 Bradford's Law of Scattering
Bradford's Law of Scattering describes a quantitative relation between journals and the papers published in these. S.C. Bradford's, Chief Librarian at the London Science Museum, made statistical analysis of two geophysics bibliographies, the Current Bibliography of Applied Geophysics (19281931) and the Quarterly Bibliography of Lubrication (19311933). He tested the journals containing references to these fields in their descending order of productivity and then divided the articles into three approximately equal zones. He termed the first one as the nuclear zone, which is highly productive; the second zone moderately productive zone; and the third as low productive zone. Bradford discovered regularity in calculating the number of titles in each of the three zones. On the basis of the observations, Bradford concluded that the ratio of the titles of journals in successive zones followed a common pattern Bradford's verbal formulation stated that if scientific journals are arranged in order of decreasing productivity of articles on a given subject, they may be divided into a nucleus of periodicals more particularly devoted to the subject and several groups or zones containing the same articles as the nucleus, when the number of periodicals in the nucleus and succeeding zones will be as 1: n: n2, where 'n' is a multiplier.
Based on Bradford's observations, Brookes suggested the following linear relation to describe the scattering phenomenon as:
F(X) = a + b logx
Where is the cumulative number of references contained in the first x most productive journals, and and are constants. This is the most widely used formulation of Bradford's Law.
Vickery extended the verbal formulation to shows that it can be applied to any number of zones of equal yield. Leimkuhler issued the following simple function for Bradford's distribution, which was named after him:
R(r) + a log(1 + br)
Where is the cumulative number of articles contributed by journals ranked 1 through r, and are parameters.
Similarly, Brooke's derivation for journal productivity takes the form
R(r) = a og (b/r)
Further, Wilkinson noticed that the formulae provided by Leimkuhler and Brookes did not really describe the same phenomenon. Starting from the late 1960s, several mathematical formulations, models, and syntheses of previous statements related to Bradford's Law have been put forth, but very little agreement exists about which model is the best. Brookes expression of the Bradford's distribution has however gained wide acceptance.
3.2 Theoretical Aspects of Bradford's
Law:
Bradford's Law Scattering describes a quantitative relationship between journals and the papers they publish. It explains that, only a small number of core journals will supply the nucleus of papers on a given topic which accounts for a substantial percentage (1/3) of the articles, to be followed by a second larger group of journals that accounts for another third, while a much larger group of journals picked up the last third.
There are two most widely recognised formulations of the so called Bradford's Law: the verbal formulation which is derived from the verbal statement of Bradford's Conclusion, and the graphical formulation, which is an empirical expression derived from the graphical survey of a distribution of periodicals.
Bradford's did not give a mathematical model for his law. Models were suggested later by Brookes, Vickery and Leimkuhler. Several authors, while explaining the scattering of articles in journals, have formulated many different models of Bradford's Law. Leimkuhler developed a model based on Bradford's verbal formulation as:
R(r) = alog(1 + br) (1)
R = 1,2,3 ... ...
While exaplaining Leimkuhler's Law, Egghe Shows that
a = [Y.sub.0]/logk (2)
b = k1/[r.sub.0] (3)
where, [r.syb.0] is the number of sources in the first Bradford's group, [Y.sub.0] is the number of items in every Bradford group (all these group of item being of equal sizes). and ' is the Bradford multiplier.
R(r) is the cumulative number items produced by the sources of rank 1,2,3....... r and a and b are constants appearing in the law of Leimkuhler. In forming Bradford groups, it is shown that the number of groups ( is a parameter that can be chosen freely.
Egghe has shown the mathematical formula for calculating the Bradford Multiplier ' as
K = [([e.sup.y] [y.sub.m]).sup.1/p] (4)
Where g is Euler's number
([e.sup.g = 1.781])
If the sources are ranked in decreasing order of productivity, then +, is the number of items in the most productivity sources.
Then [y.sub.m] are :
[y.sub.0 = [y.sub.m.sup.2]logk (5)
and
[r.sub.0 = (k1) [y.sub.m] (6)
Once is chosen, the value of k can
be calculated by using
k = [(1.781[y.sub.m]).sup.1/p] (7)
and [y.sub.0 = A/P]
where A denotes the total number of articles
Let denote the total number of journals in Bradford group, there are [r.sub.0][k.sup/i1] sources ( i = 1,2,3.......p)
T = [r.sub.0] + [r.sub.0]k [r.sub.0][k.sup.2]+ ......+ [r.sub.0][k.sup.p2] (8)
So, [r.sub.0] = T/1 + k + [k.sup.2] + ... ... ... . .+ [k.sup.p1] = T(k1)/([k.sup.p]1) (9)
Since A and T are known from the data set and are calculated, once p is calculated by the formula (7)
Gupta and Suresh Kumar have given the theoretical aspects of Bradford's Law and studied its applicability using the above method. According to Brooke's to test the conformity of Bradsford's Law, one should meet the following three implicit conditions:
(i)In dividing the journals into zones, the number of articles in each zone must remain constant.
(ii)The Bradford multiplier k must be > 1.
(iii)The Bradford multiplier must remain approximately constant.

Analysis & Interpretation
4.1 Ranking Of Journals
Core journals ranking studies are usually made to help in the selection of journals and assessing the importance of one or more journals in a particular subject field. the journals are arranged in their respective descending order of frequency. The journal contibuting the largest number of articles is ranked as number one, next is ranked two and so on.
Rank list of Journals was prepared in Table 1 total 62 ranks were awarded. Among these 'Annals of Library Science and Documentation' have first rank with 207 citations and followed by 'College and Research Library' with 184 citations, 'Herald of Library Science' occupied third rank with 160 citations, 'ILA Bulletin' with 158 citations took place fourth rank and fifth rank have...