{"id":45,"date":"2018-07-06T12:17:38","date_gmt":"2018-07-06T12:17:38","guid":{"rendered":"http:\/\/liscp10.epgpbooks.inflibnet.ac.in\/?post_type=chapter&p=45"},"modified":"2018-12-07T05:33:06","modified_gmt":"2018-12-07T05:33:06","slug":"classical-law-of-bibliometrics","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/liscp10\/chapter\/classical-law-of-bibliometrics\/","title":{"rendered":"Classical Law of Bibliometrics"},"content":{"raw":"
\"epgp<\/a>\r\n<\/span><\/div>\r\n
\r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\n \r\n\r\nI. Objectives<\/strong>\r\n\r\n \r\n\r\nAfter going through this study material you will\r\n\r\n \r\n\r\n\u2022\u00a0\u00a0\u00a0\u00a0\u00a0 know the classical laws of Bibliometrics;\r\n\r\n\u2022\u00a0\u00a0\u00a0\u00a0\u00a0 learn the formulas pertaining to the laws;\r\n\r\n\u2022\u00a0\u00a0\u00a0\u00a0\u00a0 be able to apply the laws in library environment; and\r\n\r\n\u2022\u00a0\u00a0\u00a0\u00a0\u00a0 educate yourself as to how these laws are verified.\r\n\r\n \r\n\r\nII. Learning Outcome<\/strong>\r\n\r\n \r\n

After completion of this module, you will be familiar with three classical laws of Bibliometrics and their applications. Particularly, you have learnt Bradford's law, Lotka's law and Zipf's law.<\/p>\r\n \r\n\r\nIII. Module Structure<\/strong>\r\n\r\n \r\n\r\n1.\u00a0\u00a0 Introduction\r\n\r\n2.\u00a0\u00a0 Bradford's Law of Scattering\r\n

2.1 Explanation<\/p>\r\n

2.2 Verification<\/p>\r\n

2.3 Bradford\u2019s Bibliograph<\/p>\r\n

2.4 Uses<\/p>\r\n3.\u00a0\u00a0 Zips\u2019s Laws\r\n\r\n5.\u00a0\u00a0 Summary\r\n\r\n6.\u00a0\u00a0 References\r\n\r\n \r\n\r\n1. Introduction<\/strong>\r\n\r\n \r\n

Classical laws in Bibliometrics include Bradford\u2019s law of scatter [1, 2, 3], three laws of Zipf [28, 29, 30] and Lotka\u2019s law [16]. These are purely scientific laws which are well-established formulas and the concepts embedded in them are less likely to change with time. Moreover, their validity can be verified scientifically.<\/span><\/p>\r\n \r\n

2. Bradford's Law of Scattering<\/strong><\/p>\r\n \r\n

The law was propounded by Samuel Clement Bradford (1878-1948), a British librarian, mathematician and document lists at the Science Museum in London after a laborious study of scientific literature in mid-1930s. After examining the distribution of scientific literature in periodicals and their coverage in abstracting and indexing periodicals he realized that the distribution of literature follow a particular pattern [1, 2]. He opined that \u2018the nucleus of periodicals devoted to the given subject must contain, individually, more articles on that subject than periodicals dealing with related subjects\u2019 [3]. \u2018In consequence, it is possible to arrange periodicals in zones of decreasing productivity, in regard to papers on a given subject, and the numbers of periodicals in each zone will increase as their productivity decreases\u2019 [3]. He described a scattering pattern of journals in the area of applied geophysics and lubrication. He plotted the partial sums of references against the natural logarithm of the partial sum of numbers of journals, and he noticed that the resulting graph is a straight line. On the basis of this observation, he suggested the following linear relation to describe a scattering phenomenon [2]<\/span><\/p>\r\n \r\n

F(x) = a + b log x.<\/span><\/p>\r\n \r\n

F(x) is the cumulative number of references contained in the first x most productive journal; a and b are constants. The following figure is a hypothetical, but typical, log-linear curve (as described by Bradford) showing aggregates of articles on a given subject corresponding to the number of journals. This type of a curve is usually called a Bradford curve; it is shown in page 3.<\/span><\/p>\r\n \r\n

P1 in the figure is the point at which the straight line part of the curve begins. Draw Y1P1, Y2P2, and Y3P3 such that they are parallel to the X-axis and OY1 = Y1 Y2 = Y2 Y3. Draw P1X 1, P2X 2, and P3 X3 such that they are parallel to Y-axis. Since P1P3 is a straight line and since Y 1Y2 = Y 2Y 3, X1X2 and X2X3 are equal, say r units. Let the distance between O and X is s units. Thus, if \u03b1, \u03b2 and \u00a0are the positive real numbers corresponding respectively to the logarithmic abscissa OX1, OX2 and OX3, we have, log \u03b1 = s, log \u03b2 = s + r, and log \u00a0= s+2r. That is,<\/span><\/p>\r\n \r\n

\u03b1\u00a0 = 10s, \u03b2 = 10r+s = 10s.10r , and \u00a0= 10s+2r = 10s.102r<\/span><\/p>\r\n \r\n

Substituting n = 10r, we see that the natural numbers \u03b1, \u03b2, and \u03b3 are related to each other as 1 : n : n2. On the basis of this relationship and also since OX1 represents a number of periodicals in a subject area Bradford stated his law as t \u201cIf 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 subject, they and several groups or zones\u201d<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\nIn X-axis: Partial sum of Journals (in log scale)\r\n\r\n \r\n

In Y-axis: Partial sum of articles contained in X top most journals (in linear scale) Containing the same number of articles as the nucleus, when the zones will be 1:n:n2 \u2026.\u201d<\/p>\r\n \r\n

This is called Law of Scattering or Bradford's law. He has obtained the partial sums of the journals only after the journals are ranked according to the number of articles they publish. Bradford in 1948 summarized his earlier observations in a book which contained a theoretical derivation of his law of scattering.<\/p>\r\n \r\n

Interestingly, Bradford in 1948 [3] derived his law in a different approach. In this approach, he assumed that the collection of journals is ranked (or arranged) in decreasing productivity. Productivity of a journal is implicitly defined in terms of the number of articles, in a given subject, it contains. Divide these journals into k zones. Let mk be the number of journals in the kth zone. Let rk be the average number of articles per journal in the kth zone. m1r1, m2r2,\u2026.. and mkrk are the total productivity of 1st, 2nd, 3rd, \u2026 kth zone respectively. Zones are formed such that:<\/p>\r\n\r\n<\/div>\r\nm1r1, = m2r2= m3r3 = \u2026\u2026\u2026= mkrk\u00a0 \u00a0 (A)<\/span>\r\n

\r\n\r\nSince\r\n\r\n<\/div>\r\n
\r\n\r\nr1> r2 > r3 > \u2026.. > rk\u00a0 and\u00a0 m1r1, = m2r2= m3r3 = \u2026\u2026\u2026= mkrk\r\n\r\n<\/div>\r\nWe have<\/span>\r\n
\r\n\r\nm1< m2< m3 < \u2026\u2026\u2026< mk\r\n\r\n<\/div>\r\nFrom (A), we have<\/span>\r\n\r\n \r\n\r\nmi\u00a0 = \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0i = 2,3,4,\u2026\u2026\u2026.k.<\/span>\r\n\r\n \r\n\r\nThat is,<\/span>\r\n\r\nDefining<\/span>\r\n\r\ni = 2,3,4, \u2026.. k<\/span>\r\n\r\n \r\n\r\nWe have<\/span>\r\n
\r\n\r\n\"\"\r\n\r\nBradford, in his analysis considered only three zones (k = 3). He thus had\r\n\r\n \r\n

m2 = n1m1 and m3 = n1n2m1<\/p>\r\n \r\n

He then stated, \u201c \u2026 we know no reason why n 1 and n should differ and the simple supposition we could make is that they are equal.\u201d Say, n1 = n2 = n. (Bradford (1948)). Thus, m3 = n2 m1. Therefore, he argued that the ratio of the zone sizes will be as 1 : n: n2 which is again the relationship developed in his earlier work.<\/p>\r\n \r\n

Since then many have worked in this area and came out with different approaches as well as different explanations. The author of this Unit discusses some of these works in Unit 6. Vickery [27], Bookstein [4], Brookes [5,6,7], Hubert [11,12,13], Leimkulher [15], Egghe [10], Naranan<\/p>\r\n \r\n

[17]\u00a0\u00a0 and many others have given different explanations of this Law; Some of these works were also discussed by Ravichandra Rao [21]; he also observed in one of his papers that Baradford's assumption of n1 = n2 = n is unlikely correct.<\/p>\r\n \r\n\r\n2.1 Explanation<\/strong>\r\n\r\n \r\n

Bradford conducted his study with scientific periodicals only. In certain cases the law holds good for non- scientific periodicals also. The law will be applicable if the articles pertain to a specific subject. If articles of several subjects are taken together for testing the Bradford law, the test is likely to fail. Though the definition speaks of several zones, the formula given in the definition takes care of three zones only. In certain cases the law may be applicable beyond three zones even. Bradford called the first zone as nucleus and other zones as succeeding zones. We may call the first zone as Core, second zone as Allied, and the third zone as Alien, to identify each zone specifically. Let us take a concrete example to understand the law properly.<\/p>\r\n \r\n

Suppose on a subject there are 600 articles. If these articles are equally divided into three zones, then each zone will have 200 articles. Obviously, the nucleus will also have 200 articles. If these articles pertain to five journals, the articles of the next group numbering 200, may pertain to 10 journals, 15 journals or more. If the article of the next zone (allied zone) pertain to 15 journals, then it is likely that the article of the 3rd zone (alien zone) will pertain to 45 journals. Now, we find that the articles of the three succeeding zones belong to 5, 15, and 45 journals. If the numbers are divided by 5, we get 1, 3 and 9, that is 1, 3, and 32 which represents Bradford\u2019s law,<\/p>\r\n \r\n

i.e. 1:n:n2. In Bradford\u2019s study, we generally get an approximate value of n. In reality, the articles in the three zones are only roughly equal.<\/span><\/p>\r\n \r\n

In a situation where the data ideally suits Bradford formulation, the set of journals, say, numbering 310, would be divided as 10, 10x5, and 10x5x5. The first 10 journals will belong to the core zone, the next 50 to the allied zone, and the last 250 to the alien zone. The number of papers in each zone will be the same. In reality, we do not get such data that perfectly satisfies the law. In most cases, the data satisfies the law roughly.<\/span><\/p>\r\n \r\n

2.2 Verification<\/strong><\/p>\r\n \r\n

It involves the following steps:<\/span><\/p>\r\n \r\n

i. A comprehensive bibliography on a narrow subject is to be taken. An already compiled bibliography may be taken as did Bradford. Otherwise a bibliography can be compiled. While compiling the bibliography, care should be taken to include only journal articles. Articles presented in a conference, in festschrift volumes, in collected works, etc. are to be excluded.<\/span><\/p>\r\n \r\n

The term \u2018comprehensive bibliography\u2019 needs a bit explanation. A question often asked as to the optimum number of journal articles in the bibliography that would be suitable for verifying Bradford\u2019s law. The answer is hard to come by. In Bradford\u2019s studies in one bibliography there were 1332 journal articles, and in the other 395 journal articles. If the bibliography contains around 500 articles, it is likely to be a good sample.<\/span><\/p>\r\n \r\n

If a compiled bibliography is taken, then only the journal articles are to be included leaving aside all other items such as books, conference documents and so on.<\/span><\/p>\r\n \r\n

ii. If the work is done manually, then cards are to be prepared for the entries required for the purpose. Otherwise the required entries may be entered in a computer in Excel sheet or any other suitable software.<\/span><\/p>\r\n \r\n

iii.The cards or entries are to be sorted according to periodicals.<\/span><\/p>\r\n \r\n

iv.Now, the periodicals are to be sorted according to the frequencies. The periodical with the highest frequency is to be ranked 1st, followed by others with descending frequencies.<\/span><\/p>\r\n \r\n\r\n \r\n

v.The data is to be tabulated as per the Table 1 given below.<\/span><\/p>\r\n \r\n

vi.The validity is to be tested according to the formula given above. The data in Table 1 is Bradford\u2019s data.<\/span><\/p>\r\n \r\n

Table 1 needs some explanations. The periodical having the largest number of articles, i.e. 93, ranks first followed by periodicals accounting for descending number of articles. In the ranking you will notice that sometimes two or more periodicals were responsible for the same number of articles. For example, four periodicals ranked 13th with 16 articles each. In such a case, all are\u00a0<\/span>given the 13th rank, because if we give all the periodicals 10th rank, then it would seem as if there are 10 periodicals, in fact there are 13 periodicals. By seeing the last rank in the Table, e.g. 326, we easily know the total number of periodicals contributing to the literature in the field. In actual studies the name of the periodical is also given along with the rank number. When the number of periodicals is very high, to shorten the size of the Table, the names of the periodicals are given, say up to 50th rank or even less.<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Rank<\/strong><\/td>\r\nNo. of Periodical\/s<\/strong><\/td>\r\nNo. of Articles<\/strong><\/td>\r\nCumulative Total of\u00a0Articles<\/strong><\/td>\r\n<\/tr>\r\n
1<\/td>\r\n1<\/td>\r\n93<\/td>\r\n93<\/td>\r\n<\/tr>\r\n
2<\/td>\r\n1<\/td>\r\n86<\/td>\r\n179<\/td>\r\n<\/tr>\r\n
3<\/td>\r\n1<\/td>\r\n56<\/td>\r\n235<\/td>\r\n<\/tr>\r\n
4<\/td>\r\n1<\/td>\r\n48<\/td>\r\n283<\/td>\r\n<\/tr>\r\n
5<\/td>\r\n1<\/td>\r\n46<\/td>\r\n329<\/td>\r\n<\/tr>\r\n
6<\/td>\r\n1<\/td>\r\n35<\/td>\r\n364<\/td>\r\n<\/tr>\r\n
7<\/td>\r\n1<\/td>\r\n28<\/td>\r\n392<\/td>\r\n<\/tr>\r\n
8<\/td>\r\n1<\/td>\r\n20<\/td>\r\n412<\/td>\r\n<\/tr>\r\n
9<\/td>\r\n1<\/td>\r\n17<\/td>\r\n429<\/td>\r\n<\/tr>\r\n
13<\/td>\r\n4<\/td>\r\n16<\/td>\r\n493<\/td>\r\n<\/tr>\r\n
14<\/td>\r\n1<\/td>\r\n15<\/td>\r\n508<\/td>\r\n<\/tr>\r\n
19<\/td>\r\n5<\/td>\r\n14<\/td>\r\n578<\/td>\r\n<\/tr>\r\n
20<\/td>\r\n1<\/td>\r\n12<\/td>\r\n590<\/td>\r\n<\/tr>\r\n
22<\/td>\r\n2<\/td>\r\n11<\/td>\r\n612<\/td>\r\n<\/tr>\r\n
27<\/td>\r\n5<\/td>\r\n10<\/td>\r\n662<\/td>\r\n<\/tr>\r\n
30<\/td>\r\n3<\/td>\r\n9<\/td>\r\n689<\/td>\r\n<\/tr>\r\n
38<\/td>\r\n8<\/td>\r\n8<\/td>\r\n753<\/td>\r\n<\/tr>\r\n
45<\/td>\r\n7<\/td>\r\n7<\/td>\r\n802<\/td>\r\n<\/tr>\r\n
56<\/td>\r\n11<\/td>\r\n6<\/td>\r\n868<\/td>\r\n<\/tr>\r\n
68<\/td>\r\n12<\/td>\r\n5<\/td>\r\n928<\/td>\r\n<\/tr>\r\n
85<\/td>\r\n17<\/td>\r\n4<\/td>\r\n996<\/td>\r\n<\/tr>\r\n
108<\/td>\r\n23<\/td>\r\n3<\/td>\r\n1,065<\/td>\r\n<\/tr>\r\n
157<\/td>\r\n49<\/td>\r\n2<\/td>\r\n1,163<\/td>\r\n<\/tr>\r\n
326<\/td>\r\n169<\/td>\r\n1<\/td>\r\n1,332<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTable 1- Productivity-wise Distribution of Periodicals<\/strong>[Based on Current Bibliography of Applied Geophysics 1928-1931(1)]<\/strong>\r\n\r\n \r\n\r\nTo test the law, we shall now divide the number of articles in three equal parts. If we do so, then each part will have 1332\u00f73 = 444 articles. This gives us the indication that each zone will have 444 articles. In Table 1 the number 444 is missing. It comes in between 429 and 493. The number of articles up to 9th rank is 429. Four periodicals occupy the 10th to 13th rank with 16 articles each. Adding 16 to 429, we get 445 which is quite close to 444. Thus, the first 10 periodicals accounting for 445 articles form the first zone. It is to be noted that the number of periodicals as well as articles should always be in whole numbers and not infractions. To decide the number of periodicals in the second zone, 444 is multiplied by 2, and we get 888. In Table 1 the cumulative number 888 is missing. It follows 868. The first 56 periodicals account for 868 articles. The next 11 periodicals are having 6 articles each. That means, the first 59 periodicals are accounting for 886 articles which is close to 888. Hence, in the second zone we have 59-10=\u00a0\u00a0\u00a0 49 periodicals and 886-445 = 441 articles. In the first two zones, there are 10+49 = 59 periodicals and 445+441 = 886 articles. Hence, in the third zone, there will be 326 \u2013 59 = 267 periodicals, and 1332- 886 = 446 articles.<\/span>\r\n\r\n<\/div>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Zone<\/strong><\/td>\r\nNo. of Periodicals<\/strong><\/td>\r\nNo. of Articles<\/strong><\/td>\r\n<\/tr>\r\n
1st Zone<\/td>\r\n10<\/td>\r\n445<\/td>\r\n<\/tr>\r\n
2nd Zone<\/td>\r\n49<\/td>\r\n441<\/td>\r\n<\/tr>\r\n
3rd Zone<\/td>\r\n267<\/td>\r\n446<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Table 2 \u2013 Distribution of Articles according to Zones<\/strong><\/p>\r\n \r\n

From the data, we get the value of n as 49\u00f710 = 4.9. Multiplying 49 by 4.9, we get 240 which is close to 267. The ratio of the periodicals is 10:49:267 which is roughly 1:5:52.<\/p>\r\n \r\n\r\n2.3 Bradford\u2019s Bibliograph<\/strong>\r\n\r\n \r\n

The Bibliograph [Fig. 1] can be obtained by plotting R(n) on a linear scale along the Y axis and n on a logarithmic scale along the x axis. It is best drawn on semi-log graph paper. The graph is J-shaped and turns into a straight line from a particular point.<\/p>\r\n \r\n\r\n2.4 Uses<\/strong>\r\n\r\n \r\n

i. It depicts the spread of the journal literature of the subject. The subjects of the journals harboring the literature shows how enormous are the spread and the journal variety.<\/p>\r\n \r\n

ii. It helps identify the core periodicals in a subject. Also it throws light on the allied and alien periodicals pertaining to the subject.<\/p>\r\n \r\n

iii. It produces a ranked list placing the journals according to their productivity in descending order. It helps a great deal in the selection of periodicals.<\/p>\r\n \r\n

iv. Due to budget crunch when certain periodicals need to be deleted, usually the lower ranked periodicals are deleted.<\/p>\r\n \r\n

3. Zips\u2019s Laws<\/strong><\/p>\r\n \r\n

Zipf\u2019s laws [28, 29, 30] are related to the usage of words by individuals. Interestingly, the phenomenon follows a scientific law. Most probably, the French stenographer, Jean-Baptiste Estoup (1858-1950), is the first individual to observe the hyperbolic nature of the frequency of word usage. Estoup recorded his study in his book Gammes Stenographiques published from Paris in 1916. George Kingsley Zipf (1902\u20131950), the American linguist, saw the 4th edition of Estoup\u2019s book and worked further on it and arrived at his laws in 1935.<\/span><\/p>\r\n \r\n

3.1 First - Definition<\/strong><\/p>\r\n \r\n

\u201cIf the number of different words occurring once in a given sample is taken as x, the number of different words occurring twice, three times, four times, n times in the same sample , is respectively 1\/22 , 1\/32, 1\/42, ...1\/n2 of x, up to, though not including, the few most frequently used words; that is , we find an unmistakable progression according to the inverse square, valid for well over 95% of all the different words used in the sample\u201d [13, Preface, p. vi]. Basing this phenomenon, Zipf developed the formula ab2 = k, where a is the number of words occurring b times, and k is a constant.<\/span><\/p>\r\n \r\n

It is observed that the equation satisfies quite well with the less frequently used words of the sample, which are much more in number compared to more frequently used words in the sample [30, p.47].<\/span><\/p>\r\n \r\n

3.1.1 Explanation<\/strong><\/p>\r\n \r\n

Suppose in a particular writing, the number of words occurred only once is 1440. In that case the number of words occurring 2, 3 and 4 times is likely to be 1440\u00f722, 1440\u00f732, and 1440\u00f742, that is 360, 160, and 90. Now, using this data and the formula, we can determine the value of k. We know, 1440 words have occurred only once, that means a = 1440, b = 1. Therefore, k= ab2 = 1440 x 12 = 1440. Now, using the value of k, we can find out how many words have occurred 5 times, 6 times or any other number of times. In this case, the formula will be a = k\/b2. Let us try to find out how many words have occurred 6 times. We know k = 1440, and b = 6. Putting these values in the aforesaid equation, we get a = 1440\/62 = 40; around 40 words are likely to occur 6 times each. It is to be noted that the values will change with every piece of writing, literary or non-literary.<\/span><\/p>\r\n \r\n

3.1.2 Verification<\/strong><\/p>\r\n \r\n

The manual verification of the law is highly laborious and time consuming. The best way to verify the law is to take the help of information technology as detailed under the second law.<\/span><\/p>\r\n \r\n

3.1.3 Uses<\/strong><\/p>\r\n \r\n

The use of this law in library and information science (LIS) is still negligible, maybe because it is not generally taught in our LIS courses. It will be useful in identifying the style of writing of an author. The only case I know about its application is that of a student of the University of Calcutta who is trying to find out to what extent the writing of a noted Bengali scientist has been\u00a0<\/span>influenced by a foreign lady. The details will be known when the thesis is submitted and degree awarded.<\/span><\/p>\r\n \r\n

3.2 Second Law - Definition<\/strong><\/p>\r\n \r\n

Zipf defined the second law as \u2018The conspicuousness or intensity of any element of language is inversely proportionate to its frequency. Using X for frequency and Y for conspicuousness (rank) \u2018 the law can be mathematically expressed as<\/span><\/p>\r\n\r\n<\/div>\r\n

\r\n\r\n\"\"\r\n\r\n \r\n\r\n3.2.1 Explanation<\/strong>\r\n\r\n \r\n\r\nThe words conspicuousness or intensity can be simply termed as rank, and element can be simply taken for word. The definition can be stated in simpler terms as the rank of any word of a language is inversely proportional to the frequency of its usage. The lower the rank, the higher will be the frequency.\r\n\r\n \r\n\r\n3.2.2 Verification<\/strong>\r\n\r\n \r\n

The verification of the Law came through the use of Miles L Hanley\u2019s Index of Words for James Joyce\u2019s Ulysses. Zipf found that the rank frequency word distribution \u2018approximate the simple equation of an equilateral hyperbola: r x f = C\u2019` [14, p.24], where r indicates rank and f frequency\u201d. C in the equation is the constant. The Product in Table 3 represents constant. The constant in the case of this Law is not a fixed number, but close to it. A part of the result of Zipf\u2019s experiment in reproduced below in Table 3.<\/p>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Rank (r)<\/strong><\/td>\r\nFrequency (f)<\/strong><\/td>\r\nProduct (c)<\/strong><\/td>\r\n<\/tr>\r\n
10<\/td>\r\n2653<\/td>\r\n26530<\/td>\r\n<\/tr>\r\n
20<\/td>\r\n1311<\/td>\r\n26220<\/td>\r\n<\/tr>\r\n
30<\/td>\r\n926<\/td>\r\n27780<\/td>\r\n<\/tr>\r\n
40<\/td>\r\n717<\/td>\r\n28680<\/td>\r\n<\/tr>\r\n
50<\/td>\r\n556<\/td>\r\n27800<\/td>\r\n<\/tr>\r\n
100<\/td>\r\n285<\/td>\r\n28500<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Table 3: Distribution of Words in James Joyce\u2019s Ulysses<\/strong><\/p>\r\n \r\n

A manual verification of the Law is highly laborious and time consuming. In the absence of Hanley\u2019s Index of Words for James Joyce\u2019s Ulysses Zipf\u2019s experiment would have been really difficult. The advent of information technology has given us devices with which we can verify the Law without much difficulty. The steps involved in the verification are given below [24].<\/p>\r\n\r\n