College and Research Libraries By C H A R L E S F . G O S N E L L Obsolescence of Books in College Libraries Dr. Gosnell is librarian of Queens Col- lege, Flushing, N.Y., and associate in library service, School of Library Service, Columbia University. This report is based on a thesis submitted at New York University in September 194.3. THE PROBLEM of maintaining efficient college library book collections re- quires consideration of the effects of obsolescence and planning for the segre- gation or withdrawal of obsolete mate- rials. Heretofore obsolescence has been considered principally with reference to individual and specific titles rather than to groups of books, but no general plan- ning can be done except on a quantitative basis. For evaluation of libraries by ac- crediting agencies, it is important to have a fairly simple and precise basis for com- parison of libraries and lists of books with regard to obsolescence or the presence of obsolete material. By quantitative analysis, primarily of three lists of recom- mended books and secondarily by analysis of library collections, the writer believes that he has presented a clearer picture of obsolescence than has previously been available. Tentative conclusions in the form of comparative rates of obsolescence for various groups of material are re- ported as suggestive for further study. Several years ago the writer called attention to the fact that Shaw and M o h r - hardt showed marked preference for newer books in their lists of books for college libraries.1 He pointed out that this preference fell into a rough pattern of distribution which was essentially the same in each of the lists and suggested several questions as to the nature and significance of these curves of distribu- tion. H e now presents a progress report of his efforts to answer some of these questions. T h e fundamental assumption in this study is that the compilers of the three select lists consciously or unconsciously followed certain principles of choice which are significant without reference to the particular titles chosen and that these principles may be discovered and studied by a form of documentary analy- sis of the lists. T h e principle of imme- diate interest is that of preference for the newer or more recent titles. " N e w e r " and "more recent" are of course relative terms referring in each case to the par- ticular time the list was compiled. Con- versely, this is the principle of obsolescence — t h a t older books in general have less value for use in the college library. Statistical Bibliography T h e second assumption is that mere masses of books (or titles) may be 1 " B o o k s f o r College L i b r a r i e s . " Library Journal 65:531-32, June 15, 1940. " V a l u e s and D a n g e r s of Standard Book and Peri- odical Lists f o r College L i b r a r i e s . " College and Re- search Libraries 2:216-20, June I94 1 - MARCH, 1944 115 analyzed for certain characteristics with- out reference to their individual titles. Statistical bibliography is a relatively new or uncultivated field. But the astro- nomical proportions to which some of our libraries, their catalogs, and bibliographies in general are growing must force li- brarians to consider collections of books as populations. A typical example of what can be done is the study of "certain biological properties" of literature by Wilson and Fred.2 T h i s assumption demands that individ- ual titles, especially the exceptional (and therefore more noteworthy) ones, be forgot; that attention be to the group as a whole—its averages and general trends. T h e larger the groups, the greater the play of many factors and the more reliable the conclusion. L i f e in- surance mortality tables are not primarily based on infant deaths or the longevity of octogenarians but on these and all others of the population. A study of book obsolescence or mortality will not depend primarily upon ephemera or classics but upon all kinds of books. T h e very multi- plicity of causes of death seems to lend stability to the human mortality rate. T h e causes of book mortality or obso- lescence are many, varying from pure fad through extension ef scientific knowledge, technological changes, to fundamental changes in our civilization. T h e object of the present study has been, not to dis- cover or classify these causes, but to analyze their total effect. Deterioration or destruction of books is not true obso- lescence, and no consideration has been given to the physical properties or condi- tions of books. 2 Wilson, P . W „ and F r e d , E. B . " T h e Growth C u r v e of a Scientific L i t e r a t u r e ; Nitrogen Fixation by P l a n t s . " Scientific Monthly 41:240-50, September I 9 3 S - Distribution of Imprint Dates T h e fundamental data of the study were the dates of publication of titles included in the three lists. T h e signifi- cant features of the distribution curves3 were: ( i ) There is a rapid rise in num- ber of titles per year, going backward for the first few years preceding the date of issue of each respective list; (2) T h e maximum number of titles per year oc- curs within three years preceding the publication of each list; ( 3 ) A f t e r this maximum is reached, the number of im- prints per year drops rapidly at first and then more slowly, approaching the base line of zero asymptotically in the early years. T h e initial rise may be ascribed to lag in selection of books. T h i s lag is due to delay in appearance of reviews and acceptance by scholars. T h e drop, rapid at first but slower as the age of remaining titles increases, is expressive of a preference for newer books over old or rejection of older titles for the newer, because the older ones have become obso- lete. T h i s pattern is repeated independently for each of the three lists. T h e latter part does not show in the Shaw supple- ment for 1931-38, because, as a sup- plement, titles over nine years old were automatically excluded. T h e pattern is not markedly affected by the rate of book production as derived from annual tables in the Publishers' Weekly.4 It is a func- tion of the age of the titles at the time each list was compiled rather than of any other observed variables. From the fall in the curves it is im- mediately evident that the older a title is at a given time of selection, the less 3 Illustrated in College and Research Libraries 2:218, June 1941. 4 " U . S. Book Production, 1920-1939." Publishers' Weekly 139:232, Jan. 18, 1941. v 116 COLLEGE AND RESEARCH LIBRARIES are its chances of being selected or of surviving the selective process. In gen- eral, each preceding year back from the date of selection is represented by fewer titles. T h a t is, if in a given subject group there are one hundred titles 23 years old and ninety titles 24 years old, the rate of obsolescence between age 23 and 24 is 10 per cent. If a similar select list were to be pre- pared one year later, the group of one hundred would have become one year older (from 23 to 24) and, suffering the same rate of obsolescence, be reduced to ninety. A n d if the rate from age 24 to 25 were approximately the same, the group of ninety would drop to approxi- mately eighty-one. A n d similarly, the drop from eighty-one would be to sev- enty-three. Conceivably the process con- tinues indefinitely, with the older groups becoming practically zero. Several curves were considered for fit- ting to the data, including the normal curve, the logarithmic normal curve, Pearson's types I, I I I , and I X , and oth- ers. But a satisfactory fit was not se- cured and logic indicated that the opposing forces of lag and obsolescence should be isolated. By dropping data for the rising portion of the curve for the first f e w years and limiting consid- eration to the rate of decline after the early maximum was reached, the effect of lag was substantially eliminated. T h e curves thus remaining are pre- sented in Diagram 1. D a t a for the Shaw and Mohrhardt lists have been grouped in five-year periods for simplicity, but this could not be done for the Shaw sup- plement. A similar curve for book cir- culation at Hamilton College Library is included and will be described later. These curves, plotted on a logarithmic scale, or the data, plotted in logarithms, tend to form a straight line. Pearson's criteria of moments indicate his T y p e X , the exponential curve. T h u s the curve of organic decay appears as the expres- sion of obsolescence: y = y0bx where ( y ) is the number of titles, (y 0 ) the number of titles at the maximum or initial point, with lag eliminated, and ( x ) is time elapsed. W h e n 6) — 1 b (fc>) omega, becomes the annual rate of decrease in the curve, or the rate of ob- solescence. Per cent of decrease is ex- pressed by ( i o o t o ) . T h i s rate is almost the exact opposite of the rate of compound interest. It indicates the rate at which the principal or capital is decreased instead of in- creased. By shifting the equation to logarithmic form: log y = log yc + x log b an equation of the type: Y = A + B X the curve takes the form of a straight line. By the short method of least squares this is easily fitted to the data in loga- rithmic form. For simple graphic analy- sis and illustration, the data of imprint dates may be plotted directly on semi- logarithmic grids, as already indicated. For easy computation and quick graphic checking, the data of imprint dates may be grouped into five-year periods and immediately transferred into logarithms. Plotting of logarithms is illustrated for four subject sections in Diagram 2. Rates of Obsolescence By means of the formulae and methods outlined above, the rates of obsolescence have been computed for nineteen subject MARCH, 1944 117 groups in the select lists; they are pre- sented in T a b l e I. T h e number of groups has been reduced to nineteen for two reasons. First, S h a w and M o h r - hardt did not use exactly the same clas- sifications, e.g., "Romance L a n g u a g e s " as tion of the list the number of titles chosen was 8.1 per cent smaller than for the preceding year. T h a t is, if there were 500 titles ten years old, there were some 8.1 per cent fewer, or approximately 460 in the eleven-year-old g r o u p ; and 2000 4000 . \ 30 400 1500 3000- 3 0 0 - rf go' 10 4.* E O