COST OF ADMINISTRATION[13]

COST OF ADMINISTRATION[13]

The possibility of deducing a general method for calculating the probable cost of operation of a library.

The problem of ascertaining how the cost of administration of a library is related to the various conditions and factors that affect it is the problem of finding a formula in which, by simple substitution of numbers representing or corresponding to these conditions, a reasonable or approximate cost may be obtained. The data obtainable are the conditions and actual cost in a limited number of cases. The obstacles are the difficulty of stating certain of the conditions numerically and the difficulty of deciding on the form of the formula, which must be done in advance.

We must first agree, of course, that the legitimate cost of administration of a library should bear some relation to its conditions of work. Probably no one would quarrel with this, but the first thought of one who considers the subject is generally that a large number of the conditions could, by their very nature, not be susceptible of numerical statement. Such factors as size of circulation, number of cardholders, size of building, and so on, may be stated directly in figures, and many such influence the cost of administration; but how, for instance, shall be stated numerically the character of the locality—whether foreign or native-born, wealthy or poor, etc., which also indubitably affects the cost? In this particular case this factor exerts its influence through others that may be numerically stated. So far as it necessitates purchase of foreign books, a foreign population acts to increase cost; so far as the demand for certain classes of books is concerned, cost might be increased or decreased; but size of book collections and circulation are both numerically determinable. It is possible that all conditions which would seem at first sight not to be numerical might reduce in this way, to various numerical factors. Regarding the form of the function to be used for the formula, mathematicians tell me that its determination might prove a great obstacle. Personally, it seems to me that it is probably “linear,” that is, involving only the first powers of the quantities concerned, never their squares, cubes, etc. Thus, all other things being equal, increase of book collection increase of circulation, increase of staff, etc., would approximately mean increase of cost in direct proportion; or, at any rate, not in any way involving powers above the first. I should try at the outset therefore, a simple linear formula, such as

Ax plus By plus Cz plus Du ... equals R in which x might be circulation, y number of books, z number in the staff, u cubic feet in the building, and so on. It would then be required to find values for A, B, C, D, etc. This would require, of course, as many equations as there are of these coefficients. To get each equation we select a library that we are willing to accept as being conservatively and properly operated, and substitute for x, y, etc., its reported circulation, number of books, and so on, putting in place of R its total cost of administration. Solution of this system of equations gives the coefficients, A, B, C, etc., and furnishes the working formula required. Thereafter when we wish to see whether a library is run as conservatively as the typical ones selected, its statistics would be used to substitute for x, y, z, etc., and the value of R thus obtained would be compared with the actual cost.

The labor of reducing the system of equations would depend on their number, which must equal that of the conditions. This would doubtless be great—possibly twenty or twenty-five, but the work amounts simply to doing a great deal of figuring.

I believe that this thing is worth trying, and I intend to try it myself as soon as I can secure the necessary help in doing the work of figuring, which in any case would not be nearly as great as that done to calculate a comet’s orbit. Physicists and astronomers are daily doing work of this kind, and doing it, too, on subjects regarding which there is quite as much reason to doubt the applicability of the method as in the present case. Why not try it? It admits of satisfactory “proving,” for if applied to two groups of libraries with absurdly different results, it would at once be shown to be faulty as so applied.

I believe that we librarians use the experimental method too infrequently. When it is proposed to make some change or other, I constantly hear the objection, “That wouldn’t result at all as you expect; it would do so-and-so.” But why not try it? Try it and see what happens. That is the only real test Of course, if trying will cost a large sum, or involve some serious risk, we must count the cost, but in nine cases out of ten nothing is involved but a little extra work.

In this case we are trying our experiments daily—we can’t help it. We have libraries running under all kinds of conditions and we have statistical reports of those conditions and of the resulting cost. It is surely worth while to see if we can not connect these costs and these conditions in some useful way.

I venture to close with a parable. At a national meeting of civil engineers there was a discussion of the advisability—and possibility—of ascertaining the exact distance between New York and Chicago. In the course of the discussion it appeared that numerous measurements had already been made for various purposes by different parties and under divers conditions. No two of the results agreed precisely. It was suggested by a speaker that some method of combining the results might be found so as to arrive at a practical working estimate of the distance. Objection was at once made by various members. To many the very idea of such a proposal seemed a bit of pleasantry, and they greeted it with smiles. One speaker poked fun at the idea of treating so practical a question by abstract mathematical methods. Another pointed out that the measurements had been made with various objects in view; some for railroad purposes, others by government topographers; that instruments of varying makes had been employed and that the surveyors possessed differing grades of ability. He did not see, therefore, how there was any possibility of taking all these into account. Still another thought that the best way to get at the real distance was to send out a questionnaire to persons who had traveled from New York to Chicago and find out their opinions.

It seemed to be the consensus of belief that we should never ascertain the exact distance from New York to Chicago, and that it was extremely doubtful whether there really was any such distance. Probably it varied from time to time, which would account for the varying measurements.

Is it conceivable that engineers would ever talk in this way? It is not.

But we have all heard librarians do so. Why?