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 A_x_ plus B_y_ plus C_z_ plus D_u_ ... 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.