[30]Index numbers are used to indicate changes in the value of money. The objects for which this measurement is undertaken are thus well stated by Sir R. Giffen (Second Report of the committee appointed for the purpose of investigating the best method of ascertaining and measuring variations in the value of the monetary standard. Report of the British Association, 1888): (1) The fixation of rents or other deferred payments extending over long periods of time, for which it has been desired to obtain a currency of a more stable sort than money is supposed to be. (2) To enable comparisons to be made between the value of money incomes in different places, which is often an object of great practical interest; not only individuals contemplating residential changes, but also governments and other large spending bodies, spending money in widely distant places, having to consider this question. (3) To enable historians and other students making comparisons between past and present to give an approximate meaning to the money expressions which they deal with, and say roughly what a given fine, or payment, or amount of national revenue or expenditure in a past age would mean in modern language. To which some would add: (4) To afford a measure of the extent to which trade and industry have been injuriously affected by a variation in prices; and of the correction which it would be desirable to apply to the currency. An index number is constructed by combining several items, each of which is a ratio between the price of a certain article at a particular date under consideration (_e. g._, last year or month) and the price of the same article at a period taken as base or standard (_e. g._, 1867-77, in the index number constructed by Mr. Sauerbeck, _Journal of the Statistical Society_, 1886 and 1893). These ratios are generally expressed as percentages. _E. g._, the percentage for _flour_ in 1885, as given by Mr. Sauerbeck, is 63; meaning that the price of flour in 1885 is to the average price of the same article in 1867-77 as 63:100. The term index number is sometimes applied (_e. g._, by Mr. Sauerbeck, _op. cit._) to each of these items, as well as to their combination. The percentages are usually compounded by taking an AVERAGE of them. But a result of equal generality may be obtained by taking their sum. One of the best-known index numbers, that of the _Economist_, is thus constructed. Twenty-two articles having been selected, the price of each article at the current date compared with its price at the standard period (1845-50) is expressed as a percentage; and the sum of these percentages is put as the index number. Thus the _Economist_ index number for the year 1873 is 2947; such a sum is easily reduced to the form of an average by simple division (_e. g._, 2947 / 22 = 134). Accordingly in what follows it will be sufficient to consider the latter form only.