The reader must be on his guard against misunderstanding the diagram. It does not represent the heights of the prices of the different countries compared with each other either at any one date or for the entire period. For example, the heights of the lines at the year 1860, do not indicate that American prices were lowest and French the highest at that date, or, indeed, tell anything whatever directly on that point. The various series of prices are compared within themselves, every year with the average of the prices for 1890-1899 in each country, respectively. The only comparison allowable, therefore, between the several lines, is that between the fluctuations, both as to their times and as to their directions, both as to the larger tidal movements and as to the lesser wave-like movements within the business cycles. The Figure does indicate that both American and German prices have risen somewhat as compared with the English and French prices, since the period before 1860. This figure should be studied in connection with Figure 1, in ch. 4, sec. 9, on gold production. The Figures indicate that the rapidly growing monetary use of gold offset a large part of the effects of increasing gold production between 1840-1860 and 1884-1914. Between 1884 and 1896 prices actually continued to fall after gold production had begun to climb. Likewise the growing monetary use of gold accentuated strongly the effects, between 1873 and 1883 of a comparatively small decrease in gold production.] § 4. #Index numbers.# The process of calculating general prices and changes in them has in it, inevitably, something of arbitrariness and incompleteness. For not all prices can be included, but only those of articles of somewhat standardized grades and those that are pretty regularly sold in markets where prices are publicly quoted. Any list of articles that can be selected is of unequal importance to different persons and classes of persons, at different places, at different times, and for different purposes. And yet the study of general prices as shown by any broadly selected list reveals changes which in some measure affect the interests of every member of the community. General prices are conveniently compared from one time to another through the use of index numbers. An _index number_ of any article is the per cent which its price at any certain date is of its price at another date (or of the average for a series of prices) taken as a base or standard. Thus if the average price of cotton in the base year were 10 cents (taken as 100) and the price rose to 12 cents, the index number would be 120. _A tabular index number_ is the per cent which the price of a selected group of articles at any certain date is of the price of the same group of articles at a date which has been taken as the base.[4]