According to the value of each commodity used in any one period of time (say a year) the various commodities are “weighted.” Thus you count bread (let us say) as twelve times more important than lead, because the value of the bread used in the community for one year is twelve times as much as the value of the lead used in the community during that year. Then let us suppose that the value of the leather used is three times that of the lead, the value of the iron five times, etc. You put against each commodity these “weight” numbers. Next you find out what an ounce of gold would purchase of each of those commodities in that particular year. For instance: you find it would purchase a quarter of a ton of lead, 400 pounds weight of bread, and so on, only you multiply by your weight number the use of gold in each particular article. For instance: you count the gold used in buying bread as twelve times more important than the gold used in buying lead. You then add up all the prices measured in an ounce of gold in your column; you divide by the number of items in your column, each multiplied by its weight number, and the result is that your ounce of gold for the year 1900 will be found to have a certain _average purchasing power_ which you call, for the sake of further application, arbitrarily, “100.” Then you take another year, say 1920, and you find what the ounce of gold would purchase in the same conditions, similarly weighted, in the year 1920. You discover that the ounce of gold on the average in 1920 would only purchase half the weight of stuff it purchased in 1900. In other words, prices have doubled, or, what is the same thing, gold has halved in value. You put down for the year 1920 the figure “200,” which means that average prices are twice as great as they were in 1900, and the economist’s way of saying this is: “With the year 1900 as a base, the Index Number for 1920 is 200.” In the year 1921 he makes the calculation again, and finds that prices have fallen, that is, gold has become rather more valuable as compared with other things, and prices are only three-quarters more than they were in 1900. The economist writes down: “The Index Number for 1921 is 175, with the prices of 1900 as a base.” He goes back to 1880 and finds that in 1880, after making a similar calculation, an ounce of gold would on the average buy five pounds of material where in 1900 it could only buy four. In other words, prices are lower in 1880 by one-fourth. So he writes down: “The Index Number for 1880, with 1900 as a base, is 75.” These Index Numbers taken for each year with a particular year as a _base_, or year of reference, show the fluctuations in the purchasing value of gold.