INDEX NUMBERS. 525 INDEX NUMBERS. aiming to iletermine the course of general prices, to include specialties, or rarities, or objects of such restricted use as not to be subject to the ordinary inlluences allecting prices. The character of the component price series being thus stated, how shall the number be fixed? It must evidently be huge enough to in- clude all the more important lines of staple commodities. No precise limit can be fixed. While it would seem obvious that in any efl'ort to determine general prices, the greater the num- ber of commodities embraced in the comparison, the more accurate the result, such is not the case, since, as the number multiplies, the propor- tion of articles of limited demand which are more or less removed from the primary influences af- fecting prices generally increases. The base line with which prices are compared is usually the average of a series of years, the purpose of taking such an average being to over- come any eccentricities of prices which might characterize a briefer period of time. This prac- tice is not universal, and some well-known calcu- lations have been based upon the prices of a single year. This method is justified on the ground that the prices so chosen were t*iose of normal conditions. In the combination of the price series into a general index of prices, the simple mean is the most frequent method employed, as illustrated in our first index calculation. This has been the subject of much criticism on the ground of the unequal importance of the objects concerned. To overcome this difficulty two sets of weighted averages have been proposed. The first was one which measured all articles by their importance in the national consumption as illustrated in the third calculation ; the second measures articles by their importance in individual consumption as revealed by family budgets and typified in our second calculation. In applying national con- sumption as a test, we find that calculations of such consumption are very precarious and e.xtend to comparatively few articles. In family con- sumption we can ascertain for certain groups of persons the proportions of expenditure which cover a much wider range of conniiodities. But the commodities covered by the family budgets are not the same as those covered by price statis- tics, since the former represent the retail, and the latter the wholesale markets. In the food prod- ucts this makes little dilicrence, but in textiles, metals, lumber, and the like there is no little adjustment needed to bring the prices and the relative expenditures into relation. Those who have done the most to establish more rational and at the same time more com- plicated calculations have been the first to point (iit (hat the ultimate results did'cr but slightly from those obtained by the somewhat rough cal- culation of a simple average. The index number of the London Economist is based upon the wholesale prices of 47 com- modities which by combination are reduced to 22. The quarterly prices for 1S45 to 1850 were arranged as a basis for calculation and the rel- ative prices for subsequent years upon the Janu- ary prices. The total price index for 184,5 to S^0 was 2200, and for later years the price in- dices are also expressed as an aggregate, with- out reduction to 100. As in a few cases the full number of articles was not given, this was somewhat misleading. In the following table we give the results of this calculation as published l)y the Economist, together with a reduction to the scale of 100: "ECOSOMIBT" I.VDEX NUMBER YEAR Total as puhlished Reduced to scale oJ 100 YEAR Total as published Reduced to scale o( 100 1845-50 2.200 100 1879 2,225 101 1H51 2.2U3 104 1880 2,538 lie 1881 1882 2,376 2,435 108 1858 " 2.'612 m"" m 1883 2,:)42 106 "imi"" 2.727 i'di ■" 1884 2.221 101 1862 2,878 131 1885 2.098 95 1863 3,492 159 1886 2,023 92 1864 3,787 172 1887 2,0.59 94 1865 3,675 163 1888 2,230 101 1866 3,664 162 1889 2,187 99 1867 3,024 137 1890 2.236 102 1868 2,682 122 1891 2,240 102 1869 2.666 121 1892 2.133 97 1870 2,689 122 1893 2,120 96 1871 2,590 118 1S94 2,082 95 1872* 2.835 129 1895 1,923 87 1873 2,947 134 1896 1,999 91 1874* 2,891 131 1897 1,946 88 1876 2,778 126 1898 1,891 86 1876 2.711 123 1899 1,918 87 1877 2.715 123 1900 2,145 98 1878 2,529 115 1901 2.125 97 1 1902 1,948 89 • TweDty-one articles only. The general tendencies of price movements, the rising tendency till 1873, and the subsequent downward trend as shown in these figures are amply confirmed by other investigations. The enormous rise in the period of 1801 to 1865 was due not only to the extravagant prices for cotton paid in this period, but also to the fact that in the twenty-two series represented in the total as many as three were for cotton. This fact, and the prominence given to indigo, and the absence of so important a staple as coal, led to numerous efforts to improve the calculation. Mr. R. H. Inglis Palgrave sought to remedy the defects by a system of weighing each article by its impor- tance in the national consumption — a method al- ready indicated. 'Mr. Augustus Sauerbeck published in 1886 in the Journal of the Royal Statistical Society an index number which has been brought down to date in subsequent issues of that periodical, and which is in many respects an improvement upon the older calculation. His annual prices are based upon averages of the monthly, and in some important commodities weekly prices, and these are compared with the average prices of 1867 to 1877. The tables embrace 45 .series of quota- tions; and while some commodities are repeated (in different grades), they have been chosen in such a manner that the total number of quo- tations for a group of commodities such as meats, textiles, iron and steel rc[)rospiits approxi- mately in its proportion to the whole number of quotations — forty-five— the importance of this group in the commerce of the United Kingdom. The superiority of this calculation rests, there- fore, on the nior.> trustworthy character of its material, and the breadth of choice. In France similar calculations have been based upon the import prices of commodities, and in Germany (Soetbccr's) upon the import prices of goods at Hamburg. The latter are more com- prehensive, since Hamburg was so long a free city that practically its entire trade was in com- modities imported by sea and land. The calcu-
