1. One plan is to assign as the weight of each percentage, or ratio between prices, the value of the corresponding commodity at the initial or standard period. According to this plan the index number is the ratio between these two values: the quantities initially consumed at the prices of the current date, and the same quantities at the standard prices. This method is exemplified by Sir R. Giffen's estimate of the change in the value of money between 1873 (and 1883) and _earlier_ years, in his report on prices of exports and imports, 1885, table v. 2. Another plan is to assign, as the relative importance of each percentage, its value at the particular epoch, the current year. This plan is adopted by Mr. Palgrave in his memorandum on _Currency and Standard of Value_ ... in the third report of the royal commission on depression of trade and industry, table xxvii. 3. According to another plan, the index number is the ratio between the following two values: the quantities consumed at the current date at the current prices, and the same quantities at standard prices. This plan is adopted by Mr. Sauerbeck (_Journ. Stat. Soc._, 1886, p. 595). 4. Or, instead of taking either the initial quantities or those of the current date, a mean between the two may be taken. This is the plan adopted by the British Association Committee. They estimate "the average national expenditure on each class of article at present and for the last few years"; and put for the relative importance of each commodity a round number corresponding to that estimate. Thus the estimated expenditure per annum on _wheat_ is L60,000,000, and on _meat_ L100,000,000: that is respectively 6.5 per cent., and 11 per cent. of the sum of the corresponding estimates for all the commodities utilized by the committee. As convenient approximations, the weights five and ten are recommended by the committee. If the index number based on labour ... rather than on consumption, is adopted as the standard for deferred payments, it would be proper by analogy to take as the measure of appreciation or depreciation the change in the pecuniary remuneration of a certain set of services, namely all, or the principal, which are rendered in the course of production throughout the community during a year, either at the initial or the current epoch; or some expression intermediate between the two specified. But it may be doubted whether the statistics requisite for this method are available. With regard to the second and third of the purposes above enumerated, the determination of the comparative value of money at distant places and remote times--one or other of the two methods indicated would seem to be theoretically proper.