288 KEPORT— 1887. 



liable to peculiarly large proper fluctuations. Cotton and iron, for 

 example, fluctuate in this sense much more than pepper and cloves. 



The weighting: of a geometric mean is a dehcate matter, but not beyond the 

 resources of science. A general rule is given by Dr. Macalister in the important 

 paper already frequently referred to. Suppose we have a considerable series of 

 observations belonging to a certain class, we can extract a constant which may be 

 described as the measure of fluctuation for that series or class of observations. 

 The constant thus given constitutes the loeight with which we ought to affect the 

 logarithm of an observation when we combine it, according to the arithmetic mean, 

 with others (of a different degree of precision) in order to obtain the best possible 

 measure. The data for determining this constant are afforded by series of prices 

 for successive years, such as those in Mr. Giffen's Report to the Board of Trade on 

 Prices of Exports and Imports, 1881-85. 



If in the present state of statistics and public opinion it appears too 

 difficult and delicate a matter to weight the data on the principle of fluc- 

 tuation, the practical result of this section may be thus summed up. After 

 the manner of Dr. Kraemer, select a number of (independently fluctuating) 

 articles which are found to be particularly sensitive to changes in the 

 value of money. After the manner of Jevons, find the percentage indi- 

 cating the price-variation in each article, and put the geometric mean 

 of those percentages as the required unit, or standard, or measure of 

 depreciation. Or rather, if we must treat as equal weights certain to be 

 unequal, it is better (for reasons which will be more fully stated in the 

 next section) to employ a formula which is specially adapted to such 

 jumbling of different weights : to wit, tlie Median, Examples of this 

 species of Mean have been given above. 



So far on the hypothesis that the widening circle of price-disturbance 

 has not yet spread beyond a limited area ; a case which is almost too 

 restricted and particular to be the subject of our consideration.' If we 

 suppose that the circle has completely spread, that all the compartments 

 of the economic fabric are equally penetrated by the influence of some 

 change in the supply of money, we have then a limiting case of the pro- 

 blem just discussed. 



The objection to this supposition is that, for an all-pervading percolation, 

 considerable time must, in general, be required. And then it happens — 

 what is not necessarily true of more transient oscillations, such as those 

 of an inconvertible currency — that the changes in j^rices are apt to be 

 referable to one or two leading categories : e.g., of articles which follow 

 the law of decreasing or increasing returns, after the manner exhibited 

 by Laspeyres in his classical paper ^ on the prices of Hamburg wares. 



If we examine some of the statistics adduced by Laspeyres, according to the 

 appropriate mathematical methods, we shall not discover a very serious hiatus 

 between the different categories of wares. The modulus for the fluctuation of the 

 price-variations about their average may be (roughly) estimated to be about 40 

 for any of the eleven categories discussed by Laspeyres in the masterly paper 

 entitled ' Welche Waaren.' . . . Hence we can calculate the probability that the 

 difi"ereuees between the various categories are really significant, and not merely 

 accidental. It will be found, if, with Laspeyres, we dispose the data in three 

 main divisions — Urpj-oductionen, Coloniahuaaren, Manufacte, &c. — that the 

 cleavages luithin those divisions are not important. The separation between the 

 divisions is marked, yet not very serious, not more serious than is found to exist 



' Compare the last paragraph of the Tntroductorij Si/nopsis. 



■ Jahrh.f. Nat. Oelwn. vol. iii. See also ZcitscMift f. Staatsn)isse7iscJtafT, 1872. 



