ON VAEIATIONS IN TIIK VALUE OF THE MONETARY STANDARD. 149 



fourth table he has so used both 1873 and 1883. Or the base line might 

 have been composed by taking the average prices of each article for several 

 years, after the manner of Sir. Palgrave or Mr. Sauerbeck, except that 

 the years entering into the average need not be consecutive. It may be 

 asked. What reason could there be for taking half-a-dozen years — some at 

 the beginning, it might be, and some in the middle, or at the end, of the 

 period under review ? The reason might be the very absence of a reason. 

 Suppose it were thought desirable, in order to avoid accidents, to take a 

 mean of half-a-dozen years, and not worth the trouble of including more 

 than half-a-dozen. In the absence of special objections to certain years 

 any one half-dozen is as good as any other. There are, therefore, as many 

 half-dozens as there are combinations of six to be formed out of the n years. 

 To avoid the suspicion of cookery it might be best to make a selection 

 at random — by spinning a teetotum, or by some equally arbitrary process. 

 It should be observed that the labour of taking averages over several 

 years need not be so formidable as might be supposed, {^Medians instead 

 of Arithmetic Means be employed. In view of abnormalities like the 

 irregular rise of prices in 1873, there vfould be a peculiar propriety in the 

 use of the Median.' 



Exactly similar considerations apply to the factors or proportions 

 ■which form Mr. Giffen's second table. It was open to him, as he points 

 out, to take these proportions from some other year than 1875. In fact, 

 he tried several years with substantially identical results.'^ There are, 

 therefore, at once as many factors as there are years in the series. More- 

 over any mean of these factors may be taken. Here, again, then, we have 

 2" — ! schemes to choose from. 



Well, then, any one of these (2" — 1) measuring-rods may be used in 

 connection with any one of the (2" — 1) price-scales above mentioned. 

 Thus arise (2" — 1)(2" — 1) arrangements for comparing the years in 

 respect of the level of prices. To these may be added Mr. Palgrave's 

 system of factors combined with any one of the (2"— I) price-scales. 

 This addition swells the contingent to 2" x (2" — 1). This number is to 

 be added to the previous estimate, viz., 2"x(2'' — 1), which is thereby 

 doubled, becoming 2»+ ' (2« - 1 ) . 



The question may now arise, How large is n to be ? It may be sug- 

 gested that it should be as small as possible, namely, 2. We should 

 proceed according to the method recommended by Professor Marshall,^ and 

 exhibited at length in the former Memorandum."* We should compare 

 the present year with last year only, next year with the present, and so 

 on. The fact that Professor Marshall refers to the general problem of a 

 measure based on articles of consumption, whereas we are now particu- 

 larly concerned with the volume of trade, does not appear to atiect the 

 reasons on which his recommendation is based. However, it may be well 

 to combine that principle with the practice of averages over several years. 

 At any rate, the latter procedure is countenanced by the most eminent 

 statisticians. Extending their review over a considerable tract of time, 

 they have, in effect, taken for granted that sort of solidarity between tho 

 years which we have all along supposed. Ten years, twenty years, nay, 

 even forty years, have thus been compared bdcr se. Let us take tho 



' See below, Sect. V., and the papers to which reference is there made. 

 ^ Parliamentary Papers, 1878-9, c. 2217. 

 ' Contemporary Review, March 1887. 

 « Brit. AsHOC. Report, 1887, p. 2G9. 



