266 REPORT — 1887. 



Of these methods it may be remarked that the first four seem to have 

 an advantage over the remaining two, in that the former make no 

 assumption as to the extent of the change of price, while the latter pro- 

 ceed on the supposition that those changes are small. The fifth method 

 seems to assume that we may wi-ite for p'^ jt), (1 + A'„), where the second 

 powers of A'„ are negligible. And similarly in the sixth method we 

 must be allowed to write for ^a^f^ flp^ (1 + i^S^, where /A„ X -^'„, ^A^ x A'/s, 

 &c., are negligible. No doubt, when we grant the steadiness of the pro- 



portions — , '-, &c., we can hardly refuse this additional postulate, 

 a a 



The first four methods are all equally good if our fundamental hypo- 

 thesis is strictly true. Where, as in fact, the hypothesis is only hypo- 

 thetically true, the third and fourth methods, being of the nature of 

 means, are apt to minimise error. 



On the whole, the fourth method may appear the best ; abstracting 

 the difficulty of obtaining the proper numerical data, which is beyond the 

 scope of this paper. 



The seventh method is exposed to the objection (noticed by Dr. Lehr) 

 that services cannot be weighed by hundredweights. Dr. Lehr's own 

 formula is objectionable only on account of its bulkiness. (See above, 

 note to p. 263 ) 



It might be a good plan to take the mean of the numerical results of 

 all the methods that are equally entitled to confidence (? the third, fourth, 

 seventh, eighth, and — in the absence of violent price- variations — the sixth 

 and seventh). We might thus obtain not only a better result, but also 

 the opportunity of forming an opinion upon the error incident to the 

 calculation : by how much it is likely, and by how much it is unlikely, 

 that the result should be wide of the mark. 



There are some other concrete circumstances which may entail some modifi- 

 cations of the general rule: (1) Unless the interval between the revisions of the 

 units be very short indeed we must suppose that the unit is employed at times 

 when, owing to the movements of prices (since revision), it has ceased to be exact.* 

 Ideally it might be best, instead of ;/., p'^, &c., present prices, to take for each 

 article the mean of its pieseut price and its prices in the proximate future for all 

 the period that the unit has to function unrevised. But of course we cannot know 

 the future prices, and therefore we must be content with taking present prices (or 

 it may be means of the present and the immediate past) as the best representatives 

 of the ideally preferable mean. Now, considering the fluctuations of each price 



The received formulae and Dr. Lehr's formula are equal as touching their theoretical 

 validity ; but the former (including our A B c D) have the advantage of practical 

 simplicity. 



Dr. Lehr's treatment of the rariahles as distinguished from the formula also 

 calls for remark. His object being to discover how far the power of money to pur- 

 chase Gennsseinheiten has varied, it is not quite clear why he should insist on in- 

 cluding wages, the wages of ordinary industrial or productive labour as well as of 

 stipendiary services, among the data. Do we not take sufiicient account of productive 

 labour when we take account of the finished products ? Either, but not loth, these 

 items should figure in the expression of our Unit. 



One more remark seems called for in justice to the reader whom our notice of this 

 work may have attracted. He must not be discouraged by the opening paragraphs, 

 which are both extremely obscure and not directly relevant to our present purpose. 

 The general reader is advised to begin at p. 10 (' Der begriff. Durchschnittpreis '), 

 or even at p. 28 (' Das Verfahien zur Ermittelung des Geldpreises,' &;c.). 



' This obvious circumstance is explained at some length by Held in Conrad's 

 jahrlnwh for 1871. 



