270 REPORT — 1887. 



comparing TaC'o, the height of the apparent centre of gravity at the later epoch, 

 with TjCp the height of the real centre at the earlier epoch. If we join the 

 points cc\c\, &c., we have the locus of apparent unit hugging the corrected curve 



CCyC„. 



At every step there is incurred an error, say a ' prohable error,' Am, and accord- 

 ingly what may he called an improbable error about 4Am.i These errors being 

 presumably independent, without bias in excess or defect, it follows, from the 

 theory of errors, that the total error incurred in the course of n steps is s/ntya. 

 It is a nice question how frequent the revisions of the standard should be, in order 

 that this error may be minimised. Let A< be that interval of time within which 

 there cannot possiblj' or probably occur a change of sign in Ait, owing to a variation 

 in those disturbances of the economic fabric which cause our standard to be in- 

 accurate. Then it is expedient that the revisions shall take place as often as, 

 but not oftener than, once in every such short interval. This condition points to 

 the frequent revisals - contemplated by Professor Marshall, 



It may be observed that Professor Marshall's solution is largely applicable to 

 a problem kindred to ours, but which we have not supposed to be comprehended 

 in the question set to us ; namely, to measure changes in the value of money 

 between different places. For instance, if the economic habits of the peoples of 

 the Austrian empire varied by gentle gradations along a line trending from north- 

 west to south, very much as the vital statistics of the empire are shown by Hain 

 (in his important work on ' Das Oesterreichiscbe Reich ') to vary gradually, then it 

 might be possible, so to speak, to carry the equation of utility from Bohemia 

 along to the Military Frontier. It is otherwise where natural and political barriers 

 produce discontinuity ; for instance, in the case of the United Kingdom compared 

 with the United States.^ 



Section III. 



Determination of a Standard for Deferred Payments ; not based upon the 

 items of national consumption ; calculated to afford to the consumer a 

 constant value-in-use ; no hypothesis being made as to the caiises of the 

 change in prices. (A B C d.) 



We come next to the case where the items which enter into our 

 Unit are not copied from the statistics of national expenditure, but are 

 selected on some other principle. Although the rule in this case is 

 different, the ground of the rule will be found to be much the same, 

 namely, the desirability that the advantage derived from the expenditure 

 of a unit should be as far as possible constant. To those who admit the 

 utilitarian character of the problem (as defined by the attributes ABC) 

 it will appear evident that a formula other than the direct solution can 

 only recommend itself as being a workable approximation thereto. 



Among methods which may seem to have a claim to that character 

 we may distinguish the three following : — 



(1) There is first what may be called polymetallism, the Unit based 

 upon the price of an aggregate of specified quantities of specified metals ; 

 and not only metals but other substances which possess an attribute 

 ascribed to the precious metals, peculiar fixity of value. 



(2) Next we place the index numbers of the Economist, the simple 

 average of a number of prices, especially if, as Mr. Bourne has pointed 



' The reader, according to his habits of thought, may regard u as standing either 

 for the sought unit or the utiUty which it is required to keep constant. 



- Contemporarij Rerirw, March 1887. 



' It is difficult to vmderstand the rationale of the method by which it is proposed 

 in the Massachusetts Labour Report for 1884 to bring together for comparison the 

 purchasing power of wages in England and the United States. 



