ON PRECIOUS METALS IN USE AS MONET. 225 



great many superior limits, one being afforded by each year (or at any 



rate each short period ' of years) as far back as our data reach : in England 



as far back as 1817, in France 1803. 



It remains then to consider which of all these data it is best to employ. 



Evidently the smallest superior limit will be afforded by the year (or short 



• j\ i< u- u ii, Number of coins issued . . . 



period) for which the r- — -. ; -, -, — is a minimum ; 



Number ot coins nowm circulation 



in other words, that year whose coinage has suffered least loss. Now « 

 priori there is a presumption that the coinage which has been longest in cir- 

 culation will have lost most. And this theoretical conclusion is corroborated 

 by observation. It is shown by Jevons that the ' proportions of coinage 

 surviving ' are smaller for the older coinages.^ The general truth of 

 the proposition is similarly confirmed by the results of the French 

 enquetes. 



It is proper, therefore, to select a recent coinage as that which should 

 enter into the formula above given. ^ Accordingly Jevons (writing in 

 1868) takes the period 1863-4 as his basis. The number of sovereigns 

 coined in that period, 14,678,000L, is to be diminished ■* by 600,000 

 known not to have entered into circulation. The remainder, 14,000,000 

 (nearly), is to be multiplied by W^Wt 5 ^^i^ being the ratio of the 

 total number of sample sovereigns to the number of samples of sovereigns 

 dated 1863 or 1864. The result is 75,000,000, to which may be added 

 certain sums known not to have entered into circulation, but to be ' lying 

 in bags as received from the Mint ' in the Bank of England. 



By similar reasoning ^ De Foville finds, as a superior limit to the 

 number of twenty-franc pieces in France, 175,000,000. 



De FovUle places this reasoning in a somewhat different shape, or rather in two 

 different shapes. The substantial identity of the various forms may best be 

 contemplated by the aid of symbols. Let E be the required total number of coin.s 

 in the existing circulation. Put S for the total number of samples, and s^, s.^ . . . 

 •s,. ... for the number of samples bearing date year 1,2, 3, &c., respectively (the 

 years'"' being reckoned either onwards from the date of the oldest coin in circulation, 

 or backwards from the most recent period). Let the number of coins issued from the 

 Mint for the corresponding years be Cj, c, . . . c^. By the reasoning above stated 



' Owing to the practice which used to prevaU of coining with dies which had 

 become out of date, it may not be safe to treat the yearly return as perfectly accurate. 

 See, on the practice alluded to, Jevons, Currency and Finance, p. 280 ; Martin, Journal 

 of the Institute ofBanliers, 1882, p. 311 ; De Foville, Journal de Statistique, 1886, p. II. 



^ Currency and Finance, p. 281. Jevons, in the passage referred to, is calculating 

 what may be called the absolute ]M-oportion of each coinage surviving ; but for our 

 present purpose it is sufficient to know how many times the diminution, or mortality 

 so to speak, of one coinage is greater than that of another. For this purpose we need 

 not suppose, with Jevons in the passage referred to, the total number of coins in cir- 

 culation to be known. We are concerned here only with the projxtrtiong between the 

 figures in the second column of Jevons' table at p. 281 ; and for that part of Jevons' 

 conclusion we do not require the whole of his premisses. We can deduce immedi- 

 ately from the table at p. 2(14 that part of the table at p. 281 which we here require ; 

 namely, that the proportion surviving of coins issued in '63-64 is greater than the 

 corresponding proportion for the period '.59-62, and still greater than the proportions 

 for the earlier periods. 



' This general rule and the possible exceptions are illustrated by the diagram 

 on p. 8. The whole matter is placed by De Fovilie in a clear light {Journal de 

 Statistique, 1879, p. 36 ; 188.5, p. 12). 



* Currency and Finance, p. 265. 



* Journal de Statistique de Paris, 1878 and 1885. 

 " Or short periods. See note 2 above. 



1888. Q 



