232 EEPORT— 1888. 



of samples being 384,302, for our superior limit we should have 



OQA ^00 000 



' "' = 96,000,000 (pieces of 20-fraTics) nearly ; whereas De Foville 



has 175,000.000. 



(2) We have now to criticise the logic of the 'second approximation. ' 

 which takes into account the exportations of coin. The reasoning which 

 has been described appears to be formally correct provided that the 

 period during which the exportation is supposed to act is suflBciently 

 small ; ideally diminished in the spirit of the differential calculus. But 

 it is a matter of delicacy extending the conclusion to cases in which the 

 ' period ' cannot be regarded as infinitesimal. An illustration, Jevons' 

 own, will best exhibit the difficulty. Jevons argues that, as the coinage 

 of 1863-4 constitutes about one-fifth of the existing circulation, there- 

 fore at least a fifth of the exportation during the period 1865—7 must have 

 fallen upon the coinage of 1863-4. But how is it known that the main 

 part of the exportation of 1867 (or even 1866) did not fall upon the 

 coinage of 1865 ? 



But it is needless to examine how much the reasoning leaks here, if 

 a more serious gap is caused by the omission of all reference to imported 

 coin. How do we know that the imports during the later portion of the 

 period of 1865—7 did not bring back many of the coins which the exports 

 at the beginning of the period had taken away ? 



The following correctives are suggested. For a certain period (such 

 as Jevons selected, 1865-7, or shorter) observe samples of the exports and 

 imports (opening and examining many outward-bound treasui-e-chests) 

 and thereby determine the proportion both of the exports and of the 

 imports (for that period) which consists of coins belonging to a certain 

 recent period cori-esponding to Jevons' 1863^. Then we may reason 

 thus ; placing ourselves in imagination at Jevons' epoch 1868 (or, mutatis 

 mutandis, in 1888). 



(1) Number of coins dated '63-4 now in circulation =:at most number 

 of coins issued '63-4 minus (proportion of exports '65-7, consisting of coins 

 '63-4) X (exports '65-7) plus (proportion of imports '65-7, consisting of 

 coins '63-4) x (irajDorts '65-7) minus bags in Bank of England, as men- 

 tioned by Jevons (and other known items). 



(2) (Total number of coins (of all dates) in circulation) x proportion 

 of coinage '63-4 in existing circulation (found by sample) =number of 

 coins dated '63-4 in circulation. 



(3) Total number of coins in circulation is greater than the right-hand 

 member of equation, or rather iw-equation (1), divided hy proportion of 

 coinaofe '63-4 in existing: circulation. 



This reasoning takes for granted that the invisible or unregistered 

 exports are compensated, or at least not exceeded, by the imports 

 of the same species. It must be assumed also— what has been 

 doubted upon good authority ' — that the statistics which we have are 

 fairly accurate. A chink in the logical structure may be filled up ; but 

 rottenness of the statistical material is irreparable. 



' See Soetbeer's Maferinlrn, p. 4S. It is possible that the conditions necessary 

 for the application of Jevons' method maj' fail for the United Kingdom, but may be 

 partiaEy fulfilled for some other of the ' principal countries ' which are comprehended 

 in our province. 



