224 EEPOET— 1888. 



(13) Laplace— Toy a calculation strikingly analogous to Jevons' method above 

 stated — has shown (' Thdorie Aaalytique des Probabilities,' Book II. Chapter VI.) 

 how the method of inference from samples may be used to ascertain the ' popula- 

 tion of a great empire.' There is no doubt that this method of reasoning is agree- 

 able to a sound theory of Probabilities, although in incompetent hands it has often 

 produced absurd results. We must guard against proceeding like the statistician 

 mentioned by M. de Foville, who, in order to determine the production of potatoes 

 in France, simply multiplied the production in his own commune by the number 

 of communes in France — with a result out by a hundred per cent. 



(14) Supposing the quantity of the circulation as estimated by four differ- 

 ent methods of varying trustworthiness were respectively Qp Q^, Q^, and Q^ (in 

 ascending order of worth), then the proper Mean might be 



Q, + 2Q, + 3Q, + 4Q,, 

 1+2+3+4 



MEMORANDUM BY THE SECRETARY ON JEVONS' METHOD 

 OF ASCERTAINING THE NUMBER OF COINS IN CIRCULA- 

 TION. 



Pakt I. — Exposition. 



Jevons' method consists of two stages : (1) the main line of argument, 

 and (2) what may be called a second approximation. 



(1) The first step is to ascertain the proportion in the existing circula- 

 tion of coins bearing each date, or, as ' Jevons puts it, the number of coins 

 bearing any assigned date, ' now existing in 100,000 [coins] circulating.' 

 This datum is obtained by examining a great number of coins taken at ran- 

 dom from the circulation.^ It is assumed that the proportions in which 

 this collection of samples comprises coins of different dates are approxi- 

 mately identical with the proportions which would be presented if we 

 could examine the whole existing circulation. We have thus : 



Total number of coins in circulation : Number of coins of a certain date 



in circulation : : Total number of samples : Number of samples bearing the 



assigned date. Whence 



™ , , , p . Total number of samples -vt 



Total number of coins=— , — -. 1- : — - — xNum- 



JN umber oi samples bearmg a certain date 



ber of coins of that date in circulation. 



Now the number of coins of any date now in circulation is less than 



the number of coins of that date issued from the Mint. Whence it follows 



that the total number of coins in circulation is less than 



Total number of samples , tvt r. <> • <• . i . j . 



,j= — :; „ , — ; i- : — = — X Number of coins of that date 



Number of samples bearing a certain date 



issued from the Mint. 



We have thus a figure certainly greater than — a ' superior limit ' to — the 



total number of coins in circulation. Or rather we have, or may have, a 



' Jour. Stat. Soc, 1868, p. 440 ; Currency and Finance, p. 264. 



- The principal instances of this operation known to the writer are, for England 

 165,510 coins (sovereigns and half-sovereigns) examined by Jevons in 1868; 251,107 

 by Mr. Martin in 1882 {Journal of the Institute of Bankers, 1882); by the French 

 Government 2,222,965 coins (of different kinds) examined in 1878, 1,791,808 in 1885 

 (^Bulletin de Statistique, France, 1878, 1885) ; in Belgium, 1878, 103,475 coins by the 

 Banque Nationale, 83,599 by the 3Iinistire des Finances {Bulletin de Statistique, 

 France, 1878). Of the enquete said to have been made in France in 1868 the writer 

 has not been able to tind any particulars. 



