ON PRECIOUS METALS IN USE AS MONET. 231 



g 

 from the Mint at that date ; * in symbols — c,. But we have now to take 



S ii 



account that - may be too small. It may be as much too small as S 



S 

 may be too large. The true ratio which — represents cannot then be 



larger than_Si_^. That expression, multiplied by c,, constitutes a 



s 

 perfectly safe superior limit — comparable to the safe load or breaking load 

 of mechanical construction. 



No doubt a similar degiee of evidence might be attained by repeated 

 enquetes, such as those performed by the French Government. The 

 marvellous consilience between most of the ratios yielded by the samples 

 of 1878 and 1885 goes far, as already observed, to establish the accuracy 

 of those ratios. It is, however, desirable, for the purpose of exact com- 

 putation, to have a numerical limit to the possible error of each proportion 

 which we utilise. And, at any rate, it is philosophical not to expend 

 labour in increasing our materials, when the same amount of evidence 

 could be crushed out of a smaller quantity of material by a properly 

 directed scientific process. 



Moreover, if this operation be performed, we shall be able, so to speak, 

 to cut the argument much more finely ; to obtain a smaller, perhaps much 

 smaller, superior limit than would be safe for the empirical statistician. 

 It will be recollected that a coinage of recent date was selected as the 

 basis of our calculation, because, in general, recent coinages have suffered 

 less loss. But there is some evidence that there are exceptions to this 

 rule. Now, if this evidence were confirmed by rigid application of the 

 mathematical test, we might obtain a much more favourable basis for the 

 calculation than it has hitherto been safe to employ. 



The matter is placed in a very clear light by the French statistics, 



, . 1 , , 1 , „ , ,, ,. Number of samples 



wnicn tabulate tor each year the ratio -^ ; ? — ■ -■ r (m De 



JN umber ot coins issued ^ 



Foville's notation tj). Now the expression for the superior limit may, 



after De Foville, be written 



Number of coins issued 



Number of samples ^ ^°*^^ °™^^'' of samples. 



For our purpose, to find the smallest superior limit, the largest value 

 of the ratio designated by the French as y would be the best, provided 

 that it is accurate. 



2 



De Foville employs a ratio of about -txtj-t ; but there occur in the 



French statistics the entries 7, 12, 17, nay 26 (each to be divided by 

 1000) ; and in the Belgian statistics much more startling proportions. 



Supposing we were assured that :j-7^ was a genuine ratio (the coinage 



of the particular year corresponding having suffered particularly little — 

 a quite reasonable supposition, as De Foville shows), then, the number 



' See above, p. 225 and p. 227. 



