OCR METHOD OF DETERMINATION. 



These means of twelve agree, of course, much better. 

 The first is the lowest, 8.313; the second is the highest, 

 8.352. The range is 0.039 r 39 milligrammes; only about 

 one half of the range of the means of sixes. 



Combining again these means two and two consecutively, 

 we obtain the me an weight by twenty fours of Half Eagles : 



8-333 8-339 8-340 8-337- 



These agree much closer again, the entire range being 

 only 7 milligrammes. 



The means, by forty eight Half Eagles are : 8.336 and 

 8.338, differing by only 2 milligrammes. 



The mean of these two is 8.337 for 96 Half Eagles weighed. 



We see how gradually the mean becomes more fixed, less 

 subject to fluctuation, as the number of individuals used for 

 that mean increases. 



This has led scientists to suppose, that we obtain a higher 

 accuracy as we increase the number of observations. 



We gain concordance expressible by a small probable 

 error but we have not approached the true weight. We 

 shall find this very mean 22 milligrammes low as a very 

 sound constant error. 



We understand the fallacy of this common conclusion. 

 The same number of Half Eagles in another city would not 

 even have given the same results, since other years of coin- 

 age most likely are more frequent in other towns, and above 

 all, the actual weight of all Half Eagles in circulation is low* 

 due to abrasion. This will vary greatly in time and rapidity 

 of circulation and for gold coin also with the greater or 

 less care exercised in withdrawing light coins from circula- 

 tion. The United States are not very particular in this 

 matter. 



Out of the 102 Half Eagles weighed, the following were 

 light coins: 



8.235 8.235 8.257 8.270 8.280 8.282 8.284 

 8.296 or about 8 per cent below 8.300. 



As a matter of fact, the actual coin in common use has a 

 larger number of light weights than this percentage, because 

 the teller did not hand me any coin but such as he considered 

 good coin. 



