THE ERRORS OF PRECISION. 



The 61 silver dollars coined between 1889 and 1891 gave a 

 mean weight of 26.405 grammes; 1890 is their mean year of 

 coinage. 



The mean weight of these 61 dollars exceeds the mean 

 weight of the 68 which are 8^ } 7 ears older, by 0.117 

 grammes; hence the abrasion was at the rate of 0.137 in the 

 ten years, between 1880 and 1890. 



Calculated Weight of New Coin. 



If we were permitted to assume the same amount of 

 abrasion during the ten years from 1890 to 1900, we would 

 fix the mean weight of a silver dollar at the mint in 1900, 

 before entering into circulation, at 26.54 grammes, namely, 

 to the mean weight, 26.405 for 1890 we would add the 

 abrasion 0.137 found for ten years in the eighties. 



Since now the abrasion of new coins is not necessarily 

 the same per year as the abrasion for older coins that have 

 already lost the most prominent points by abrasion, this 

 calculated weight of 26.54 as the mean weight of a new 

 silver dollar coined at our mints in 1900 is only a lower limit 

 itself. 



In that mean weight the tolerance will figure as an equally 

 possible variation above and below the mean 



Testing the Result. 



I was unable to secure at banks and even at the U. S. 

 Subtreasury in the City of St. Louis any silver dollars that 

 had not yet been in public circulation. 



But the legal weight was stated to be 412 .50 grains, which 

 is equivalent to 26.730 grammes. Hence we see that an 

 estimate from the mean weights is still too low by 19 centi- 

 grammes. 



Even the means of the highest observed is still one centi- 

 gramme below the legal standard. 



But in four of the ten lots of twenty silver dollars, the 

 heaviest exceeded by a few centigrammes the legal standard. 



It is well understood that it is impossible to produce 

 coins of the exact weight fixed by law; a practical limit is 

 assigned, called the "tolerances'* 



