THE ERRORS OF PRECISION. 



The range in any one series of twenty silver dollars 

 varies from 61 to 105 centigrammes, averaging 83 centi- 

 grammes for each series of twenty coins. 



Mean Weight not True Weight. 



But can we for a moment accept the mean weight of the 

 two hundred silver dollars actually weighed as the true 

 weight of a United States Silver Dollar? Is the mean 26.39 

 grammes actually determined from two hundred weighings, 

 the true weight of our silver dollar? Is the mean value of 

 the means of ten series of twenty determinations each the 

 true weight? 



Most assuredly not; nor would we obtain that true weight 

 by indefinitely continuing this work of actual weighing the 

 coins in circulation. 



We have here a plain case showing the fallacy of accept- 

 ing the mean value as the true value, even if determined by 

 ten series of twenty experimental determinations each. 



Effect of Wear. Abrasion. 



In this case the cause of the error of the mean is well 

 understood : it is due to the wear or abrasion produced by 

 circulation, and this is not equal for the different coins but 

 varies according to the actual handling each coin has under- 

 gone since leaving the mint. 



And the amount of this abrasion will roughly depend on 

 the length of time the coin has been in circulation, which 

 time is determined by the year of coinage stamped on each 

 coin. 



It would be exceedingly interesting to give our full data 

 of observation on this subject, an account of its importance 

 on the common scientific practice of taking the mean value 

 as the true value ; but our space will allow only the following 

 general points to be stated: 



Frequency in Circulation. 



The frequency of coin of any given year is most remark- 

 ably different, and not at all equal, as might have been 

 supposed. 



