THE PROBABLE ERROR OF THE ME AX. 



Not having been able to obtain new silver dollars, even 

 at the United States Subtreasury in St. Louis, I cannot 

 determine the value of the actual tolerance .practiced in 

 coining our silver dollars. 



A single stray new silver dollar of 1901, a rara avis in the 

 West, was just trapped and found to weigh 26.77 grammes, 

 which is 4 centigrammes above legal weight. 



Estimate from Quarters. 



But I succeeded in getting absolutely new quarters, at the 

 Boatmen's Bank. The mean weight was 6.250 grammes; 

 the heaviest 6.30, the lightest 6.20, showing a tolerance 

 either way of 5 centigrammes. 



If we could be permitted to take the new quarters as one 

 fourth of a new silver dollar, the latter would weigh 25 .000 

 grammes and show a greatest tolerance of 20 centigrammes 

 either way. 



But this mean is i .73 grammes below the legal standard; 

 accordingly we must suppose that the legal weight of a 

 quarter is considerably less than the fourth of the legal 

 weight of the silver dollar. 



This shows, how complex even so simple a case as the 

 experimental determination of a common silver dollar coin 

 becomes when tried, without reference to the law governing 

 the coinage. 



Now, chemists have tried to experimentally determine the 

 weight of the atoms without reference to the general Laws 

 of Nature. No wonder they made a mess of it, and now 

 want to settle it by vote. 



III. THE PROBABLE ERROR OF THE MEAN. 



Scientists hold, that the probable error of a single 

 observation is at such a distance from the mean that it is an 

 even wager or an even chance for a single actual observation 

 to fall within this distance or beyond it. 



In other words, if we arrange all observed values in the 

 order of their magnitude, one half of all should fall nearest 

 the mean and be not more distant therefrom than is measured 

 by the probable error of a single observation. 



