68 ABSOLUTE ATOMIC WEIGHT. 



In this way we shall see, by contrast, the effect of the 

 greater value of the material used in producing much more 

 accurate work at the mint and a consequent greater accuracy 

 in our determination. 



This corresponds exactly to the difference between ordi- 

 nary chemical analysis and atomic weight determinations. 



Roughly speaking, the work on gold coins is ten times as 

 accurate as the corresponding work on the silver coins. 

 Accordingly we have to weigh to the milligramme. 



We shall restrict ourselves to such subjects of this inves- 

 tigation as are immediately applicable to our atomic weight 

 determinations. 



The Mean Weight of the Half Eagle. 



The most suitable United States Gold Coin for this study 

 is the Half Eagle, corresponding to the English Sovereign 

 and to the German Twenty Mark coin. Its value is five 

 dollars. It is the most common gold coin of the world. 



Drawing six such coins at a time at the Bank, I have 

 gradually obtained over one hundred such coins, exactly as 

 they were current during the first six months of this year, 1901 . 



Each coin was weighed to the milligramme and the mean 

 of each lot of six coins was calculated. The following table 

 gives these means in lots of sixes in the order of time: 



8.298 8.328 8.346 8.359 8.331 8-337 8.340 - 

 8.348 8.340 - 8.343 - 8.337 8.340 - 8.333 - 8.349 ~ 



8-339 - 8.327 8-334 - 



These means vary quite considerably. The first is the 

 lowest, 8.298; the fourth is the highest, 8.359. The range 

 of these means (of six each) is 0.061 or 61 milligrammes. 



The mean weight, of six each, 75 not the true -weight, very 

 evidently. 



Let us see, how the means will run jf we combine con- 

 secutively two of the groups, so as to get the means of 12, 

 then of 24, and lastly of 48 coins, in the order of time, 

 exactly as they came gradually to hand. 



The means of twelve coins each are: 8.313 8.352 

 8-334 s -344 8.341 8.339 8-34 1 8.333- 



