THE CONSTANT ERROR OF THE MEAN*. 21 



difficult to estimate and comprehend than the mere abrasion, 

 influenced by more or less rapid circulation and by peculi- 

 arities in the frequency of certain coinage years over others ; 

 but they are not less real than errors due to abrasion. 



The unavoidable errors affecting the different chemical 

 processes are, however, not all working one way, as it is 

 necessarily in the abrasion of a coin making actual weight in 

 circulation always lower than its original and true legal 

 weight. 



Lower and Higher Limits. 



Indeed, for many chemical processes we have means of 

 knowing whether they are giving the atomic weight too 

 high or too low. See Rule of Berzelius, p. 3. 



Accordingly, in such cases we know whether we obtain 

 a higher or a lower limit of the atomic weight found by the 

 chemical operation employed. 



This will enable us to fix a higher and a lower limit of the 

 atomic weight sought, but in no case is the exact or absolute 

 atomic weight thus determined ; for we have no chemical 

 means of ascertaining the exact amount of the excess or 

 deficiency due to the chemical operations used. 



The special example here considered, namely the experi- 

 mental determination of the true weight of a given coin by 

 the process of actually weighing the coin, at hand, shows in 

 a striking manner the insufficiency of mere empirical or 

 experimental work in the determination of any given quan- 

 tity actually occuring in nature or commerce. 



Laboratory Work Alone not Enough. 



The determination of the atomic weight of a chemical 

 element being a much more complicated process, involving 

 not only weighings but also chemical operations that bring 

 the material operated upon into chemical circulation, will 

 now be understood to require something more than mere 

 laboratory work and weighings, and even much more than 

 the calculation of the probable error of their mean value. 



