THE ERRORS OF PRECISION. 



The weighings give the ratio Pb O : Pb = a, from which, 

 for O = 16 assumed, the value for the atomic weight is easily 

 calculated. 



The material used should be absolutely pure, the change 

 absolutely complete and without loss, and all weighings 

 absolutely exact. 



Strictly speaking, it is impossible to produce any material 

 in an absolutely pure condition. It is equally impossible to 

 completely convert any such substance into some other form 

 of combination, without loss of any particle of matter, or 

 without the accession of any particle of some other com- 

 position or nature. 



Hence the chemical work required in atomic weight 

 determinations can only be done approximately, not with 

 absolute accuracy. 



In other words, the chemical or laboratory work can only 

 give us the atomic weight affected with a certain mhinte 

 error, which this chemical work in any given single case is 

 unable to determine. 



By varying the chemical process involved in the deter- 

 mination, we therefore find different values for the atomic 

 weight of the same element, because the minute chemical 

 errors involved are necessarily different in the different 

 processes. 



Every page of this book, giving the record of all the 

 chemical determinations actually made during a century, will 

 show these differences, which often are quite considerable 

 in amount. We shall as an example for this introductory 

 exposition, give all the results obtained by Mallet for the 

 atomic weight of gold. 



For these reasons, and also simply as a matter of fact and 

 record, the mere laboratory work of the chemist cannot give 

 us the true or absolute value of the atomic weight of any 

 element. The empirical values so obtained we shall subject 

 to a thorough but a very simple mathematical examination 

 to deduce from these conflicting empirical values the true 

 atomic weight, freed from the unavoidable errors of the 

 laboratory work. 



