422 wells: interpretation of mineral analyses 



If the arguments set forth in the preceding discussion are vahd 

 the relative discrepancies in the last columns are the best indices 

 of the agreement of the data found with the formula assumed. 

 To say that 10.95 has a discrepancy of —0.5 per cent from the 

 theoretical value 11 is very simular to expressing 10.95 as 11. X 

 0.995. In my opinion the "mean relative discrepancy" is probabl}^ 

 the best single value which can be found to indicate the order of 

 agreement of a mineral analysis with the formula. 



The principal conclusions in this paper may be summarized 

 as follows: 



1. "Differences" are not a good measure of concordance when 

 comparisons are made between several numbers of different mag- 

 nitude or where different chemical elements are concerned. The 

 discrepancies should also be thought of as factors or percentages 

 of the quantities involved. 



2. Before a mathematical simplification in analytical data is 

 attempted the nature of possible errors and their mode of trans- 

 mission to the final result should be considered. 



3. The analytical percentages of a mineral analysis will in 

 general contain some random errors and will certainly contain 

 errors characteristic of the individual elements. The errors will 

 however tend to be proportional to the quantities of substance 

 involved. If the chemist wishes to bring up the accuracy of all 

 the constituents to their full measure in the determination of the 

 whole mineral, he should devote his chief attention first to the 

 constituent which he believes to be subject to the greatest abso- 

 lute error and next to the other constituents in the order in which 

 they occur by weight beginning with the predominating one. 



4. Any method of comparing the analytical data with theory 

 which involves a distribution of the discrepancies may mask 

 some relations, such as those of solid solution or the presence of 

 a free element and should therefore be used only in the case of 

 pure compounds. 



5. The percentage of the essential constituents found should 



first be expanded to 100 per cent and then compared directly with 



the theoretical percentages. Or the combining ratios found may 



, 1.- T 11 ji r J molecular weight assumed , ,, 



be multiplied by the lactor -—- and the atom 



numbers thus found compared with theory. 



