VAN ORSTRAND AND WRIGHT: MINERAL ANALYSES 521 



multiples of unity. His final comparison on the basis of equal 

 weights is therefore theoretically incorrect. 



The method of Van Horn and Cook^ which Schaller proposed 

 to improve can be obtained by substituting the appropriate 

 quantities in equation (3) but to assign arbitrarily the weight 

 infinity to a particular weight percentage is evidently contrary 

 to the analytical facts and the method is accordingly not rigorous. 



Wells takes the observed weight percentages for the x values 

 and substitutes them in equations (14) with the weights pi = 

 •rr^ ih = .T2~S . . . Pn = -^n'^- This system of weights results 

 from the assumption that the difference between the observed 

 sum and 100 is a sum either of positive or of negative systematic 

 errors, each one of which is proportional to the corresponding 

 observed percentage number. He then finds the differences 

 between the new values and the theoretical weight percentages 

 derived from the chemical formula (''absolute discrepancies") 

 and finall}" divides each value thus obtained by its formula weight 

 percentage and finds its "relative discrepancy in per cent." In 

 other words he weights each "absolute discrepancy" and thus 

 introduces a new set of weights. The arithmetic mean of these 

 relative discrepancies "the mean relative discrepancy" taken 

 without regard to algebraic signs is considered by Wells to be the 

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

 agreement of a mineral analysis with the fonnula. It is evident 

 however that in each of his methods, Wells has practically re- 

 peated Schaller's errors in a slightly different form, and in addi- 

 tion, has adopted a final criterion which consists in taking the 

 average of quantities of unequal weight. 



On page 417^ Wells objects to the use of equations (6) and 

 (7) on the basis that constant errors, and systematic errors, 

 proportional to the x values, are not taken into account. In 

 our first paper we used the term systematic error in a sense 

 different from that adopted by Wells. We referred to those 

 cases in which the method of analysis of any given component 

 gives results which are consistently too large or too small, but 



* Am. J. Sci. (4), 31:518. 1911. 

 ' hoc. cit. 



