WRIGHT AND VAN ORSTRAND : MINERAL ANALYSES 227 



percentages of column 1 by the proper atomic (respectively 

 molecular) weights;* from these mol numbers, we have 



S : As : (Ag2 + Cus) = 0.5444: 0.1008: 0.3975 



and infer that the correct chemical formula numbers are 



S : As : (Ag2 + Cu,) = 55 : 10 : 40 = 11 : 2 : 8. 



These numbers (column 3) are th«n multiplied by the proper 

 atomic (respectively molecular) weights and the (x) values of 

 the equations (1) obtained (column 4). The value of m is now 

 found from equation (3) by dividing the sum of the products of 

 the observed values (y) (column 1) and the theoretically correct 

 values (x) (column 4) by the sum of the squares of (x). On 

 multiplying the (x) values by the value oi 7n ( = 0.049682) thus 

 computed we find the values in column (5); the differences be- 

 tween the observed (y) and computed (y') values (o — c, column 

 1 — column 5) are a proper measure of the degree of approxima- 

 tion of the actual analysis to that computed from the inferred 

 chemical formula. The rigorous test would consist in computing 

 the probable error of a single observation but this procedure is 

 perhaps unnecessary for data of the character here considered. 



Second 7iiethod. This method is a mathematical refinement 

 of the first method but it does not give values which are of suffi- 

 ciently greater precision to warrant the extra labor involved in 

 computation nor does the assumption that {x) contains errors of 

 observation seem to be rigorously justified unless errors in the 

 atomic weights are of sufficient magnitude to be taken into account. 

 In this method it is assumed that both the {x) and the {y) values of 

 equations (1) contain errors of observation. The proper value of 

 m to meet the conditions is then obtained from the equation 



(4) 



\ rrix/ 



wherein 



* In his paper Schaller did not state the atomio (respectively molecular) weights 

 which he used in his computations. They are readily found, however, by dividing 

 the numbers of the first column by the corresponding ones of the second. They are 

 S = 32.07; As = 75.00; (Ag,) = 215.82; (Cua) = 127.13. 



