230 WRIGHT AND VAN ORSTRAND I MINERAL ANALYSES 



weights, and are therefore differently weighted because the mole- 

 cular (respectively atomic) weights are different. In the present 

 case these objections do not seriously affect the results obtained, 

 but the objection is nevertheless valid and the methods are in 

 error to that extent. 



Seventh, eighth and nmth methods. In these methods the adjust- 

 ments are made on the assumption that the mol numbers are 

 theoretically correct {x values), while the molecular ratios (y) 

 contain the errors of observation. This is a still further depart- 

 ture from correct theory, and neither these methods nor those 

 noted in the last paragraph are to be recommended. The values 

 obtained by the seventh method involving adjustment by least 

 squares are listed in column 7, while the differences (o — c) 

 between columns 3 and 7 are given in column 7a. Similarly, the 

 results obtained by use of the ninth method, which corresponds 

 to method 3, are given in column 8 and the differences (o — c) 

 in column 8a. It may be noted here that insofar as the numerical 

 computations are concerned, it is immaterial which set of quantities 

 (x or y) are assumed to contain errors of observation when equa- 

 tion (6) is used, but different results are obtained when the quan- 

 tities are adjusted by means of equations (3) and (4). 



Schaller's method is in error in the following details of principle : 



1. Comparisons are made between mol numbers and molecular 

 ratios on the assumption that the mol numbers are theoretically 

 correct while the molecular ratios contain the errors of observa- 

 tion. The objections cited under methods 7 to 9 apply, therefore, 

 to his method. 



2. The numbers given in his column (2), page 98, are of unequal 

 weight and the arithmetic mean is not, therefore, a correct aver- 

 age. 



3. The final values in his last column near the bottom of page 

 98 are obtained by dividing the computed numbers in his column 

 (3), page 98, by the molecular ratios. These values are accord- 

 ingly of different degrees of approximation because differently 

 weighted. 



4. His method may be stated in the form of an equation by 

 putting 



