VAN ORSTRAND AND WRIGHT! MINERAL ANALYSES 525 



then compute the weights from formula (12). The latter is 

 the rigorous method of procedure and should be adopted when- 

 ever practicable. 



In general, however, it is not essential that weights be assigned 

 to the observed values. It is generally sufficient to compare 

 the theoretical values directly with the abserved values, a method 

 which chemists adopted from the first and have used consistently 

 up to the present time. For the comparison of several analyses 

 of the same mineral the established method of direct comparison 

 of the weight percentages listed in the analyses is usually sufficient 

 and satisfactory. 



In case it is desired to test for systematic errors, or to obtain 

 a more precise agreement between observation and theory, 

 equation (6) or (7) should be used. Equation (6) is the simplest 

 from the standpoint of computation, but necessitates the use of 

 weighted residuals. Equation (7) is a little more difficult to 

 compute but the difficulty of using weighted residuals is avoided. 

 Since there are not, in general, sufficient data available to enable 

 one to assign weights correctly, it follows that equation (7) most 

 nearly represents the facts. The values obtained from (6) differ 

 only slightly from those obtained from (7) and may be used as a 

 sufficient approximation. Equation (5) is enj;itled to considera- 

 tion for the reason that the sum of the percentage residuals 

 vanishes. (See equation 3.) It is defective in that a prepon- 

 derance of weight is given to points near the origin. The same 

 is true of (6), but to a much less degree. The application of the 

 remaining equations, of which there is an infinite number, in- 

 volves the use of weights for which no valid reason can be given 

 except for certain special cases. 



Percentage errors are best computed from the differences be- 

 tween the theoretical weight percentages and the observed, or 

 the computed, weight percentages. 



