WRIGHT AND VAN OSTRAND : MINERAL ANALYSES 231 



in equation (5). Since the weights are here inversely propor- 

 tional to the {x) values, it follows that small molecular ratios 

 are adjusted more accurately than the larger numbers. 



Summary. Of the methods available for comparing the ob- 

 served results of a mineral analysis with those obtained from the 

 chemical formula to which the analysis corresponds approxi- 

 mately, the best method is to ascertain first the weight numbers 

 (derived from the chemical formula by multiplying these ratios 

 by the proper molecular weights), and then to adjust these values 

 to the given analysis by the least square method. Since the com- 

 putations involved are, however, somewhat laborious, and further- 

 more, since there are a limited number of observations and the 

 systematic errors of observation are, in general, large as compared 

 with the accidental errors, the simple method (3) (equation 6) is 

 preferable for general use. It furnishes results which are very 

 nearly correct and consists simply in reducing the weight num- 

 bers proportionately so that their sum is equal to that of the given 

 analysis. In other words, we compare the actual analysis directly 

 with the weight percentage analysis computed from the inferred 

 chemical formula, both analyses having a common sum. The 

 differences between the observed and computed values are then 

 a sufficient measure of the degree of agreement of observation 

 with theory. The two general formulas (3) and (6) furnish the 

 best solutions of the present problem. In these formulas y may 

 be taken to represent weight percentages, mol numbers or molecu- 

 lar ratios, while x represents respectively the weight numbers, the 

 molecular ratios or the mol numbers. Equation (3) always gives 

 a more precise adjustment, but equation (6) is in general suffi- 

 ciently accurate for the computations here considered. The 

 relation between weight percentages and weight numbers is 

 rigorous. The relations between mol numbers and molecular 

 ratios are lacking in rigor, but are usually sufficiently accurate 

 for the purpose. ' 



