224 WRIGHT AND VAN ORSTRAND : MINERAL ANALYSES 



The underlying purpose of such calculations is not, however, to 

 improve a chemical analysis by mathematical manipulation, which 

 is obviously impossible, but to obtain a logical basis of comparison 

 for the given analysis with the analysis calculated from the chemi- 

 cal formula. In the following paragraphs the different methods 

 which are available for such comparisons will be discussed with 

 reference to their accuracy and general applicability. It will be 

 shown that the best general method is to compare the actual 

 analysis of the mineral with the weight percentage analysis de- 

 rived from its chemical formula. This method is, moreover, in 

 conmion use. The method suggested by Schaller is not only in- 

 ferior to this and to the other methods considered below, but it is 

 incorrect in principle in certain details. 



The problem is based on Dalton's fundamental law of simple 

 atomic or molecular ratios, namely, that in a homogeneous chemi- 

 cal substance in which the relations are not veiled by solid solu- 

 tion, the atomic and molecular proportions can be expressed by 

 small whole numbers. In practice, however, we find that because 

 of various sources of error (lack of purity of material analyzed, 

 inaccuracy in chemical methods and impurities in reagents 

 employed, errors in atomijc weights, personal equation of analyst), 

 the actual data of a mineral analysis, after reduction to mol 

 numbers, only approximate whole numbers in their ratios, the 

 deviations being usually small and to be treated as errors of obser- 

 vation. In the present problem, only the final results of an 

 analysis are given and the above sources of error can not therefore 

 be differentiated and properly weighted, but have to be considered 

 together and all analytical data equally weighted. It should be 

 noted that in chemical data of this character, the systematic 

 errors are relatively large, and that, furthermore, they can not 

 be distinguished in the analytical data, as given, from the acci- 

 dental errors. Too refined mathematical treatment is, therefore, 

 unnecessary and misleading. For the sake of completeness, 

 however, the various available methods will be considered below, 

 even tho several of them are hardly to be recommended for the 

 reasons cited above. 



From the mol numbers of an analysis we infer by inspection the 



