wells: interpretation of mineral analyses 417 



the whole numbers of the formula 11, 2 and 8 than the numbers 

 above. Schaller also expressed the numbers in another form 

 intended to show their variation from whole numbers more clearly 

 as follows 11 XO.993, 2 x 1.01 and 8 xO.996. In this form devia- 

 tions from the requirements of theory are shown as factors of 

 the quantities involved. 



Wright and Yan Orstrand begin their discussion on page 224 

 as follows: ''The underlying purpose of such calculations is not, 

 however, to improve a chemical analysis by mathematical mani- 

 pulation, which is obviously impossible, but to obtain a logical 

 basis of comparison for the given analysis with the anal3^sis calcu- 

 lated from the chemical formula." Unfortunately, while object- 

 ing to "mathematical manipulation'' the authors of the second 

 paper appear to have recommended and rejected methods of cal- 

 culation on purely mathematical grounds entirely apart from any 

 consideration of the necessary chemical relationships involved. 



In the first method of calculation described they begin by infer- 

 ring that the correct numbers are 11, 2 and 8. They then derive 

 by the method of least squares a "weight percentage composi- 

 tion" (column 5) for comparison with the analysis which totals 

 99.84. In other words they present a basis of comparison that 

 totals less than the original investigators obtained in their analysis, 

 viz., 99.89, and conclude "the differences between the observed 

 (y) and computed (y') values {o-c, column 1-5) are a proper 

 measure of the degree of approximation of the actual analysis to 

 that computed from the inferred chemical formula." Let us see 

 how this works out. Assuming equal errors in all the percentages 

 of an analysis of the mineral in question, say, 0.10, we come out 

 of the comparison with the following differences: 0.05, 0.09,0.05 

 and 0.08. In other words the chemist should have unequal errors 

 in his percentages to obtain a perfect comparison! Now as a 

 matter of fact he does have unequal errors in his percentages, and 

 these errors are roughly proportional to the percentages involved. 

 Working out the scheme on the assumption that the errors are 

 the same fraction, say 1 /200th of all the percentages gives no 

 differences whatever. Obviously the more nearly all errors can 

 be made proportional to the quantities of substance involved the 

 better the comparison will turn out on the whole. 



