Penfield — Interpretation of Mineral Analyses. 23 



Before entering upon the discussion of these ratios, let it be 

 understood that the analysis of tourmaline is one of the diffi- 

 cult problems of analytical chemistry, and although Riggs made 

 duplicate and often triplicate determinations of B 2 3 and H 2 

 in almost all cases, and duplicated somewhat more than half 

 of his determinations of SiO„ and F, only single determinations 

 of other constituents are recorded in his paper, while Jannasch 

 and Kalb record only single determinations. Also it is to be 

 borne in mind that although both Riggs and Jannasch and 

 Kalb undoubtedly used carefully selected tourmaline fragments 

 for analysis,* still there is nothing to indicate that slight 

 amounts of foreign materials might not have been present in 

 some of the specimens analyzed. Keeping these facts then 

 well in mind, let us examine the ratios as presented in the fore- 

 going tables. It is granted that the ratios are not exactly 

 4:1:20, and to get exact ratios from mineral analyses is not to 

 be expected, but the close approximation to 4:1: 20 in the case 

 of the two analyses by Foote and the author, of sixteen out of the 

 twenty analyses by Riggs, and of eight out of the nine analyses 

 by Jannasch and Kalb, constitutes an overwhelming amount of 

 evidence in support of the empirical formula of the tourma- 

 line acid, H^B^Si^O^. It is safe to state that there does not 

 exist a series of thirty silicate analyses of any one mineral 

 yielding ratios which approximate so closely to whole numbers 

 as the tourmaline analyses referred to above. That some 

 analyses fail to yield a ratio as close to rational numbers as 

 desired, reflects discredit neither upon the analyst nor upon the 

 character of his work, for the material for analysis might not 

 in all cases have been pure. Take, for example, No. 17 of the 

 series of Riggs, brown tourmaline from Hamburg, 1ST. J., occur- 

 ring in calcite. The ratio of SiO„ : Total PIydrogen=-4:20*6. 

 Evidently the bases are too high, and this particular analysis is 

 peculiar in that it shows 5*09 per cent CaO, while the next 

 highest percentage of CaO recorded is 3*70. The material 

 might well have contained some calcite, either as small 

 included nodules, or as an infiltration along cracks, and if 

 the amount of calcite be assumed as 1*78 per cent, equivalent 

 to 1 per cent CaO, the analysis would add up to 100*82, which 

 is not too high for such a complicated substance, and the ratio 

 of Si0 2 : Total Hydrogen would become 4'00 : 20-3 or 3-94 : 

 20*00. To assume that the Hamburg material probably con- 

 tained some calcite seems far more reasonable than to specu- 

 late, as Prof. Clark does, upon some complex formula especi- 

 ally adapted to suit this particular analysis. Again, Nos. 18, 

 19, and 20 of Riggs, and 9 of Jannasch and Kalb indicate either 



* Compare foot-note, this Journal, IV, vii, p. 115, 1899. 



