Penfield — Interpretation of Mineral Analyses. 31 



and marcasite as FeS 2 ; calcite and aragonite as CaC0 3 ; rutile, 

 octahedrite and brookite as Ti0 2 ; and cyanite, andalusite and 

 sillimanite as Al 2 SiO B . If, therefore, for these compounds the 

 simplest formulas are employed, it seems certainly a great pre- 

 sumption to state that in the case of tourmaline the complex 

 three-fold formula had been definitely proved. 



Finally Tschermak, who, like Clarke, does not seem to take 

 into consideration that some analyses may not be reliable, tries 

 to explain the composition of the tourmalines from Pierrepont 

 and Gouverneur (Nos. 19 and 20, p. 22), and Tamatawe (No. 9, 

 page 22), by assuming the existence of a third molecule, Tn — 



Si M B.Al 8 Mg ja H 8 O ai - B 6 Al 4 16 .2(Si 3 Al 2 H 4 O n .Si 3 Mg 6 Cy, in 

 which the portion (Si 3 A] 2 H 4 11 .Si 3 Mg 6 1!! ), is supposed to be 

 analogous to phlogopite. It does not seem reasonable, how- 

 ever, to believe that the tourmalines from the localities in 

 question are essentially different from those from other locali- 

 ties, and need, consequently, different formulas, especially 

 since we have a recent analysis of the Pierrepont, and an early 

 analysis of the Gouverneur varieties of tourmaline by Ram- 

 melsberg, both of which conform to the H 20 B 2 Si 4 O 21 formula. 

 Summary. — As shown by the tabulation of ratios on pages 

 21 and 22 there exist a series of recently made and carefully 

 executed tourmaline analyses which give ratios of Si0 2 : B 2 3 : 

 Total Hydrogen approximating closely to 4 : 1 : 20, from which 

 the empirical formula of the tourmaline acid, H 20 B 2 Si 4 O 21 , is 

 derived. That a few analyses do not yield ratios agreeing as 

 closely as desired to 4 : 1 : 20 is not to be wondered at, when 

 the difficulties presented by the analysis are taken into con- 

 sideration, together with the fact that the material analyzed 

 might not in all cases have been perfectly pure and homo- 

 geneous. As far then as analytical evidence may be relied 

 upon for establishing the formula of a mineral, it may be con- 

 sidered as definitely proved that the empirical formula of the 

 tourmaline acid is i? 20J # 2 6Y 4 (9 21 . The science of inorganic 

 chemistry has not yet reached such a state of development that 

 it can be proved, as stated by Tschermak, that the threefold 

 formula, H 60 B 6 Si, 2 O 63 , is the correct one. The empirical 

 formula H 30 B 3 Si 6 O 3l , proposed by Clarke, can rest only on the 

 analytical evidence supplied by a few analyses of Riggs and 

 one by Jannasch and Kalb which yield ratios approximating 

 to 4:1: 19%33 (page 22), and there are good reasons for 

 believing that these ratios would not be obtained a second time 

 if the analyses were repeated. Since tourmaline always yields 

 sufficient water to form two hydroxyl radicals, it may be con- 

 sidered as probably, if not absolutely, proved that the formula 

 of the tourmaline acid should be H^iOH^^BJSif)^. Beyond 

 this point it seems safe only to speculate and it cannot be con- 



