

30 Penfield — Interpretation of Mineral Analyses. 



ble method, unite in testifying that accurate and reliable esti- 

 mations of B 2 3 were exceedingly difficult, in fact almost im- 

 possible, to obtain. Jannasch and Kalb employed Bodewig's* 

 modification of Marignac's method for estimating B 2 3 , weigh- 

 ing boron as KBF, ; hence, considering the complex character 

 of tourmaline, their determinations are certainly as close to the 

 truth as could be expected (see page 22), especially when it is 

 taken into consideration that some boron would be lost if 

 a double fusion with alkali carbonate was not made. 



Tschermak seeks to explain the composition of tourmaline as 

 a mixture of two complex silicate molecules, as follows : 



Si 11 B,Al IB Na 4 H 8 M =B 6 Al 4 1 ..4(Si 1 Al I NaH 1 1 ,)=r«. 



Si 12 B 6 Al 10 Mg 12 H O 63 =B 6 Al 4 O 1 ,2(Si 3 Al 3 H 3 O ] ,Si 3 Mg 6 O 1 J=7 7 m. 



The radical (Si 3 Al 3 NaH 2 12 ), in Tu is the generally accepted 

 paragonite formula, and (Si 3 Al 3 H 3 12 .Si 3 Mg 6 12 ) in Tm is 

 Tschermak's typical meroxene formula, except that a part of 

 the hydrogen in meroxene is replaced by potash. Thus tour- 

 maline is supposed by Tschermak to contain mica molecules in 

 combination with the boron radical B 6 A1 4 1B . 



In order to express the composition of the two varieties of 

 tourmaline analyzed by Foote and the author, the following 

 relations are employed : for Haddam Keck, Tu ti , Tm^ and for 

 DeKalb, Tu 19 , Tm 31 . The foregoing relations when written 

 out in linear form are, respectively, Si 612 B 306 Al 774 Mg 84 Ka 176 H 394 

 3213 , and Si 6 „ B 300 Al 678 Mg 444 Na 52 H 326 O 3160 . Thus with expressions, 

 each containing about 5500 atoms, Tschermak shows that the 

 calculated percentages agree in a satisfactory manner with the 

 results of the analyses after the latter have been very much 

 simplified by making numerous substitutions and recalculating 

 to 100 per cent. 



The two formulas of Tschermak, Si 12 B 6 Al ]6 lSra 4 H 8 63 (Tu) 

 and Si ]2 B 6 Al 10 Mg 12 H 6 O 63 (Tm) are both derived from an acid 

 H 60 B 6 Si ]2 O 63 , which is three times the empirical formula H 20 B 2 

 Si 4 21 proposed by Foote and the author. Tschermak states 

 that to refer tourmaline to the simpler acid H 20 B 2 Si 4 O 21 is a 

 decided step in the wrong direction, since it was shown ten 

 years ago that the three-fold formula was correct. True, by 

 taking suitable mixtures of Tschermak's Tu and Tm molecules, 

 it is possible to calculate theoretical percentages which agree 

 closely with the results of simplified analyses, but that fact 

 does not necessarily prove the correctness of the formulas 

 under consideration, and that the true constitution of tourma- 

 line has been established. In his admirable Lehrbuch der 

 Mineralogie Tschermak gives the composition of both pyrite 



*Zeitschr. Kryst., viii, p. 211, 1883. 



