28 Penjield — Interpretation of Mineral Analyses. 



of Clarke's two types. Thus to express the composition of 

 the green tourmaline from Haddam Neck, where the ratio of 

 SiO„ : Total Hydrogen is very close to 4:20, Clarke employs an 

 equal number of basic and acid molecules as follows : 



Basic. l0Al.(SiO 4 ).(BO,) > .BO,(AlOH).Al t Li i H 4 . 



( 3Al 5 (Si0 4 ) c (B0 2 ) 2 .B0 3 Ca.Fe 4 H 4 

 Acid. \ lAl 5 (Si0 4 ) 6 (B0 2 )„.B0 3 Ca.Al 3 NaH 2 



( 6Al 5 (Si0 4 ) 6 (B0 2 ) 2 .B0 3 NaH.Al 3 NaH 2 . 



Prof. Clarke is very ingenious in his use of figures, and the 

 agreement between the calculated percentages and the results of 

 the analysis is indeed most satisfactory ; but what is gained ? 

 The analysis gave a ratio of almost exactly 4 : 20 and a mix- 

 ture of ten of the basic and ten of the acid types of Clarke's 

 molecules must yield a ratio of exactly 4 : 20 ; hence it is a fore- 

 gone conclusion that the theory must agree with the analysis. 

 In order to bring about the agreement, however, a mixture of 

 molecules is employed containing an aggregate of 1092 atoms. 



If we are to accept the idea that formulas must in some way 

 be found to suit all analyses, and, therefore, it is necessary to 

 have pairs of formulas of acid and basic types, why not accept 

 as the acid type for tourmaline the formula proposed by Ram- 

 melsberg, H ]R B 2 Si 4 O 20 ? By substituting two bivalent (AlOH) 

 groups for four hydrogen atoms, and then reducing to the 

 simple hydrogen expression, we obtain for the basic type H 22 

 B 2 Si 4 22 , and by the proper replacement of the hydrogen atoms 

 by metals and the combination of the two types of formulas, 

 theoretical compositions could be calculated to a degree with 

 all of the analyses. Indeed, these two formulas have some 

 advantage over Clarke's, in that they are simpler, and priority, 

 at least for one of them, can be claimed. Doubtless other 

 pairs of formulas could be devised which would suit all vari- 

 ations presented by tourmaline analyses. 



One other illustration presented by Clarke in support of his 

 theory may here be cited, black tourmaline from Auburn, 

 Maine, No. 2 of Riggs (page 22). The composition is ex- 

 pressed as follows : 



Basic. 35Al s (SiOJ 6 (BO a ) a .B0 8 (A10H).Fe 4 H 4 . 



Aid j 2Al 5 (Si0 4 ) 6 (BCg 2 .B0 3 Ca.Fe 4 H 4 

 AcuL I 27Al 5 (Si0 4 ) 6 (B0 2 ),B0 3 NaH.Al 3 NaH 2 . 



The aggregate number of atoms in the above mixture of 

 molecules is 3499. Let it be observed (page 22) that as far as 

 the ratio of Si0 2 : Total Hydrogen is concerned this analysis 

 is one of the very best, the ratio of Si0 2 : Total Hydrogen 

 being 4 :20'03, which would require the basic and acid types of 



