Penfield — Interpretation of Mineral Analyses. 27 



Another difficulty also, which Clarke evidently recognizes, is 

 that there is no appropriate place in his molecule for the 

 attachment of fluorine, and hence he suggests that the fluorine 

 may sometimes replace the group B0 2 , an equivalent, as 

 stated by him, which is strongly indicated in the cappelenite 

 group of minerals. Now from a chemical standpoint the group 

 cited containing cappelenite, melanocerite, caryocerite and 

 tritomite, seems poorly adapted for illustrating an important 

 chemical principle, since the composition of all of the minerals 

 of the group is very complicated, and only in the case of one 

 mineral, tritomite, have direct determinations of B 2 3 been 

 made. Clarke's formula, it will be observed, is applicable 

 directly to the three analyses of Riggs' (Nos. 18, 19 and 20, 

 p. 22) which are low in bases, or high in silica : it will there- 

 fore be convenient to designate it as the acid formula A. In 

 order to adapt his formula to the many analyses in which the 

 ratio of SiO„ : Total Hydrogen is approximately 4: 20, Clarke 

 presents a modification of his formula consisting in the substi- 

 tution of a basic, bivalent, aluminium-hydroxide radical (AlOH) 

 for two of the hydrogen atoms of his acid, and he always 

 2'epresents the (AlOH) radical as replacing the two hydrogen 

 atoms attached to B0 3 . Fluorine in this formula is considered 

 as combined with aluminium to form a bivalent radical (A1F) 

 isomorphous with (AlOH) instead of replacing the B0 2 group. 

 A hypothetical molecule containing the (AlOH) radical and 

 employed for expressing the composition of the green tourma- 

 line from Haddam JSIeck is as follows : 



Al.(Si0 4 ).(B0 1 ) i .B0 1 (AIOH).Al 1 Li i H 4 . 



By substituting for the metals in the foregoing formula their 

 equivalent of hydrogen, and simplifying, there results an ex- 

 pression which may be designated the basic formula B, so 

 designated because it contains more hydrogen atoms than the 

 acid formula A. The two are given together for compari- 

 son : 



A, Acid formula, H M B s Si 6 31 . 



JB, Basic for mida, H 3J B 3 Si f 32 . 



The empirical formula of the tourmaline acid, as derived by 

 Footeandthe author, H 20 B 2 Si 4 O 21 , is equivalent to H 30 B 3 Si 6 O 31 ^, 

 which is exactly midway between the acid and basic formulas 

 of Clarke. Thus in order to find expressions that will yield 

 calculated percentage values agreeing with the several analyses 

 becomes again not a matter of chemical science, but rather an 

 arithmetical problem, and one, too, which is bound to succeed ; 

 for, given the two formulas, some mixture of the molecules 

 can be found to fit any analysis which falls within the limits 



