108 Pen field and Foote — Composition of Tourmaline. 



On treating the analyses according to the customary method 

 of deriving a formula (dividing each constituent by its molec- 

 ular weight and finding the ratio of the quotients) it was 

 found that although the Si0 2 and B 2 3 were present in the 

 proportion of 4:1, no definite relation could be detected between 

 the silica, the different kinds of oxides, and the water. It was 

 decided, therefore, to determine the relative number of hydro- 

 gen atoms equivalent to the metals and thus learn the acid 

 from which tourmaline is derived. This was readily accom- 

 plished by dividing the constituents by appropriate fractions of 

 their molecular weights ; for example, since the aluminium 

 atoms in A1 2 3 replace six hydrogens, the quantity of A1 2 0, 

 was divided by one-sixth of its molecular weight, the FeO by 

 one half of its molecular weight, etc. Since fluorine is 

 regarded as playing the same role as hydroxy], its ratio was 

 added directly to that of the hydrogen. The result of this 

 treatment is very satisfactory. The first analysis gives the 

 ratio of Si0 2 :B 2 3 : 11 = 4:1 : 19-90, and the second 4:1-02: 

 19*98. Both ratios approximate so closely to 4:1:20 that 

 there can be no reasonable doubt that the acid from which 

 these tourmalines are derived is H 20 B 2 Si 4 O 21 . This formula 

 may seem at first somewhat complex, but it is not especially 

 so for a boro-silicic acid. It can not be simplified by division, 

 and it is based upon the very best kind of evidence, namely, 

 the close approximation to rational numbers of the two ratios, 

 which are derived from widely separated types of tourmaline. 



Before discussing the possible constitution of this acid, it will 

 be shown to what extent the analyses of other investigators 

 confirm the results obtained by us. 



Keview of Rammelsberg's Analyses. — The analyses 

 appear with certain variations in his different publications, 

 and the results which will be discussed here are given in his 

 Miner alchemie, 1875. These are quoted in the sixth edition 

 of Dana's Mineralogy, and where there is occasion to refer to 

 individual analyses they will be designated by the numbers 

 assigned to them in the latter work. The same plan also will 

 be adopted for the analyses of Biggs, Jannasch and Kalb and 

 others. Thirty-five analyses are given by Rammelsberg, of 

 which No. 34 is not complete. 



Adopting the same method of calculation as applied to our 

 own analyses, and using one-fourth of the silica as unity, the 

 ratios of Si0 2 : B 2 3 were found to vary between 4 : 1*21 and 

 4 : 0*71, and the ratios of SiO a to the total hydrogen atoms 

 between 4 : 16*5 and 4 : 19*7. The result of grouping the ratios 

 of the hydrogen atoms is as follows : 



Limits of variation, 16'5 — 175 17-5 — 18-5 18-5 — 19-5 19*5 — 19*7 

 Number of analyses, 8 12 12 2 



