32 Penfield — Interpretation of Mineral Analyses. 



sidered that the ideas presented are capable of being definitely 

 proved. All of the analyses indicate that at least half of the 

 hydrogen atoms of the tourmaline acid, are replaced by alu- 

 minium, and this fact, coupled with the idea that it seems 

 reasonable to unite the two hydroxy 1 radicals with the two 

 boron atoms, led to the suggestion by Foote and the author* 

 that the characteristic feature of all varieties of tourmaline is 

 an aluminium-borosilicic acid, JI 3 Al 3 (B.OIT)„Si 4 O 10 . In this 

 acid the mass effect of the (Al 3 (B.OH),,Si 4 19 ) is regarded as so 

 overwhelming that it makes no difference how the nine remain- 

 ing acid hydrogen atoms are replaced, whether largely by 

 aluminium and to a trifling extent by bivalent metals and alka- 

 lies, or largely by magnesium and to a trifling extent by 

 aluminium and alkalies, the result in all cases is tourmaline 

 with its characteristic crystalline structure. That trivalent, 

 bivalent and univalent metals, playing as it were the role of 

 isomorphous constituents, may unite in replacing the nine 

 hydrogen atoms of the tourmaline acid, is indeed a remarkable 

 feature of isomorphism, but it furnishes an explanation of the 

 composition of tourmaline, and one which can be compre- 

 hended, in part at least. 



Looked at from the standpoint of an instructor, what expla- 

 nation of the chemical composition of tourmaline can be given 

 to a student provided the ideas of Tschermak prevail ? Only 

 this, that the composition is exceedingly complicated ; that 

 there are two molecules Tu and Tm (page 30), exhibiting cer- 

 tain analogies to minerals of the mica group, which mix in 

 varying proportions, and that by taking appropriate multiples 

 of the two molecules theoretical compositions can be calculated 

 to agree with the results of analyses, provided the latter are 

 very much simplified. By taking molecular mixtures contain- 

 ing in the aggregate several hundred and even thousand atoms, 

 as done by Clarke (page 28) and Tschermak (page 30), it would 

 seem as though chemists or perhaps arithmeticians might aspire 

 to devise formulas for expressing the chemical composition of 

 any sort of substance of which any kind of an analysis has 

 ever been made. 



*Loc. cit., p. 118. 



Sheffield Laboratory of Mineralogy and Petrography, 

 Tale University, New Haven, June, 1900. 



