122 Penfield and Foote — Composition of Tourmaline. 



magnesia and iron, and are hence designated' as Magnesia-Iron 

 Tourmalines. These two groups, however, grade into one 

 another. The fusibility of these intermediate groups of tour- 

 malines varies from 4/5 to 3, and decreases as the amount of 

 iron and magnesia increase. 



Although in this series of thirty-five analyses there are pro- 

 nounced groups or types of tourmaline which may be recog- 

 nized, nowhere in the series do the ratios of R'", K", B/ and 

 H approximate so closely to rational numbers that a definite 

 formula for any one type can be instituted. Riggs and Jan- 

 nish and Kalb, however, have given special formulas for 

 different types of tourmaline (pages 100 and 101) based upon 

 multiples of the acid H 18 (B.OH) 2 Si 4 19 . Deducting from 

 their formulas appropriate multiples of the aluminium-boro- 

 silicic radical [Al 8 (B.OH) 9 Si 4 19 ], it is found that the nine vari- 

 able hydrogens of the tourmaline acid are replaced by metals 

 of different valences in the following proportions : 



R'" R" R' H 

 Riggs 7-0 0-0 1-3 0-7 



I. Lithia tourmaline . 



II. Iron tourmaline. _. 

 III. Iron-magnesia tour. Jann. and Kalb 4*0 4*0 0-7 0*3 



Jann. and Kalb _.. 6 '0 1*4 1-3 0*3 



Riggs. 5-0 2-6 0-7 0*7 



Jann. and Kalb. _. 5-0 3*0 0"7 0*3 



Concerning the formulas for lithia tourmaline, Riggs' cor- 

 responds closely to No. 1, and Jannasch and Kalb's to Nos. 7, 

 8, 9 and 10 of our series (compare the table on p. 120), but 

 neither of these complicated formulas furnishes a satisfactory 

 expression for this type as a whole. Similar statements might 

 be made concerning their formulas for iron tourmalines and 

 for iron magnesia tourmalines. The endeavor to express the 

 composition of tourmaline or of one of its types by a definite 

 formula may be compared to the attempt to express the com- 

 position of the dark varieties of sphalerite by a formula. Thus 

 Zn n Fe 4 S 16 would correspond to sphalerite, containing about 50*5 

 per cent of zinc and 15*7 per cent of iron, but zinc and iron 

 are isomorphous and can mutually replace one another in 

 sphalerite, and a variety containing less iron would have to be 

 expressed by a different formula. When, however, we under- 

 stand the isomorphous relations existing between zinc and 

 iron, and express the composition by RS, where R=Zn and 

 Fe, the composition becomes very much simplified. 



In tourmaline we have an isomorphous relation of a very 

 peculiar nature, for in the acid H 9 Al 3 (B.OH) 2 Si 4 19 the nine 

 hydrogens may be replaced to a large extent either by the 

 trivalent metai aluminium or by the bivalent metals magnesium 



