114 Penfield and Foote — Composition of Tourmaline, 



As already stated, Rammelsberg admits that his water deter- 

 minations are too low; he also states that the formula for a 

 complex mineral like tourmaline cannot be determined from 

 a few analyses but must be derived rather from the average of 

 many determinations. If then it may be assumed that his loss 

 on ignition, when corrected for the oxidation of the iron, gives 

 a close approximation to the amount of water, his results 

 on the whole agree with the formula H 20 B 2 Si 4 O 21 . It may 

 also be stated that if the analyses are not corrected they lead 

 to no satisfactory formula. 



Eeview of Riggs' Analyses. — Twenty analyses of Ameri- 

 can tourmalines were made by Riggs, and the ratios derived 

 from them furnish the very best evidence of the accuracy of 

 his results. The ratios are as follows : 









Total 









Total 



No. 



Si0 2 



B 2 3 



hydrogen. 



No. 



Si0 2 : 



B 2 3 



hydrogen 



36. 



4 



: 090 



: 20-2 



46. 



4 : 



0-96 



, 20-2 



37. 



4 



: 0-93 



; 20-5 



47. 



4 : 



0-98 : 



20*08 



38. 



4 



; 0-92 



19*5 



48. 



4 : 



1-01 



1 20*06 



39. 



4 



: 0-94 



19-7 



49. 



4 : 



1-01 



, 20-32 



40. 



4 



: o-96 : 



193 



50. 



4 : 



0-98 ! 



19-2 



41. 



4 



0-92 : 



19-7 



51. 



4 : 



0-91 



: 19-6 



42. 



4 



0-97 : 



19-8 



52. 



4 : 



0-94 J 



20-11 



43. 



4 



094 ; 



20-03 



53. 



4 : 



097 



: 18-9 



44. 



4 



: 88 



; 20'2 



54. 



4 : 



0-98 ; 



19-8 



45. 



4 : 



0-95 ; 



20-03 



55. 



4 : 



1-01 ! 



i 20-6 



The average of these ratios is 4 : 0*95 : 19*88, or a very close 

 approximation to 4 : 1 : 2$, which indicates that tourmaline is 

 derived from the acid H 20 B 2 Si 4 O 21 . It is pointed out by Riggs 

 that "the boric acid found invariably falls short of the theory." 

 This is generally, though not always, the case, and it is pre- 

 sumed that this slight defect in the analyses is due to the fact 

 that it is not always possible to obtain a correct determination 

 of boric oxide by the Gooch method without a second fusion of 

 the silicate with sodium carbonate, which Riggs does not men- 

 tion having made. It is not indicated by the ratios that these 

 analyses "give as a general tourmaline formula the simple 

 boro-orthosilicate R 9 B0 2 2Si0 4 " suggested by Biggs. The 

 nearest approach to this is analysis No. 53, in which the ratio 

 of Si0 2 to the total hydrogen is 4 : 18*9. The ratios with few 

 exceptions show a very close approximation to the rational 

 numbers 4 : 1 : 20. In eleven cases the numbers for the hydro- 

 gen ratios vary between the narrow limits 19*8 and 20*2; How 

 exact the analyses must be in order to yield such ratios may be 

 best understood when it is known that a difference of one-half 

 of one per cent in the estimation of either silica or water would 



