26 Penfield — Interpretation of Mineral Analyses. 



possible to determine both SiO„ and B 2 3 by difference, and 

 this treatment of Rammelsberg's analyses was fully discussed 

 by Foote and the author. In the present instance it is only 

 necessary to repeat here the ratios between Si0 2 and Total 

 Hydrogen derived from the two analyses, which are to be com- 

 pared with Numbers 19 and 20 (page 22) of Riggs. 



Si0 2 : Total H. Si0 2 : Total H. 

 Black tourmaline, Pierrepont, analyzed in 1889, 4-00 : 20-2 3-96 : 20-00 



Brown tourmaline, G-ouverneur, analyzed in 1850, 4 - 00 : 20 - 7 3'86 : 20-00 



Thus Rammelsberg's results for these two varieties conform 

 to the H 20 B 2 Si 4 O 21 formula, rather than to the more complicated 

 one proposed by Clarke. The analysis of the black tourmaline 

 from Pierrepont is one of the last, if not the very last, analysis 

 made by Rammelsberg, and he claimed for it a high degree of 

 accuracy.* The ratio derived from it is certainly very close to 

 4:20. 



As an aluminium boro-silicic acid, Clarke writes his formula 

 in linear form as follows : 



Al 6 {Si0 4 ) 6 (B0 2 ) 2 .B0 3 H 2 .H 1 , 



The composition of the black tourmaline from Pierrepont 

 (I) and the brown tourmaline from Gouverneur (II), as derived 

 from Riggs' analyses, are then expressed by him as follows : 



13Al 6 (SiOJ 6 (B0 2 ) 2 .B0 3 Ca.Mg 4 H 4 

 I. \ 7Al.(Si0 4 ) 9 (BO;);.BO,Mg.Mg 4 H 4 



2Al 5 (Si0 4 ) 6 (B0 2 ),B0 3 Na,Al 2 Na 4 H, 



5Al 5 (Si0 4 ) 6 (BOJ 2 .B0 3 Ca.Mg 4 H 4 

 II. \ 3Al 5 (Si0 4 ) 6 (B0 2 ),B0 3 Mg.Mg 4 H 4 



2Al 5 (Si0 4 ) 6 (B0 2 ) 2 .B0 3 NaH.Al 2 ISa 2 H 4 . 



The above molecular mixtures when united become : 



I- Al 114 Mg 87 Ca 13 Na 12 H 84 B 66 Si 132 682 and 

 H. Al M Mg„Ca 5 Na.H 41 B i0 Si M O m . 



Thus, taking multiples of a molecule containing a large num- 

 ber of atoms, and admitting of many variations in the replace- 

 ment of the hydrogen atoms, it becomes a matter not of chem- 

 ical, but rather of arithmetical skill to so choose the numbers 

 that the calculated percentage values shall agree with the 

 results of the analyses: and all this labor when there is good 

 evidence for believing- that owing- either to slight defects in the 

 analyses or impurities in the materials the two analyses in ques- 

 tion fail by a little only to give ratios like those of the remain- 

 ing analyses. 



*Abhand. K. Akad., Berlin, 1S90. 



