Penfield — Interpretation of Mineral Analyses. 21 



compound is a simple one, instead of giving the ratio, an excel- 

 lent method is to give the calculated composition, which can 

 then be compared directly with the results of the analysis. 

 Lastly, for determining a formula one or two good analyses are 

 of more value than many indifferent ones, hence it will often 

 prove best to make new analyses on material of unquestioned 

 purity. This may be done not wholly with the idea that the 

 new analyses are better than those made by other investigators, 

 but, knowing all about the quality of the material and the 

 working of the analyses, it will be possible to exercise better 

 judgment in summing up the results of the investigation, and 

 to present with greater force the arguments needed in support 

 of the proposed formula. 



Turning now to the consideration of tourmaline, two new 

 analyses were made by Foote and the author, upon material of 

 ideal purity and with the use of most carefully studied methods. 

 The results need not be repeated here, but it will be stated 

 that, with the exception of a single water determination, all 

 constituents were determined in duplicate ; that in twenty out 

 of a total of twenty-three instances, the discrepancy between 

 duplicate determinations did not exceed O10 per cent ; and 

 that the maximum variation in the remaining three instances 

 was 0*18 per cent. The single water determination which was 

 not duplicated was controlled by a closely agreeing estimation 

 of loss on ignition. In working out the ratios from these 

 analyses, the method was adopted of calculating for the metals 

 their equivalent of hydrogen, including fluorine with hydrogen, 

 since tourmaline contains hydroxyl with which fluorine is 

 isomorphous. Thus the ratio was found between Si0 2 , B 2 3 , 

 and Total Hydrogen, from which the empirical formula of the 

 tourmaline acid was derived. For the sake of the present dis- 

 cussion the ratios will be repeated in two forms : with one- 

 fourth of the Si0 2 as unity and also with one-twentieth of the 

 Total Hydrogen as unity. This latter method has been here 

 adopted, because a few relations can be brought out better in 

 the discussion by so doing. The ratios of the two analyses are 



as follows : 

















Si0 2 



: B 2 3 



• Total H. 



Si0. 2 



: B 2 3 



: Total H. 



De -Kalb 



4-00 



: 1-01 



. 19 90 



4-02 



1-01 



: 20-00 



HaddamNeck. 



4-00 



: 1-02 



: 19-98 



4-00 



1-02 



: 20-00 



These ratios approximate very closely to the whole numbers 

 4:1:20; such close approximations, in fact, are seldom obtained, 

 and cannot in these two instances be regarded merely as mat- 

 ters of accident; they are the reward, rather, of careful analyti- 

 cal work on material of unquestionable purity. As soon as 

 the ratios were worked out, it was seen at once that at least one 

 important key to the solution of the tourmaline problem had 



