Penfield — Interpretation of Mineral Analyses. 29 



Clarke's molecules to be present in nearly equal proportion. 

 There are employed by Clarke, however, 35 hasic and 29 acid 

 molecules, from which the ratio of Si0 2 : Total Hydrogen = 

 4:20*06 is readily calculated: thus the ratio as derived from 

 Clarke's molecular mixtures is farther removed from 4 : 20 than 

 that derived from the analysis itself, and yet Prof. Clarke 

 makes the following statement : " It will be noticed that the 

 molecule A" (with him the basic one) "is in excess of the other 

 two; a condition which fits the analyses, but which is incom- 

 patible with the formula proposed by Penfield and Foote." 

 It may be stated, however, that the H 20 B 2 Si 4 O 21 formula of 

 tourmaline is not based upon hypothetical molecular mixtures, 

 but, fortunately, upon actual analyses, and good ones, like the 

 one by Riggs lastr cited, where the ratio is almost exactly 4 : 20. 

 This example furnishes a good illustration of the fact that 

 ratios are more serviceable in support of a formula than com- 

 parison between percentage values. 



And, finally, Prof. Clarke, in the concluding pages of this 

 article, presents his reasons for believing that the radical 

 (= Al — B0 2 ) may be replaced "in part by the similar groups 

 (= Al — OH) and (= Al — F)," or, in other words, that hydroxy 1 

 and fluorine are equivalent to, and isomorphous with, B0 2 . 

 Clarke bases this conclusion upon the fact that, in many of the 

 analyses of Riggs, and Jannasch and Kalb, the amount of B 2 O s 

 found is not sufficient to yield a ratio of Si0 2 : B 2 3 =4: 1 (see 

 page 22), and the deficiency seems to him to be too great to be 

 due to experimental errors. For explaining the occasional low 

 determinations of B 2 3 referred to, there is a far simpler way 

 than the one proposed by Clarke : special pains were taken by 

 Foote and the author to ascertain the conditions for accurately 

 determining B 2 3 in tourmaline, and it was found that by 

 fusing the mineral with five times its weight of sodium car- 

 bonate and extracting with water, a little boron was still 

 retained by the residue ; a fusion of the residue with another 

 portion of sodium carbonate was therefore made, and the boron 

 was then determined by the well known Gooch method. It 

 was further demonstrated that two fusions with sodium car- 

 bonate were sufficient for extracting all of the B 2 3 . Professor 

 Riggs has kindly informed the author that in making his 

 boron determinations by means of the Gooch method, he fused 

 only once, but used, however, ten times as much sodium car- 

 bonate as mineral. It is hence probable that a double fusion 

 with five times the weight of sodium carbonate is better than a 

 single fusion with ten times the weight. As may be seen on 

 page 22 the ratio of Si0 2 : B 2 3 is very close to 4 : 1 in the 

 majority of Riggs' analyses. All who had occasion to deter- 

 mine boron prior to the description by Gooch of his admira- 



