48 B. B. Biggs — Composition of Tourmaline. 



seriting water be low, those of boric acid, where estimated by 

 difference, ought to be correspondingly high, and so they are 

 in a few cases In the greater number of analyses, however, 

 they are unaccountably low, unless we suppose, as I am inclined 

 to, that the silica determinations were high, representing in 

 some cases, besides actual silica, more than a per cent of impu- 

 rities. If all this be true, in working out his ratios, Rammels- 

 berg found in water and boric acid two variables instead of 

 the two constants that they probably are, and one need not 

 wonder that he found it difficult to discover unity in his 

 analyses. 



It is scarcely necessary to say that certain constituents found 

 in tourmaline are non-essential, but have been thrust upon them 

 by their associates. The idea that a tourmaline must have its 

 fluorine was long since exploded. 



If we study the essential constituents in the light of their 

 molecular or atomic ratios, we will find some very interesting 

 relations. The ratios of certain elements are constants in all 

 varieties of tourmaline. Si : B : H : = 1 : \ : § : 5 - 2. All the 

 other constituents are variable and within rather indefinite 

 limits. Considered individually they are enigmas. If, how- 

 ever, the bases, including hydrogen, be reduced to a common 

 univalent basis and be consolidated, the results fall into line 

 with the above ratios. This reduction may be made in either 

 one of two ways, and with almost equally good results. In 

 the table of the ratios of constants given below it will be no- 

 ticed that the oxygen ratio is invariably slightly in excess of 

 the amount necessary to the silicon and boron even though we 

 assume both the Si0 4 group as we certainly must, and the 

 group B0„ as is also necessary if we would give account for the 

 oxygen. This small residual is to be disposed of. It can be 

 done by postulating either an A1 = or the 0-H group. Both 

 hypotheses have been used in constructing the following table. 

 R( a ) is the univalent equivalent of the bases with the oxygen 

 excess incorporated in an A1=0 group, R( 2 ) the univalent 

 equivalent of the bases on the basis of an assumed 0-H group. 

 The table is given in full that the extent of the variations, 

 from what seem to be simple ratios, may in no wise be con- 

 cealed, as is often the case, when averages are given. The hy- 

 drogen ratio, though already included in R, is given by itself, 

 being one of the constants. For much the same reason the al- 

 kali ratios are also given, although here the constancy would 

 seem to be limited to a type. This at least appears to be true 

 for the iron and lithia varieties. 



