Penfield and Foote — Composition of Tourmaline. 123 



and iron without any decided change in crystalline form. This 

 leads to the consideration of a certain phase of isomorphism 

 which, as it seems to us, has not been considered with suffi- 

 cient care, namely, the mass effect of complex radicals in 

 influencing or controlling crystallization. Thus in their sim- 

 ple salts we do not regard sodium and potassium as isomorph- 

 ous with calcium, but in some complex silicates, zeolites for 

 example, we recognize Na 2 and K 2 as isomorphous with, or at 

 least capable of replacing, calcium, barium and strontium. In 

 some of the phosphates, dickinsonite and fillowite for example, 

 we have sodium (Na 2 ) playing the same role as calcium, man- 

 ganese and iron in replacing the hydrogens of phosphoric acid. 

 In the garnet-sodalite group we have minerals with isometric 

 crystallization, to which the following formulas have been 

 assigned :* 



Ca„Al (SiO V Grossularite ) ^ 

 FeAI(SiO Almandite } Garnet 

 (Cl-Al)Na 4 Al a (Si0 4 ), Sodalite 

 (NaS0 4 -Al)Na 4 Al 2 (Si0 4 ) 3 Noselite 

 (NaS0 4 -Al)(Na 2 , Ca) 2 Al 2 (Si0 4 ) 3 Hatiymte 

 (NaS 3 -Al)Na 4 Al 2 (Si0 4 ), Lazurite 

 [(OH, F, Cl) 2 .Al] 6 Al 2 (Si0 4 ) 3 Zunyite 



When it is taken into consideration that isometric crystalliza- 

 tion is exceptional in the group of silicates, we are led to 

 believe that the sexivalent radical [Al 2 (Si0 4 ) 3 ], by virtue of its 

 mass effect, controls or dominates the crystallization of these 

 minerals. Not only are they isometric, but, with the excep- 

 tion of zunyite, which is tetrahedral, they all crystallize com- 

 monly in dodecahedrons. In sodalite, noselite and lazurite, 

 such unlike constituents as chlorine, and the univalent sulphate 

 and polysulphide radicals (NaS0 4 V and (NaS 3 ) / play the same 

 part in the complex molecules. It is moreover probable that 

 these unlike constituents are isomorphous in the sense that 

 they can mutually replace one another, for Brogger and Back- 

 strom have described homogeneous material containing the 

 lazurite, hauynite and sodalite molecules, while appreciable 

 quantities of chlorine are almost always found in noselite and 

 hauynite, thus indicating the presence of the isomorphous 

 sodalite molecule. It is to be expected that the larger and 

 more complex the radical the more potent will be its mass 

 effect in controlling or determining the crystal form. Thus in 

 sodalite, noselite and hauynite the* radical is very large,. 

 [R' 4 A] a (Si0 4 ),], E' 4 =Na 4 or Ca 2 . 



Tourmaline, it would seem, furnishes an example somewhat 

 analogous to that presented by the garnet-sodalite group. In 



* Brogger and Backstrom, Zeitschr. fur Kryst., xviii, p. 209, 1890. 



