62 PROCEEDINGS OP THE AMERICAN ACADEMY 



covered a biaxial structure of which the optical plane is parallel to 

 different edges of the hexagon on different parts of the plate- 

 It must, however, be remembered that, as by the process of twinning 

 we have described the structure of the magnesian micas approaches 

 thatof uniaxial crystals, rhombohedral and other planes characteristic of 

 the hexagonal system begin to appear on the crystal. This is ilhis- 

 trated not only by the crystals of Biotite from Vesuvius and from 

 Greenwood Furnace, N. Y., but also by the more perfect crystals of 

 Hallite from Chester County, Pa. In other words, the process of twinning 

 we have illustrated in this paper produces hexagonal crystals in external 

 form as ivell as in optical characters ; and the question naturally arises, 

 May not the hexagonal crystals of other minerals be formed in a similar 

 way ? — that is, may they not be developed from twinned molecules, 

 which, though in their aggregate producing an hexagonal structure, 

 singly would develop into biaxial crystals ? Bearing on this point, we 

 have discovered some very remarkable evidence. 



We have in our possession a plate of Elba toi;rmaline cut perpen- 

 dicular to the axis, in which the polarizing microscope shows on 

 different zones a separation of the hy^Derbolas, which amounts in 

 some positions to eight degrees ; and in moving the plate across the 

 field the optical divergence varies precisely as on plates of phlogopite 

 and vermiculite. There is certainly no external evidence of lamination 

 on tourmaline crystals, for the mineral is remarkably compact, and the 

 crystals have not even a basal cleavage : but it will be remembered how 

 readily some of the varieties pass by alteration into micas of the mag- 

 nesian type ; and this change to a foliated structure, in which the 

 lamination is parallel to the base of the original hexagonal crystal, 

 may be facilitated by a grouping of the molecules of the tourmaline, in 

 the manner represented by Fig. 7. 



We have also a plate of amethystine quartz, in which a beam of 

 parallel polarized rays of light exhibits a twinning almost as symmetrical 

 as that shown in Fig. 5, — the three zones being most beautifully mapped 

 out by the alternating bands of right and left handed quartz, which are 

 such a familiar phenomenon of these crystals ; but, besides this, in 

 each of these zones, near the border of the plate, can be distinguished 

 a biaxial structure with an optical divergence of several degrees ; and, 

 on one other plate of amethyst we have had an opportunity of exam- 

 ining, we have also seen under the polarizing microscope the biaxial 

 curves at one or more points. 



These facts most distinctly suggest the theory that the optical phe- 

 nomena of quartz are produced by a molecular structure similar to that 



