270 Prof. J. P. Cooke on the Vermiculites. 



both of phenacite and of beryl is more closely allied to that of 

 chrysoberyl and corundum than the received theory of their 

 chemical constitution would indicate. 



We would not convey the impression that in all these crystals 

 the appearances we have described are strongly marked, or that 

 they have passed wholly unnoticed hitherto. Every one who 

 has become familiar with the optical properties of crystals must 

 have noticed that, with many always regarded as uniaxial, there 

 is not unfrequently in some positions a small separation of the 

 cross into the hyperbolas which are characteristic of biaxial 

 structure. But these irregularities, although long known, have 

 never been satisfactorily explained. They have been hitherto 

 residual features not accounted for by the received theory of 

 crystalline structure, which explains so satisfactorily the general 

 order of the phenomena observed with the polariscope. We have 

 endeavoured in this paper to trace their true significance : — first 

 by showing that the appearances we are discussing are precisely 

 similar to the effects which can be obtained by known means 

 with mica plates \ and secondly by observing, on different spe- 

 cimens of various minerals, every intermediate stage between the 

 unmistakable effects of twinning on plates of mica or vermicu- 

 lite, and the delicate phases of the same phenomena seen with 

 sections of crystals of tourmaline, corundum, or phenacite. One 

 other illustration of our theory. 



The rhombic angle of Witherite (native baric carbonate) is 

 118° 30 7 ; and the all but universal hexagonal macling of crys- 

 tals of this species is a well-known fact*. The rhombic angle 

 of Aragonite (the corresponding form of calcic carbonate) is 

 116° 10'; and the much greater divergence of this angle from 

 120° determines, as is also known, a style of macling which is 

 usually quite different from that of Witherite. In the isomeric 

 calcite, however, we have the type of all hexagonal forms. 

 Hitherto the crystalline forms of calcite and Aragonite have been 

 regarded as being as widely separated as possible ; and a compa- 

 rison of these two well-known mineral species has furnished one 

 of the most striking illustrations of dimorphism. But may not, 

 after all, the comparatively small physical differences between 

 these two minerals correspond to a crystallographic difference no 

 greater, fundamentally, than the difference between the rhomb 

 of 116° 10' and the rhomb of 120° ? 



The macles of chrysoberyl and Witherite are illustrations of a 

 general truth, fully recognized in mineralogy, that all rhombic 

 crystals whose angles approach 120° tend to form hexagonal 

 macles. The optical phenomena described in this paper certainly 

 suggest the theory that a perfect hexagonal form and structure 

 * See figures, Dana's ' System of Mineralogy/ p. 697. 



