64 PEOCEEDINGS OF THE AMERICAN ACADEMY 



to Fig. 2, which is so very characteristic of this species.* Corundum 

 differs chemically from chrysoberyl, in that a portion of the alumina 

 in the former is replaced by glucina in the latter. Corundum has a 

 perfect hexagonal form, and, fundamentally, may not the only crystal- 

 lographic difference be that, in consequence of the replacement, a 

 rhomb of 120" changes to a rhomb of llO'' 46'? Now we have a 

 plate of macled chrysoberyl, showing the normal wide divergence of 

 the optical axes at certain points on its borders, and a nearly uniaxial 

 structure at the centre, where there is an obvious interpenetration 

 between the individuals of the made, and where the superposition of 

 the several laminte is most beautifully shown by a polarized beam of 

 parallel rays. We have also a section of a corundum crystal, present- 

 ing phenomena similar to those seen with the plate of tourmaline, 

 described above. Further, we have observed like phenomena on a 

 section of jihenacite ; and, although the last mineral contains silica, 

 yet if the molecules of SiO^ are crystallographically equivalent to 

 those of Al.^ Oq, it may be that the molecular structure both of phena- 

 cite and of beryl is more closely allied to that of chrysoberyl and 

 corundum than the received theory of then" 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 

 endeavored in this paper to trace their true significance : first, by 

 showing that the appearances we are discussmg are precisely similar 

 to the effects which can be obtained by known means with mica 

 plates ; and, secondly, by observing on different specimens of various 

 minerals every intermediate stage between the unmistakable effects 

 of twinning on plates of mica or vermiculite, and the delicate phases 

 of the same phenomena, seen with sections of crystals of tourmaline, 

 corundum, or phenacite. One other illustration of our theory. 



* See also Dana's System of Min., 5th ed., Figs. 154, 155, p. 166. 



