SYSTEMS OF CRYSTALLIZATION. 



from the rhombohedral and the square prismatic, \ve are not led to 

 distinguish the latter two from each other; inasmuch as they have no 

 optical difference of character. But this distinction is quite essential 

 in crystallography ; for these two systems have faces formed by laws 

 as different as those of the other two systems. 



Moreover, Weiss and Mohs not only divided crystalline forms into 

 certain classes, but showed that by doing this, the derivation of all the 

 existing forms from the fundamental ones assumed a new aspect of 

 simplicity avd generality ; and this was the essential part of what 

 they did. 



On the other hand, I do not think it is too much to say as I have 

 elsewhere said* that " Sir D. Brewster's optical experiments must have 

 led to a classification of crystals into the above systems, or something 

 nearly equivalent, even if crystals had not been so arranged by atten- 

 tion to their forms."] 



Many other most curious trains of research have confirmed tne 

 general truth, that the degree and kind of geometrical symmetry cor- 

 responds exactly with the symmetry of the optical properties. As an 

 instance of this, eminently striking for its singularity, we may notice 

 the discovery of Sir John Herschel, that the playiliedml crystallization 

 of quartz, by which it exhibits faces twisted to the right or the left, is 

 accompanied by right-handed or left-handed circular polarization re- 

 spectively. No one acquainted with the subject can now doubt, that 

 the correspondence of geometrical and optical symmetry is of the most 

 complete and fundamental kind. 



[2nd Ed.] [Our knowledge with respect to the positions of the opti- 

 cal axes of the oblique prismatic crystals is still imperfect. It appears 

 to be ascertained that, in singly oblique crystals, one of the axes of 

 optical elasticity coincides with the rectangular crystallographic axis. 

 In doubly oblique crystals, one of the axes of optical elasticity is, in 

 many cases, coincident with the axis of a principal zone. I believe no 

 more determinate laws have been discovered.] 



Thus the highest generalization at which mathematical crystallogra- 

 phers have yet arrived, may be considered as fully established ; and 

 the science of Crystallography, in the condition in which these place 

 it, is fit to be employed as one of the members of Mineralogy, and thus 

 to fill its appropriate place and office. 



Philosophy of the Inductive Sciences, B. viii. C. iii. Art. 8. 



