SYSTEMS OF CRYSTALLIZATION. 243 



crystals, were afterwards discovered ; and these 

 were, in 1817, classified by Sir David Brewster, 

 according to the crystalline forms to which they 

 belong. This classification, on comparison with the 

 distinction of Systems of Crystallization, resolved 

 itself into a necessary relation of mathematical 

 symmetry: all crystals of the pyramidal and rhom- 

 bohedral systems, which from their geometrical 

 character have a single axis of symmetry, are also 

 optically uniaxal, and produce by dipolarization cir- 

 cular rings ; while the prismatic system, which has 

 no such single axis, but three unequal axes of 

 symmetry, is optically biaxal, gives lemniscates by 

 dipolarized light, and, according to Fresnel's theory, 

 has three rectangular axes of unequal elasticity. 



Many other most curious trains of research have 

 confirmed the general truth, that the degree and 

 kind of geometrical symmetry corresponds exactly 

 with the symmetry of the optical properties. As 

 an instance of this, eminently striking for its sin- 

 gularity, we may notice the discovery of Sir John 

 Herschel, that the plagihedral 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 respectively. 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 (M). 



R 2 



