SYSTEMS OF CRYSTALLIZATION. 237 



Symmetry, and the crystal will consist of three divi- 

 sions, ranged round this axis, and exactly resembling 

 each other. According to Weiss's nomenclature, 

 such a crystal is " three-and-three-membered." 



But this is only one of the kinds of symmetry 

 which crystalline forms may exhibit. They may 

 have three axes of complete and equal symmetry at 

 right angles to each other, as the cube and the 

 regular octohedron; or, two axes of equal sym- 

 metry, perpendicular to each other and to a third 

 axis, which is not affected with the same symmetry 

 with which they are; such a figure is a square 

 pyramid; or they may have three rectangular axes, 

 all of unequal symmetry, the modifications referring 

 to each axis separately from the other two. 



These are essential and necessary distinctions of 

 crystalline form ; and the introduction of a classifi- 

 cation of forms founded on such relations, or as 

 they were called, Systems of Crystallization, was a 

 great improvement upon the divisions of the earlier 

 crystallographers, for those divisions were separated 

 according to certain arbitrarily-assumed primary 

 forms. Thus Rome' de Lisle's fundamental forms 

 were, the tetrahedron, the cube, the octohedron, the 

 rhombic prism, the rhombic octohedron, the dode- 

 cahedron with triangular faces: Hauy's primary 

 forms are the cube, the rhombohedron, the oblique 

 rhombic prism, the right rhombic prism, the rhombic 

 dodecahedron, the regular octohedron, tetrahedron, 

 and six-sided prism, and the bipyramidal dodeca- 



