732 W. A. T. SMITH DETERMINATION OF CRYSTAL CLASSES 



The class names adopted in both tables are those used in the textbooks 

 of Dana and Krause. In several instances where Dana gives no name to 

 the group, one suggested by analogy from other related groups has been 

 given parenthetically. 



It should be noted that the terms 6-fold, 4-fold, etcetera, as used 

 throughout these tables, refer to the number of times a crystal form can 

 be brought into like positions merely by rotation about an axis without 

 involving reflection in a plane at the same time (alternating axis). Con- 

 sidering the symmetry of the completed form, the class containing the 

 rhombohedron of the third order ( Trirhombohedral Group of Dana) 

 would have a singular 3-fold axis of symmetry, since it may be brought 

 into three like positions by simple rotation through 360 degrees about its 

 singular axis. Considering the development of a complete form from a 

 single plane, however^ it has a 6-fold alternating axis, since each plane 

 in the upper or lower half of a form characteristic of the class may be 

 obtained from an adjacent plane in the opposite half of the crystal by a 

 rotation of 60 degrees, followed by reflection in a plane perpendicular to 

 the axis of rotation. For determinative purposes the simpler of these 

 two aspects has been taken, not only in this class, but in all cases where 

 an alternating axis is concerned. Whether the Ehombohedral and Tri- 

 rhombohedral Groups of Dana belong to the Hexagonal System or to the 

 Trigonal is another question and one which appears to the writer to 

 depend on the fundamental definition of these two systems or subsystems. 

 Without discussing the question (which is aside from the scope of this 

 paper), the writer will merely state that on this point he has followed 

 Dana and has placed both classes in the Trigonal division of the Hex- 

 agonal System. 



Table No. 1 

 a. with center of symmetry 



1. With one or more planes of symmetry: 



(a) With but one axis of symmetry having a period greater than one- 

 fold and with a single plane of symmetry, which is perpen- 

 dicular to this axis. 

 Axis 6-fold — Hexagonal Bipyramidal Class or Pyramidal Group, 



Hexagonal System. 

 Axis 4-fold — Tetragonal Bipyramidal Class or Pyramidal Group, 



Tetragonal System. 

 Axis 2-fold — Monoclinic Prismatic Class or Normal Group, Mono- 

 clinic System. 

 (&) With more than one axis having a period greater than one-fold and 

 more than one plane of symmetry. 

 Jj: With one or more singular axes and planes of symmetry perpen- 

 dicular to them. 



