wherry: reply to dr. tuTTOn's discussion lOl 



wrong and entirely unacceptable" is, as the writer endeavored 

 to show, a direct corollary to the Braggs' work. And since 

 Dr. Tutton elsewhere in his discussion accepts the results of the 

 Braggs, it seems evident that he does not appreciate the writer's 

 viewpoint at all. 



The writer made no attempt to revive the "old method of 

 regarding crystal classes as holohedral, hemihedral, and tetarto- 

 hedral," but merely used such terms, following Dana, as con- 

 venient, brief designations of certain symmetry classes. None 

 of his conclusions would be altered were the classes to be referred 

 to by numbers or by any other method. Nor has he denied that 

 "every one of the 32 possible classes has its own absolutely 

 unique elements of symmetry" or that "a structure [as a whole] 

 either possesses the elements of symmetry of a particular class 

 or it does not." 



It certainly seems inconsistent in Dr. Tutton to assert that 

 "there are only fourteen space-lattices," in the same paper in 

 which he accepts the correctness of the Braggs' work on diamond. 

 For the structure they assign to that mineral, though not in- 

 cluded among Bravais's fourteen, is, according to the criterion 

 used by Dr. Tutton in his discussion, a space-lattice. Each 

 point of this structure may be "imagined to represent a poly- 

 hedron of such a nature that when an unlimited number are 

 packed together in contact, space is completely filled." In 

 this case the polyhedron is a regular tetrahedron, so far modified 

 by faces of the rhombic dodecahedron that each tetrahedral 

 face has the shape of a regular hexagon.^ X-ray studies have 

 shown, moreover, similar lattices to exist, as for instance a tri- 

 gonal one in bismuth. How many others may be discovered 

 by subsequent research the writer would not venture to pre- 

 dict, but he certainly would not claim that our present knowledge 

 is complete and final in this (or any other) respect. 



As far as pyrite is concerned, the underlying structure is 

 admittedly not a simple space-lattice, but compound, or com- 



* Compare Adams. Nole on the fundamental polyhedron of the diamond lattice. 

 This Journal 8: 240. 1918. 



