ADVANTAGES OF THE METHOD 385 



symmetry. It is manifestly secondary, being produced by the planes and 

 axes of symmetry. It is unnecessary to retain it as a distinct element of 

 symmetry. 



ADVANTAGES OF THE METHOD 



The classification outlined in the foregoing discussion is believed to 

 possess certain advantages. 



It is based on symmetry, the basis of the modern development of crys- 

 tallography. 



It recognizes the likeness of closely related groups and points out the 

 analogies between them. 



It recognizes seven instead of thirty-two units and develops all by one 

 general method. 



The name of the class suggests both the symmetry and crystal form. 

 It introduces few new names, and these it is believed are significant. It 

 does not displace accredited names. 



It expresses the larger physical and geometrical relations which exist 

 among crystals. 



It is in harmony with the fundamental mathematical development of 

 the subject. 



It is elementary, and is readily followed by the elementary student. 



Part II : Historical Review 



REVIEW OF THE DEVELOPMENT OF THE THIRTY-TWO GROUPS OF CRYSTALS 



Work of previous investigators. — The classification of crystals into 

 thirty-two groups constitutes one of the most important contributions to 

 the science of crystallography. It was developed by the labors of a num- 

 ber of independent investigators, chief among whom are Hessel, Bravais, 

 Moebius, Gadolin, Curie, Fedorow, Minnigerode, and Schoenflies. An 

 outline of their work will be given and its relation shown to the classifica- 

 tion proposed in the preceding pages. Their results will be discussed 

 somewhat more fully because of the great historic interest of the subject. 



All of these investigators have had one aim, to predict all forms of 

 crystals which may possibly occur. The basis of their investigations has 

 been the conception of symmetry, of which all have recognized two funda- 

 mental types: (1) symmetry produced by a repetition of identical parts 

 by rotation; (2) symmetry produced by the repetition of similar parts by 

 reflection, together with various combinations of these two processes. 



With respect to their methods, the investigators form two classes: (1) 

 those who have first sought to develop all possible types of symmetrical 

 figures, and then to determine which of these may occur in crystals, in 

 harmony with the law of the Eationality of Parameters, the fundamental 



XXXIV — Bull. Geol. Soc. Am., Vol. 20, 1908 



