BULLETIN OF THE GEOLOGICAL SOCIETY OF AMERICA 

 VOL. 20, PP. 369-398, PLS. 31-32 DECEMBER 21, 1909 



PROPOSED CLASSIFICATION OF CRYSTALS BASED OF THE 



RECOGNITION OF SEVEN FUNDAMENTAL 



TYPES OF SYMMETRY 1 



{Read before the Society December SI, 1908) 



BY CHARLES K. SWARTZ 



CONTENTS 



Page 



Introduction 370 



Part I : Proposed classification of crystals 371 



Preliminary considerations 371 



Definitions 371 



Theorems 372 



Development of classification 373 



Basis of classification 373 



Types of symmetry 374 



Development of groups and classes of crystals 374 



Summary of development 377 



Reference of the classes to the accepted systems of crystals 377 



Characteristics of the seven classes 378 



Larger divisions of crystals 380 



Integrity of the seven classes of crystals 380 



Elementary development 381 



Inferences 383 



Relative rank of classes and systems 383 



Relative rank of the systems 3S3 



Relations of the rhombohedral and scalenohedral groups 384 



Center of symmetry 384 



Advantages of the method 385 



Part II : Historical review 385 



Review of the development of the thirty-two groups of crystals 385 



Work of previous investigators 385 



Hessel 386 



Bravais 388 



Moebius 389 



Gadolin 300 



Curie 391 



Fedorow 302 



Minnigerode 392 



1 Manuscript received by the Secretary of the Society July 31, 1909. 



XXXIII— Bull. Geol, Sqc, Am,, Vol. 20, 1908 (369) 



