350 SCIENCE PROGRESS 



The advance on Bravais' conception which has given lasting 

 fame to the name of Sohncke consists in the removal of the 

 limitations involved in supposing all the similar particles or 

 units of which a homogeneous system consists or their similar 

 environments to have the same orientation. When this 

 important extension of the definition of homogeneity of structure 

 had been achieved and the number of distinct types of symmetry 

 thus reached had been shown by Sohncke to be 65, a further 

 analysis of the geometrical features of these various types 

 was soon made by Fedorow, Schonflies and Barlow ; the 

 purely geometrical investigation of the subject was then found 

 to be practically closed. 



The perfectly general definition of homogeneity which was 

 ultimately attained is applicable to all kinds of strictly homo- 

 geneous structure however complicated the composition ; any 

 number of varieties of particles may be simultaneously present. 

 The characteristic feature of such a structure is that it presents 

 identity of aspect as viewed from a fixed point before and after 

 being subjected to any one of a definite series of movements 

 made by the structure as a whole (coincidence movements). 



The complete crystal symmetry of the structure resides 

 therefore in the group of coincidence movements characterising 

 it, this group of movements possessing elements of symmetry 

 strictly corresponding to those of some one of the 32 classes of 

 crystal symmetry known to the crystallographer. For the sake 

 of simplicity, however, the crystallographer supposes a crystal 

 to have a geometrical centre to which he refers its elements 

 of symmetry ^ and thereby reduces these elements to four kinds : 

 (i) an axis or axes of symmetry, (2) a plane or planes of symmetry, 

 (3) a centre of symmetry, and (4) a kind of symmetrical opera- 

 tion compounded of two of these which produces a change of 

 orientation. To these four should in strictness be added the 

 property of constancy of angular inclination of faces ; this 

 characterises all classes of crystal symmetry, including the 

 lowest form of anorthic symmetry which possesses none of the 



' The crystallographer uses the term "symmetry" to imply the orderly dis- 

 tribution of the parts of the crystal about certain planes or axes or about a centre. 

 A crystal structure may be such that it is symmetrical about both planes and axes 

 as well as a centre ; it may also possess only one of these so-called " elements of 

 symmetry." The crystal is said to be of a high or low order of symmetry 

 according as its structure may be referred to many or few such elements of 

 symmetry. 



