6 Mr. W. Barlow on Crystal Symmetry. 



For the purpose of classification, homogeneous structures 

 thus defined can, like Gadolin's systems of crystal faces, be 

 placed in the same class when the number and arrangement 

 of like directions is the same in them*. 



The similarity of the relation of two directions to the 

 homogeneous structure may either amount to identity, or, in 

 certain cases, it may be such that the aspect of the ultimate 

 structure viewed from one of them is the mirror-image t of 

 its aspect viewed from the other direction. As an illustration 

 of what is meant : — In a system of transparent cubic cells 

 filling space, a cell when viewed in a certain direction pre- 

 sents the aspect shown in fig. 2, and when looked at in a 

 direction enantiomorphously similar to this, the aspect shown 

 in fig. 3. In the following argument identical similarity will 



Fio-. 2, 



be dealt with first, leaving mirror-image or enantiomorphous 

 similarity for treatment later. 



Identically E elated Directions — Possible Variety of Axes 

 of Symmetry. 



Two important properties are involved by the identical 

 repetition of the same formation which has just been defined. 



I. A mass thus constituted can be geometrically partitioned 1 

 into identical space units the number of different orientations 



* Comp. Gadolin, Memoire, &c, p. 25. 



t The use of the term mirror-image does not imply the existence of a 

 plane of symmetry, or, indeed, in any way express the relative orienta- 

 tion of the two like directions — it merely conveys that the aspect of the 

 system of crystal properties viewed in the one direction, bears to its aspect 

 regarded in the other direction the kind of resemblance that a right hand 

 bears to a left. The system of crystal properties taken by itself, without 

 reference to the position of an observer, is, in such cases, identical with 

 its own mirror-image (comp. below, p. 31). 



\ This partitioning may be merely an ideal one not possible actually, 

 and not corresponding to any conceivable physical subdivision. 



