388 Proceedings of Poyal Society of Edinburgh. [sess. 
When considered in this way the trigonal and hexagonal 
systems are referred to the Bravais axes, using the appropriate 
symbols. It is important, however, that students should he made 
acquainted with the mode of referring certain crystals to rhombo- 
hedral axes, with Miller’s original symbols ; therefore those classes 
for which such axes can be adopted should subsequently be 
brought together into a rhombohedral system by themselves. The 
classes to which this is applicable are those, belonging to the tri- 
gonal and hexagonal systems, which do not possess elements of 
symmetry higher than those pertaining to a (geometrical) rhombo- 
hedron. Consequently, all classes possessing a simple hexagonal 
axis, and also those which possess a principal plane of symmetry, 
are excluded from the rhombohedral system, which therefore 
includes — 
The trigonal pyramidal class 
,, ,, trapezohedral class 
,, di-trigonal pyramidal class 
,, hexagonal rhombohedral class 
„ „ scalenohedral class 
| 
i The above list contains all the represented classes which are 
usually included in the trigonal system, and doubtless this is the 
principal reason why two classes which are, strictly speaking, hexa- 
gonal, are generally placed in the trigonal system. It appears to 
me, however, that considerable advantage is obtained by first 
deducing the trigonal and hexagonal classes in a strictly systematic 
manner, and, after the student has become acquainted with them, 
introducing the use of rhombohedral axes as an alternative method 
of dealing with a certain group, represented in both of the preced- 
ing systems, before passing on to the cubic system. 
( Issued separately February 1 , 1905 .) 
