1904-5.] Dr Hugh Marshall: Crystallographical Notes. 387 
latter ; they are the classes of dioptase and calcite respectively. 
Instead of being classed in the hexagonal system, however, they 
are generally placed in the trigonal system, the scalenohedral one 
being known as the di-trigonal scalenohedral class. The principal 
axis of symmetry is, of course, a simple trigonal axis, as well as 
one of hexagonal compound symmetry, but that is no sufficient 
reason for departing from the strictly systematic method of treat- 
ment. The result of doing so is to complicate matters for the 
student quite unnecessarily. 
For the purpose of introducing the student to the various crystal 
classes, it would therefore appear to be best, after treating of the 
triclinic, the monoclinic, and the rhombic systems, to take up the 
tetragonal system, and, after this has been gone over, to proceed to 
the hexagonal and, lastly, the trigonal systems : the close analogies, 
allowing for the exceptions in the trigonal system as referred to 
above, render the study of the latter systems quite simple. 
The various classes might then be tabulated as follows, the sym- 
metry of the different systems being expressed in general terms : — 
Systems and Classes. 
Symmetry. 
n = 4 
Tetragonal. 
71 = 6 
Hexagonal. 
71=3 
Trigonal. 
%-gonal axis of com- 1 
pound symmetry j 
Bi-sphenoidal 
Rliombohedral 
%-gonal axis 
Pyramidal 
Pyramidal 
Pyramidal 
w-gonal axis ; n lateral 1 
axes (digonal) J 
1 
Trapezohedral 
Trapezohedral 
Trapezohedral 
w-gonal axis of com- 1 
pound symmetry ; n/2 
planes intersecting in 
axis ; nf 2 lateral axes 
(digonal) J 
Scalenohedral 
Scalenohedral 
w-gonal axis ; n planes ] 
intersecting in axis J 
Di- tetragonal 
pyramidal 
Di-hexagonal 
pyramidal 
Di-trigonal 
pyramidal 
w-gonal axis ; one plane ) 
normal to axis J 
r 
Bi-pyramidal 
Bi-pyramidal 
Bi-pyramidal 
w-gonal axis ; n lateral ] 
axes (digonal) ; plane 
normal to each axis J 
i- 
Di-tetragonal 
bi-pyramidal 
Di-hexagonal 
bi-pyramidal 
Di-trigonal 
bi-pyramidal 
