46 On the Drawing of Figures of Crystals. 
is parallel with the edge 6 : a’; the edge a : €(Po ) is parallel with 
the edge a: 6 or M: 6; the edge 6’ : € has the direction of a line 
from @ to ¢; the edge a’: e( wP) is parallel with the edge P : a; 
and finally the edge e : 0’ has the direction of a line drawn from p 
to ¢. | 
In this manner the intersections of all possible planes may be de- 
termined and transferred. It should be observed that similar parts 
of acrystal are similarly modified. Figure 12 is a completed repre- 
sentation of a crystal which presents the planes above designated, viz. 
OP. wPmo. mPa .P.2P.2P2.4P2.Pa .3Pa .2Pa@ . oP 
PrN Sys a ar tot ao eae EY et ar Oe 
This same descriptive expression applies equally to fig. 18, which 
contains the same planes as fig. 12, but differently proportioned in 
size. ‘The planes M have been diminished by the enlargement of 
e, thus producing a modified rhombic prism. ‘The directions of the 
intersections are identical with those in fig. 12. ~ This figure illus- 
trates a preceding remark ($ 19), that the descriptive expressions 
of planes indicate merely their situation and not their size. 
According to the same method, crystals may be projected in each 
of the crystallographic classes, after their axes have been accurately 
laid down. It was remarked that the figure employed for determin- 
ing the intersections should be large: in a large figure slight varia- 
tions from the true direction or position of lines produces errors of 
less magnitude. Also the lines should be carefully and delicately 
drawn. With the point of a needle on glazed cards, a very great 
degree of accuracy may be attained. 
PROJECTION OF SIMPLE SECONDARY. FORMS. 
21. Monometric system.—The projection of many of the simple 
secondary forms,—for example the trisoctahedrons, the hexoctahe- 
drons, &c.—by the method of construction which has been explain- 
ed, would be a long and tedious process; at least when compared 
with the more simple method, depending on the relative lengths of 
the axes and the rhombic and trigonal interaxes in these forms. 
The right lines passing through the centre of the octahedron to the 
centres of its edges, are called rhombic interazes ; and those which 
pass to the centres of the faces, are the trigonal interaxes. In the 
several monometric forms, the extremities of one or more of these 
interaxes extended or diminished in their lengths, occupy the ver- 
