On the Drawing of Figures of Crystals. 35 
through the points B and Fig. 3. 
B’, parallel with CC’, and A 
through C, C’, parallel with 
the axis BB’, a plane figure 
abed is formed, which is a 
horizontal section of the 
cube. Through the points 
a, b,c, d, draw lines parallel 
with the vertical axis 4A’, 
and extend them each side 
of these points, to a distance 
equal to the vertical semi- 
axis MA. By connecting the upper and also the lower extremities 
of these perpendiculars by lines parallel with the lines ad, bc, cd, da, 
the figure will represent a cube. 
The cube may also be projected by drawing lines from M to the 
center of each edge of the octahedron, and then extending these 
lines to double their length. ‘Their extremities are the vertices of 
the angles of the cube; and by connecting them a representation of 
the cube is formed. 
8. Dimetric System.—In the dimetric system of crystallization, 
the vertical axis is of. varying dimensions, while the horizontal axes 
are equal as in the monometric system. ‘The vertical axis may be 
made to correspond to the dimensions in a dimetric crystal, by laying 
off on rs and MA’, (taken as units,) extended if necessary, a line 
equal to 53 or if 6, the horizontal axis of the prism, =1, the line 
should equal a (the vertical axis) merely. After determining thus 
the points A”, A’, the dimetric octahedron may be in the 
same manner as the regular octahedron above described, except that 
the points A”, A” should be substituted for A, A’, The method 
of describing the cube, already explained, may be employed also for 
the right square prism. Another right square prism may be repre- 
sented by drawing lines parallel ith the vertical axis, through the 
extremities of the horizontal axes, making them equal to the vertical 
axis, and uniting their extremities. Also another square octahedron 
may be constiacted by connecting the points a, 6, c, d, with the ex- 
tremities of the vertical axis. 
9. Trimetric System.—The monometric axes may be adapted 
to trimetric forms as follows: if the axis b=1, lay off MA” and 
