On the Drawing of Figures of Crystals. 35 
through the points B and 
B’, parallel with CC’, and 
through C, C’, parallel with 
the axis BB’, a plane figure 
abcd is formed, which is a 
horizontal section of the 
cube. Through the points 
a, b,c, d, draw lines parallel 
with the vertical axis 4/4’, 
and extend them each side 
of these points, to a distance 
equal to the vertical semi- 
axis MA. By conneeting the upper and also the lower extremities 
of these perpendiculars by lines parallel with the lines a8, 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. 'Theit 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 MA and MA’, (taken as units,) extended if necessary, a line 
a, 
equal to Zio if 6, the horizontal axis of the prism, =1, the line 
should equal @ (the vertical axis) merely. After determining thus 
the points A”, A’”, the dimetric octahedron may be formed 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 with 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 constructed by connecting the points a, 0, ¢c, d, with the ex- 
tremities of the vertical axis. 
9. Trimetric System.—The monometric axes may be rere 
to trimetric forms as follows: if the axis 6=1, lay off MA” and 
