492 
ON DRAWING CRYSTALS 
of its horizontal projection being = 1. Draw A B the ver- 
tical pyramidal axis of the hexahedron, Fig. 9. Take 
A =z A BV0.8204, C D = C" D" = C"^ D"' 
= i A B V0.8204, and join the lateral angles D, D", 
D"^ by straight lines with the apices A and B^ of the py- 
ramid ; the result is the required pyramid P of pyramidal 
Zircon. 
Problem IV. To draw the Pyramid (P)^ of Pyramidal 
Zircon, 
We obtain an eight-sided pyramid by the following pro- 
cess. 1. Produce the axis of the four-sided pyramid on 
both sides to an indefinite, but equal length ; 2. Enlarge 
the faces of that four-sided pyramid from which the eight- 
sided one is to be derived ; S. Draw triangles upon them, 
equal and similar to those of the pyramid, the bases of the 
triangles coinciding with the base of the pyramid ; 4. Join 
the lower points thus determined with the upper apex, the 
upper points with the lower apex of the lengthened axis ; 
and, 5. Pass planes through every one of these lines and 
the adjacent lateral solid angles of the original pyramid. 
The rule for drawing the figure of an eight-sided pyramid 
will therefore be thus. Project the four-sided pyramid as 
above. Lengthen the axis AX (Fig. 10)till A^X^ is =3 AX, 
the pyramid required being (P)^. Draw CA^^B^ equal, 
similar, and opposite to C A B^ in the prolongation of its 
plane ; in like manner C X" B^ C X^" B, C A"i B, &c. 
Join A", A"^ &c. with A^ ; X", X"^ &c. with X^ ; B, C, 
B, X^ with both A^ and X^, and also with the intersections 
S, &c. produced by the lines A^ A"^ with X^ X"i, 
A^ A" with X^ X", &c. The result will be the projection 
of the pyramid (P)^. 
The same pyramid will also be obtained by proceeding 
