506 
ON DRAWING CRYSTALS 
with the terminal edge M A^, that part M M^" of the axis, 
which corresponds to its terminal edge M C^^^, must be 
equal to three times the part M M^, which corresponds to 
the terminal edge M of the four-sided pyramid. The 
last is indicated by the exponent 3 in the sign of the eight- 
sided pyramid. If the same process, by which the faces 
O P Q and O Q have been obtained contiguous to the 
angle C^, be applied to every one of the other solid angles 
similarly situated, all the faces of (P)^, sixteen in number, 
will be produced, and thus the triple combination P. (P)^. 
P-f- CO completed, as it is represented in Fig. 14. 
The fourth and last of the simple forms to be added to 
3 
the preceding combination is '^^^ ^^^^ 
3 
P+3 is z=z . a, a being the axis of P ; that of -^—^ P+3 
therefore =: S . a. A face of this form, passing through 
the point C^^^, or through the horizontal line A^" C^^^, will 
at the same time pass through the line M C^^^, which is one 
of the terminal edges of (P)^. The edges of combination 
between these two forms are therefore parallel to the alter- 
nating terminal edges of the eight- sided pyramid, and also 
to the terminal edges of the four-sided pyramid. Hence 
the quadrangle RSUT in Fig. 14 will be one of its 
faces, the angles of which are determined by taking W S 
= -WY, VR = - VX, VT =z-YZ, and W U =: -WK. 
The junction of these points by straight hnes gives the out- 
line of the face. If repeated on all the homologous edges, 
this process finally yields the 15th figure for the pyramidal 
3 
combination of P. (P)^. P+ <^5 the species 
of pyramidal Zircon, 
