44 On the Drawing of Figures of Crystals. 
rection mr, that of P with o', the direction of np. ‘The intersec- 
tions of a, 5, M are parallel with mo; those of a’, 0’, M, have the di- 
rection bn, as determined above. The edge a: 0’ is drawn in the 
direction ne, explained above as the intersection of npb and nmo. 
Finally the edge M : a’ is drawn parallel with mb, and the edge 
M : 0’, parallel with pb, which in fig. 9, is obviously the intersection 
of pbn with M. The planes 6 and 0’ do not meet; were the plane 
a’ wanting, their intersection would have been drawn parallel with — 
«8 or parallel with the edge a’ ; 0’. 
20. In this manner a sketch of a crystal may be made or rectified, 
or a figure may be drawn, whose prototype has not been observed. 
The crystallographic expressions however, do not indicate the size of , 
the planes. ‘The edge M : 0’ might have been so drawn as not to 
‘have formed an intersection with the plane P. Again, these sec- 
ondary planes might have been so extended, that in connection 
with the corresponding planes on the other angles, they should ob- 
literate mostly or entirely the primary faces.. ‘The intersections of 
the planes would not however be changed in direction. There 
would be new intersections of planes on opposite parts of the same 
primary face, which it would be necessary to determine in the above 
manner. 
21. We may now add the planes 2Pm, 2Pm, Po, and mP; 
the two former are replacements | ye: 
of the longer terminal edge é, the 
third is situated on the shorter edge 
é, and the last is a replacement of 
a lateral edge. We may also sup- 
pose that 2Po meets the planes 
aand 6; 2Po, the plane 0; Po 
the planes a and 0’, and m P, the 
planes a’ and 6’. It is therefore 
necessary to determine the direc- 
tion of these intersections. For 
this purpose fig. 9 is redrawn (fig. 
11) to avoid confusion from the 
multiplicity of similar lines, (this 
would not be required in practice,) and the lines in the preceding 
figure, not including the new planes, are here dotted. 
The plane nfuv is so drawn that an equals 5¢ and af=$ of te, 
which fulfills the conditions for the plane 2Pm (2.3. :1). Again 
