44 On the Drawing of Figures of Crystals. 
rection mr, that of P with 0’, the direction of np. The intersec- 
tions of a, 6, M are parallel with mo; those of a’, 6’, M, have the di- 
rection 6n, as determined above. The edge a: 6’ is drawn in the 
direction ne, explained above as the intersection of npb and mmo. 
Finally the edge M : a’ is drawn parallel with mb, and the edge 
M:30, 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 — have been deeds parallel with 
« or parallel with the edge a’ ; 
20. In this manner a sketch = a coves 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 : 6’ 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 23Pw, 2Pm, Pw, and wmP; 
the two former are replacements 
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 2Pa meets the planes 
aand 6; 2Po, the planed; Po 
the lente a and 0’, and @ P, the 
planes a’ and 0’. 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. 
 ntuv is so drawn that an equals }€ and at=3 of te, 
which fulfills the conditions for the plane 2Po (2: :1). Again 
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