34 On the Drawing of Figures of Crystals. 
lars to HH’. On the left hand ver- ¥ iee* 
tical, set off, below H’, a part H’R, 
eae 
equal to ~b=—H’M; and from R 
draw RM, and extend the same to 
the vertical N’. B’B is the projec- ¢—___N|_MJ-“_y'_ 
tion of the front horizontal axis. ar 
2. Draw BS parallel with MH’, || 
and connect S,M. From the point FY 
T in which SM intersects BN, draw 
TC parallel with MH. A line (CC’) A 
drawn from C through M, and extended to the left vertical, is the 
projection of the side horizontal axis. 
3. Lay off on the right vertical, a part HQ equal to : MH, and 
make MA=MA’= MQ; AA’ is the vertical axis. 
Proof. 1. By construction, MN (the first projection of the semi- 
axis BM, N being in the line HH’) : MH (the first projection of MC) 
::1: r, which is the ratio required in the preceding demonstration. 
Again, by construction, BN ; NM:: RH’; H’M::1:s, therefore 
ay 
1 
BN (the second projection of BM)=~ MN, which is also the ratio 
required above. BB’ is therefore correctly the front horizontal axis. 
2. From the method of construction, 
H'S(=BN) : TN(=HC)::H’M: NM::cos6 : sino. 
Therefore HC is the true depression of the axis CC’; for in the 
preceding demonstration, the depressions were proved to equal re- 
spectively tanecosd and tanesind, and consequently to have the 
ratio of cos d : sind. 
3. MH=cosd and HQ is the sine of the same angle. MQ is 
therefore the radius in the same circle (fig. 1.) and equals the ver- 
tical semiaxis ; for the position of the eye does not change the ap- 
parent length of this axis, since it is situated in the plane of projec- 
tion 
AA’, ('C, BB’, are therefore the projected monometric axes. 
The values of r and s, commonly taken are, r=3, s=2, in which 
case, d ¢ 18° 26’ and «=9° 28’. It is not unusual to give s the value 
3, in which case e=6° 20’. This affords a narrower terminal plane. 
7. The regular octahedron may now be drawn, by connecting 
the extremities of the horizontal axes, and then uniting them by 
right lines with the points A, A’, as in fig. 3. If lines be drawn 
