STEREOGRAPHIC, ORTHOGRAPHIC, GNOMONIC, ANGLE PROJECTIONS. 67 
jection, which was used by Postel in 1581, the polar distances x are directly 
proportional to the circular arc p, and are plotted as x = . 
In the equator 
angle projection the concentric polar degree circles are equidistant (as on the 
sphere) while the azimuth great circles are the radii of the circular projection 
plat. In the meridian angle projection (Plate 1 1 ) both great and small circles 
become oval curves resembling hyperbolas. This particular projection, 
which apparently has not been used before in optical work, is preferable to 
TABLE 3. 
p 
Gnomonic: 
*-tg/> 
Stereographic: 
,.*- 
Orthographic: 
x sin p 
Equidistant 
* 
Angle 
*~90 
0.. 
O.OOOOO 
O.OOOOO 
O.OOOOO 
O.OOOOO 
O OOOOO 
5.. 
.08740 
.04366 
.08716 
.05485 
05556 
10.. 
. 17633 
.08740 
. 17365 
. 10076 
15. 
if >> 
.26705 
. 13165 
.25882 
. 16475 
16667 
20'.. 
36397 
. 17633 
. 342O2 
.21986 
22222 
25.. 
.466} 1 
.22l6q 
.42262 
.27510 
27778 
30.. 
. 57735 
26705 
. 50000 
.33071 
33333 
35 
.70021 
. 31 53O 
-57358 
.38645 
.38889 
40 
.S^QIO 
363O7 
.64270 
. 44244 
44444 
45 
1 .OOOO 
.41421 
. 7O7 I I 
.49868 
. 50000 
50 
I . 1918 
.4663 1 
76604 
- 55513 
. 55556 
5 
I . 428 1 
. 52O57 
.8lQI $ 
.6l 175 
.61 1 1 1 
60 
I .7321 
. 57735 
.86603 
.66847 
.66667 
65.. 
2. 1445 
.63707 
.90631 
.72516 
.72222 
70.. 
2.7475 
.70021 
.93969 
.78167 
.77778 
75-- 
3.7321 
.76733 
.96593 
83777 
.83333 
80.. 
5 . 67 1 3 
.83910 
.98481 
.89314 
.88889 
85.. 
1 1 .430 
.91633 
.00619 
.04740 
04.144 
90. 
00 
I .O 
I .O 
1 .0 
1 .0 
the others because its polar distances are not distorted at the margin. The 
relative accuracy of the different parts of the projection is therefore more 
nearly uniform and approaches that of the sphere. Some distortion is of 
course present as is evident from the fact that both the quarter circle and 
TT 
the radius represent 90, the length of the former being - greater than the 
latter. The distortion of the polar angles is nil throughout while that of the 
tangential azimuthal angles increases from angle true projection at the 
center to - to i at the margin. 
2 
But this distortion is less than that in the 
other perspective projections and the angle projection is accordingly better 
adapted for use in optical work than any of the preceding projections. The 
terms equator and meridian angle projection have been adopted for this pro- 
jection in preference to the longer terms equator and meridian equidistant 
zenithal or Postel projections. 
