the latter case we find the general expression 
Y. = OF 20202 + 2b2r2 4 28812 — ht di rt 
from an analytical determination of the coordinates of the intersection 
a 
points. | # 
The corresponding x-coordinates of the intersection points are 
b2 + d2 — r2 (3) 
NX — ;., E 
T 2b 
Obviously, also the x-parallaxes due to the distortion can easily be 
determined from the residual y-parallaxes. 
The general expression for the radial distortion is obtained from (1) 
and (2) as 
2br p, (4) 
Tr 
dr = SL 
\/2b2d2 + 2b2r2 + 2d2r2 — bt — df — rt 
  
For the relation b = d we find 
2b p, (5) 
  
For the intersection points between the fundamental circles we have 
r — d. 
From (2) and (3) we find 
  
  
ÍT ECTS (6a) 
oec A 97 
2 
b (6b) 
X = > 
Forb = d we find 
ae b y3 (7a) 
Jr 9 
b (7b) 
X c > 
As is immediately clear from fig. 1, the radial distortion will not 
cause any y-parallax in the points indicated by (6) and (7) under the 
assumed conditions. It is also evident that no y-parallaxes will be caused 
by the radial distortion along the base 1—2 and along the line 7—8. 
The coordinate y, can be determined graphically or numerically. In