Points on the earth’s surface can be projected orthogonally on the 
tangent plane if the radii of the aerial picture be extended by 
hr'3 
The direct influence for the curvature of the earth on a stereo model 
Every line on the earth parallell to the base has the same curvature 
radius. Here the base line represents this curvature. With origin in the 
left nadir point we have according to Fig. 1. 
(13) 
If the two pictures of a stereo pair are corrected according to for 
mula (3) the changes of the heights along lines parallell to the base 
line can be written 
b 
1 
dh c — (b 2 + 3x 2 — 3bx) (14 
ZR 
(14 b) 
Thus the sum of the influence on the heights according to eq (13) 
and (14 b) is 
2x 2 —■ 2bx 4- b 2 
(15) 
The indirect influence on the heights from the relative orientation 
By correcting for the curvature of the earth, y-parallaxes are intro 
duced in the model. From Fig. 6 we obtain 
(16 a) 
p y = Ay — k • y3 
y • dr 2 
(16 b) 
1 
(16 c) 
p y = k • b 2 • y where k = 
From eq (16 c) it is evident that p y is linear in y. 
From this fact it is immediately clear that the y-parallaxes intro 
duced by the correction are eliminated by a ^-rotation. 
The differential formula for the relation between p y and <p is 
x y , (x — b)y t 
Py = — h d Pl + h d P2 
(17) 
502