491
(10 a)
Hy
B
H B
T) [x2 + ( T -y> !
2RH + x 2 + (
B
y)‘
4. The indirect influence of the correction of earth-curvature.
According to formula (9v) we have in point B/
B
B 3
B 3
( dry ) 91 RH + B 2 2RH + B 2
From this formula we obtain the following correction of <p 2 :
4(dr v ) 91 • H
d<p 2
2 B 2
2HB
RH + B 2
f
2HB
2RH + B 2
(11)
(12)
From symmetry we find dw 2 = 0. The other elements of relative
orientation causes first degree deformations.
d<p 2 causes the following elevation-deformations:
dH = —
~H 2 + (y -
B n
-y) 2
2HB
2HB
2
RH + B 2
2RH + B 2
B
J
(13)
5 The sum of those elevation-deformations, which can not be
compensated by the absolute orientation.
The terms of higher degree can be summarized as follows:
a) The magnitude of the curvature of the earth:
x 2 + y 2
dH
2 R
(3)
b) The direct influence of the correction:
From formula (10 a) we obtain:
H (8 x 2 y + 8 y 3 + 12 By 2 + 6 B 2 y + 4 Bx 2 + B 3 )
dH = —
+
+
(10 b)
2 B (8 RH + 4 x 2 + 4 y 2 + B 2 + By)
H (4 Bx 2 + B 3 — 6 B 2 y + 12 By 2 — 8 x 2 y — 8 y 3 )
2 B (8 RH + 4 x 2 + 4 y 2 + B 2 — 4 By)
In the denominators 8RH will predominate. Beacuse of that the
other terms can be neglected. From (10 b) we then obtain the
following terms of higher degree:
x 2 . 3 y 2
dH = 2R + (1 ° C)