photo and (x, z) of the right photo are paral- 
lel. In such case the relationship between 
the theodolite image co-ordinates (x, z) on 
the left photograph, (x, Z) on the right 
photograph and the inserts co-ordinates (X, 
Y, 2) according to figure 3 are: 
B 
  
  
  
  
X = % x - 
X-X 
B. 
X c 
x cc X 
By By 
21 = 2 — and 25 - Z — + B 
1 X- X 2 X = X Zz 
2 59 (24 ti22)72 
ya. = 21 =~ 22 
Where B, is the horizontal distance between 
the two theodolite stations which is an un- 
known value. The value of B, can be obtained 
as follows: 
  
- Assume any value for B. such as B, and ob- 
" tain the ground co-ordinates of the two 
ends of the known line. 
- Calculate from the ground co-ordinates the 
length of that known line. 
- The correct value Bx — B. 
True length of the known line 
Calculated length of the known line 
  
The (X, Y, Z) co-ordinates obtained by the 
above equations give the inserts co-ordinates 
referring to a system of axes as given in 
figure (3) with an origin as the perspective 
center of the left photograph, the X axis is 
parallel to the given X axis and the Z axis 
is a vertical line parallel to the plump bob 
direction at the origin. A sample of the 
inserts co-ordinates (X, Y, Z), and the accu- 
racy of the measurements V, which are calcu- 
lated by using the given equations are given 
in table (3). ; 
ight theodolite 
z Istation 
Figure 3 - The relations between the insert coordinates 
(X,Y,Z) and the theodolite images coordinates 
(x, 2) and(x, z). 
114