are computed from the differences between the given and the calculated coor- 
dinates. A comparison between the values of OXp, OYp and OZp estimated from 
the simulation (Columns 4, 5 and 6), and the developed formulas (Columns 7, 8 
and 9) are given in Table I. 
It is clear from Table I that the values of OXp, OYp and OZp estimated 
through the use of the proposed formulas are very close to the values obtain- 
ed from simulation. 
V. THE OPTIMUM POSITION OF THE TWO THEODOLITE STATION FOR A 
PLANE 
The position of the two theodolite stations relative to a plane object 
is determined by the base distance (B), the object distance (D) and the theo- 
dolite elevation (E). The observer in the field has to choose the values of 
B, D and E so that oXp, oYp and 0Zp reach their minimum values. The values of 
B, D and E which minimize the values of OXp, OYp and OZp are called the 
optimum base distance (Bo), the optimum object distance (Do) and the optimum 
elevation (Eo) respectively. 
Unfortunately, there are no real values for Bo, Do and Eo which minimize 
the values of OXp, oYp and OZp. As an example oYp has minimum value at 
Do - 0 while oXp has minimum value at D - 0. Accordingly, one cannot have Bo 
and Do to minimize simultaneously both values of OXp and OYp. Accordingly, 
the optimum base distance Bo and the optimum object distance Do may be taken 
to satisfy only one of the following conditions 
a. To minimize the value of OXp. 
b. To minimize the value of OYp. 
C. OXp = OYp. 
Most of the close-range photogrammists prefer to have homogenity between 
the accuracies of the measured coordinates. Accordingly, it is highly 
recommended in photogrammetry to have OXp 7 OYp (condition c) rather than 
having the maximum accuracy of OXp (condition a) irrespective of the accuracy 
of OYp or having the maximum accuracy of OYp (condition b) irrespective of 
the accuracy of OXp. Accordingly, the optimum base distance Bo and the opti- 
mum object distance Do are chosen to minimize the values of OXp and OYp for 
OXp = OYp. The optimum theodolite elevation Eg is taken to minimize the 
value of OZp. 
V-1 The Optimum Bo and Do That Maximize the Accuracy Along X-axis and Y-axis 
for OXp z OYp 
The difference F between 0°Xp and 0%Yp can be written in this form 
  
  
  
B= atx ;- oly (23) 
p p 
Substituting the values of OXp and oYp from equations (20) and (21) one gets 
6 2 4 6 4 
(oe co. Tr. p-GQm.ip.-.p5. 8.5 
p^ 7D? iQ D? 24D? 52D2 
2n? 
- - 2D*] (24) 
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