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p B? 5 3 8 
(18) 
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2 5 5 
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(19) : 
The validity of the developed formulas is performed on a computer where 
the X, Y and Z coordinates of 121 targets, forming a net 50 by 10 meters, on 
a plane are given. These targets are 5 m apart along the X-axis and 1 m 
apart along the Z-axis. The positions of the two theodolites, (on a line pa- 
rallel to the targets plane)B, D and E are given in columns 1; 2 and 3 of 
taken as a Table I. The horizontal and the vertical directions a and y of each target 
ible error on are calculated from each theodolite station using the target coordinates and 
the coordinates of the theodolite station. The computed directions are 
given random errors of N (0,1"). The target coordinates are recomputed from 
Yi and 0Zj of 
  
  
  
horizontal Table I : A comparison between the standard deviation values 
S (17, 18 (in mm) obtained from the simulation and the deve- 
plications. loped formulas 
oF OYp and 
Theodolite Position Simulation Developed Formulas 
NE 
B (m) D (m) E (m) ex. No SE ex ov 4 
age accuracy 
OXp, OYp 2.5 1.0 1.5 16.59 0.79 53.20- 16.25 0.78 3.06 
rating 2.5 25.0 1.5 1.61 2.33 0.40 1.61 2.35 D. 30 
Legration of 2.5 25.0 4.5 1.61 2.33 0.29 1.61 2.35 0.26 
is known 12.5 5.0 1.5 0.67 0.21 0.16 0.65 0.21 0.15 
12.5 5.0 4.5 0.67 0.21 0.12 0.65 0.21 D.11 
12.5 25.0 1.5 0.32 0.50 0.13 0.32 0.50 0.13 
ire on a line 12.5 50.0 1.5 0.47 1.49 0.22 0.48 1.51 0:22 
metrical - 25.0 5.0 1.5 0.28 0.16 0.11 0.27 0.15 0.10 
he Y; coor- 25.0 12.5 1.5 0.14 0.18 0.09 0.14 0.18 0.09 
the plane 25.0 12.5 3.0 0.14 0.18 0.10 0.14 0.18 0.08 
.5B) where 25.0 12.5 4.5 0.14 0.18. 0.10 0.14. 0.18 0.08 
(-É) to 25.0 12.5 4.5 0.14 0.18 0.09 0.14 0.18. 0.08 
elevations 25.0 25.0 1.5 0.16 0.29 . 0.12 0.16 0.29 0.12 
d OZp of a 25.0 50.0 1.5 0.27 0.78 . 0.20 0.27 0.79 0.19 
'or the 37.5 5.0 1.5 0.19 0.15 0.11 0.19 0.15 0.11 
| these 37.5 12.0 1.5 0.11 0.17. 0.10 0.11 0.17 0.10 
37,5 25.0 1.5 0.13 0.24. 0.13 0.13 0.24 0.12 
6 37.5 50.0 1.5 0.22 0.56 0.20 0.23 0:57 0.19 
2, B" 50.0 5.0 1.5 0.33 0.16 ; 0.12 0.35 0.16 0.11 
52 50.0 12.5 1.5 0.16 0517; 0.12 0.17 0.17 0.11 
50.0 25.0 1.5 0.14 0.22. 0.14 0.15 0.22 0.13 
(20) 50 50.0 1.5 0.21 0.46 . 0.20 0.22 0.47 0.20 
  
the interpreted directions. The standard deviation values of the simulation 
7