This document contains field data from a surveying exercise including stadia readings, horizontal angles, angular errors, distance and accuracy calculations, and coordinate adjustments. Stations A, B, C and D were surveyed and their coordinates were determined. Total angular error was found to be 29'30" which is unacceptable. Angular corrections were applied and distances, latitudes, departures and final coordinates were computed. The accuracy was calculated to be 1:127 which does not meet the required standard.

1. Field Data:
Point Stadia Reading 1: Stadia Reading 2: Horizontal Angle:
A T - 170 T - 169.3 173° 27' 40" /2
M - 159 M - 159
B - 147.9 B - 149 86° 43' 50"
V - 90° 10' 20" V - 90° 13' 00"
B T - 161.3 T - 154.7 194° 33' 40" /2
M - 153.5 M - 153.5
B - 145.3 B - 142.2 97° 16' 50"
V - 89° 44' 54" V - 89° 47' 40"
C T - 175.3 T - 175.6 188° 20' 40" /2
M - 165 M - 165
B - 155 B - 154.3 94° 10' 20"
V - 89° 46' 20" V - 89° 54' 00"
D T - 168.6 T - 166 164° 37' 00" /2
M - 158 M - 158
B - 147.3 B - 150 82° 18' 30"
V - 90° 04' 00" V - 90° 04' 20"

2. Angular Error & Angle Adjustments
Total Angular Error = 360° 29' 30" - 360°
= 29' 30" (Not Acceptable)
Station Field Angles Correction Adjusted Angles
A 86° 43' 50" - 0° 7' 22" 86° 36' 28"
B 97° 16' 50" - 0° 7' 22" 97° 09' 28"
C 94° 10' 20" - 0° 7' 23" 94° 02' 57"
D 82° 18' 30" - 0° 7' 23" 82° 11' 07"
Total 360° 29' 30" 360° 0' 0"
Distance Calculation
Formula Used:
K x s x sin^2(θ) + C x cos(θ) K = 100 C = 0
Station Length Bearing Cos Sin Latitude Departure
A
100 x (169.3-149) x sin ^ 2 (90° 13' 00") N 3° 23' 32" w 0.998 0.059 20.259 -1.198
= 20.30 m
B
100 x (154.7-142.2) x sin ^ 2 (89° 47' 40") N 86° 14' 04" w 0.065 0.998 0.813 -12.475
= 12.50 m
C
100 x (175.6-154.3) x sin^2(89° 54' 00") S 7° 48' 53" W 0.991 0.135 -21.108 -2.876
= 21.30 m
D
100 x (166-150) x sin ^ 2 (90° 04' 20") N 90° E 0 1.000 0 16.000
= 16.00m
A
Total 70.10m -0.036 -0.549

3. Accuracy Calculation:
Accuracy = 1 : (P/Ec)
Ec = [(sum of latitude)² + (sum of departure)² ]^½
P = Total Perimeter
Calculation:
Accuracy = 1: (70.1 / 0.550)
= 1:127
The traversing is not acceptable.
Adjustment of Latitude and Departure
Total Correction = (Total Misclosure / Perimeter ) x Length
Station Unadjusted Correction Adjusted
Latitude Departure Latitude Departure Latitude Departure
A
20.259 -1.198 0.010 0.159 20.269 -1.039
B
0.813 -12.475 0.007 0.098 0.820 -12.377
C
-21.108 -2.876 0.011 0.167 -21.097 -2.709
D
0 16.000 0.008 0.125 0.008 16.125
A
Total -0.036 -0.549 0.036 0.549 0.000 0.000

4. Computation of Station Coordinates
Assumed Station A Coordinates: (100.000, 0.000)
Station Adjusted Latitude Adjusted Departure Y-axis Coordinates X-axis Coordinates
A 0.000 100.000
20.269 -1.039
B 20.269 98.961
0.820 -12.377
C 21.089 86.584
-21.097 -2.709
D 0.008 83.875
0.008 16.125
A 0.000 100.000
Final Coordinates
Station Coordinates
A (100.000, 0.000)
B (98.961, 20.269)
C (86.584, 21.089)
D (83.875, 0.008)