I. Traverse Adjustment by Coordinates
1. Coordinates Galore
Most software compute and carry coordinates through each step of the traverse computations. Until final traverse adjustment, the coordinates go thru a series of values. For example, in a traditional nonleast squares approach coordinates would be computed:
 From raw measurements and directions using unadjusted angles, then,
 After angles are adjusted, and,
 After the traverse is adjusted  these are the final coordinate values.
While coordinates are not needed for manual computations, they can be included. If so they are usually computed after angles are balanced: we will refer to these as preliminary coordinates.
2. Adjustment Process
The traverse misclosure is determined by comparing the preliminary coordinates of the end point to its known starting coordinates:
Loop traverse, Figure I1:
Figure I1 
On a loop traverse, the coordinates of the first point can be known or assumed.
Link traverse, Figure I2.
The coordinates of the traverse endpoints must be known in the same system.
In this case E and H are known.
Figure I2 
When the traverse is adjusted, corrections are applied directly to the preliminary coordinates (J') to obtain final coordinates (J), Figure I3 and Equations E3 and E4.
Figure I3 
Equations E3 and E4 
The line correction affects the line's endpoint, that is, the position of J changes relative to the position of I by the latitude and departure corrections of the line IJ.
Because the coordinates of J change, the coordinates of the next point, K, must change by the same amount plus the correction of the line JK, Figure I4:
Figure I4 
The position shift from K' to K'' is the same as the shifts from J' to J.
This pattern of accumulating corrections continues until the final point where the adjusted coordinates should equal the known values.
Using the Compass Rule:
Equations E1 and E2 
To compute coordinate corrections, the equations are modified to:
Equations I1 and I2 
where ΔN_{i1} and ΔE_{i1} in each are the cumulative previous corrections.
3. Examples
The traverse examples here are the same ones used as previous computation examples so we can check these against earlier results.
a. Loop Traverse
Figure I5 
Previously computed unadjusted latitudes and departures are:
Line  Bearing  Length (ft)  Lat (ft)  Dep (ft) 
AB  S 68°05'35"W  472.68  176.357  438.548 
BC  N 19°46'00"W  216.13  +203.395  73.093 
CD  N 45°55'20"E  276.52  +192.357  +198.651 
DA  S 54°59'15"E  382.24  219.312  +313.065 
sum: 
1347.57  +0.083  +0.075 
(1) Compute preliminary coordinates from the raw latitudes and departures:
(2) Determine latitude and departure closure errors:
Lat err = N_{A'}  N_{A} = 500.083'  500.000' = +0.083'
Dep err = E_{A'}  E_{A} = 2000.075'  2000.000' = +0.075'
Note that these match the latitude and departure column sums above.
(3) Compute and apply corrections to the coordinates using the Compass Rule, Equation (I3).
Line AB
Because point A is a control point, its coordinates are not modified. The corrections are applied to the line's endpoint, point B.
Line BC
Remember to include the corrections for the previous line.
Line CD
Line DA
The corrected preliminary coordinates match the beginning coordinates of point A.
These coordinates also match those computed in the Coordinates section.
b. Link Traverse
Figure I6 
Previously computed unadjusted latitudes and departures are:
Line 
Direction 
Length 
Lat 
Dep 
QR 
S 56°23'38"E 
398.75' 
220.700' 
+332.104' 
RS 
S 75°17'42"W 
422.89' 
107.347' 
409.038 
ST 
N 43°05'47"E 
604.49' 
+441.402' 
+413.004' 

sums: 
1426.13' 
+113.355' 
+336.070 
(1) Compute preliminary coordinates:
Point 
North (ft) 
East (ft) 

Q 
2600.480 
1391.670 

Lat_{QR} 
220.700 
Dep_{QR} 
+332.104 
R 
2379.780 

1723.774 
Lat_{RS} 
107.347 
Dep_{RS} 
409.038 
S 
2272.433 

1314.736 
Lat_{ST} 
+441.402 
Dep_{ST} 
+413.004 
T 
2713.835 

1727.740 
Lat err = 2713.835'  2713.780' = +0.555'
Dep err = 1727.740'1727.810' = 0.070'
(2) Compute and apply corrections to the coordinates using the Compass Rule, Equation I3.
Computations for each line are not shown, but their results are tabulated below.
Point 
N' (ft) 
ΔN (ft) 
N (ft) 
E' (ft) 
ΔE (ft) 
E (ft) 
S 
2379.780 
0.015 
2379.765 
1723.774 
+0.020 
1723.794 
T 
2272.433 
0.031 
2272.402 
1314.736 
+0.041 
1314.777 
Q 
2713.835 
0.054 
2713.781 
1727.740 
+0.071 
1727.811 
check 
check 