J. Forcing Closure
1. General
Forcing closure means to take an open link traverse, Figure I1, and create a closed loop traverse by connecting the end points.
Figure J1 
While this does result in a perfectly closed traverse it cannot account for any errors in the original open link. Forcing closure is commonly applied to initially map a property description whose last course reads similarly to "thence back to the point of beginning." A description like this is open since it does not specify length or direction of the closing line.
2. Procedure
An open traverse< Figure I2, is closed by making it meet the closure condition:
Equations D3 and D4 
Figure J2 
When the latitudes and departures are added, the amount by which they don't equal zero are the latitude and departure of the closing line, Figure I3.

Figure J3 
Equations J1 and J2 
Once the latitude and departure of the closing line are determined, its length and direction can be computed from equations we've used before:
Equation J3 

Equation J4 
The mathematical signs on the closing latitude and departure determine in which quadrant the line is.
3. Example
Determine the closing line's length and direction for the open traverse shown in Figure I4.
Figure J4 
a. Compute the latitudes and departures of the traverse lines
Line 
Latitude 
Departure 
AB 
400.973' 
97.808' 
BC 
83.759' 
+508.092' 
CD 
+367.513' 
39.600' 
b. Sum the latitudes and departures
Line 
Latitude 
Departure 
AB 
400.973' 
97.808' 
BC 
83.759' 
+508.092' 
CD 
+367.513' 
39.600' 
sums: 
117.219' 
+370.684' 
c. Determine the latitude and departure for the closing line
d. Then its length and direction
4. Summary
Forcing closure should never be done instead of closing a traverse using measurements or known endpoints. Being able to compute a missing line is no substitute for measuring it since errors can't be isolated. In the above example, if the length of line BC was misrecorded as 514.95 instead of 541.95 that error won't be discovered but the traverse could still be forced to close. The length and direction of the closing line are dependent on, and absorb, all measurement errors and mistakes.