---
title: "Omitted measurement, non-adjacent affected sides"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:omitted-measurement-nonadjacent-sides"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/omitted-measurement-nonadjacent-sides
site: BCT Engineering
---

# Omitted measurement, non-adjacent affected sides

Surveying II · Chapter 1: Traversing

- Asked in: 2077 Chaitra, 4 marks; 2073 Bhadra, 4 marks; 2072 Asoj, 6 marks; 2076 Baisakh, 4 marks (asked 4 times)
- Video: [Case V | Omitted Measurement | When affected legs are not adjacent | Prashant YT | Surveying |](https://www.youtube.com/watch?v=EBPdiwI9_f8) — Prashant YT
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/omitted-measurement-nonadjacent-sides
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

Describe the procedure of how one can tackle a case of omitted measurement when affected legs are not adjacent.

## Short answer

Shift known lines between the two unknown lines to make them adjacent. Sum latitudes and departures of all known lines to obtain the closing line. The two unknown lines and closing line form a triangle; solve for missing lengths or bearings using sine/cosine rules, then restore original positions.

## Answer

When two quantities of a closed traverse are missing, they can be found from $\Sigma\text{Lat}=0$ and $\Sigma\text{Dep}=0$. If the lines with missing data are **not adjacent**, the known lines lying between them are shifted so that the two unknown lines come together. This is allowed because the closure of a traverse depends only on the lines taken, not on their order.

#### Procedure
1. Compute latitude $L\cos\theta$ and departure $L\sin\theta$ of every line with complete data.
2. Sum them: $\Sigma\text{Lat}$ and $\Sigma\text{Dep}$ of all the known lines.
3. Draw (or imagine) the known lines placed one after the other, and the two unknown lines at the ends so that the figure closes. The closing line then has

$$
\text{Lat}_c=-\Sigma\text{Lat},\qquad \text{Dep}_c=-\Sigma\text{Dep},\qquad
l=\sqrt{\text{Lat}_c^2+\text{Dep}_c^2},\qquad \tan\phi=\frac{\text{Dep}_c}{\text{Lat}_c}
$$

4. The two unknown lines and this closing line form a triangle (the unknown lines are made adjacent, see the sketch). Solve the triangle:
   - Both **lengths** missing: use the sine rule, the angles being known from the known bearings.
   - Both **bearings** missing: use the cosine rule, all three sides being known.
   - **One length and one bearing** missing: use the sine/cosine rule or the quadratic in the unknown length (two possible solutions; select the one that suits the sketch).
5. Find the missing bearings from the triangle angles, then restore the lines to their original positions. Check by computing $\Sigma\text{Lat}=0$ and $\Sigma\text{Dep}=0$.

```text
 Order in field:  AB(?) BC CD DE(?) EA
 Reordered:       AB(?) DE(?) | BC CD EA (known)

            P
           /\
   AB(?)  /  \  DE(?)
         /    \
        /______\
       Q    l    R
 l = resultant of the known lines BC, CD, EA
```

If more than two quantities are missing, they cannot be found by calculation and the lines must be re-measured in the field.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Why is it allowed to shift the known lines so that two unknown non-adjacent lines come together?
   A. Shifting the lines removes the angular error
   B. Closure of a traverse depends only on the lines taken, not on their order
   C. Latitudes change sign when lines are reordered, which helps the solution
   D. The unknown lines are always parallel to the known lines
   Answer: B. The sums of latitudes and departures do not change when the order of lines is changed, so the traverse still closes. (Key point: Why lines can be shifted)

2. After the known lines are placed head to tail, what are the latitude and departure of the closing line?
   A. Lat_c = -SigmaLat and Dep_c = -SigmaDep of the known lines
   B. Lat_c = +SigmaLat and Dep_c = +SigmaDep
   C. Lat_c = SigmaDep and Dep_c = SigmaLat
   D. Lat_c = SigmaLat/n and Dep_c = SigmaDep/n
   Answer: A. The unknown lines must cancel the known sum, so the closing line is equal and opposite to the resultant of the known lines. (Key point: Closing line components)

3. If the bearings of both unknown lines are missing, which rule solves the triangle formed with the closing line?
   A. Sine rule, since the angles are known
   B. Bowditch rule
   C. Cosine rule, since all three sides are known
   D. Transit rule
   Answer: C. With both lengths and the closing length known, three sides are known, so the cosine rule gives the angles. The sine rule is for both lengths missing. (Key point: Both bearings missing)

4. What is done if more than two quantities of the traverse are missing?
   A. Use the transit rule to estimate them
   B. Assume the angular misclosure is zero and compute them
   C. Solve with three triangles
   D. They cannot be calculated; the lines must be re-measured in the field
   Answer: D. Only two closure equations (SigmaLat=0, SigmaDep=0) exist, so at most two unknowns can be found by calculation. (Key point: Limit on unknowns)

## Related in Surveying II

- [Omitted measurement cases, traverse plotting](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aomitted-measurement-cases-plotting) — Surveying II, chapter 1
- [ODM principle, tacheometric field procedure](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aodm-principle-field-procedure-theodolite) — Surveying II, chapter 2

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