---
title: "Gale's table, coordinates of all points"
subject: "Surveying II"
chapter: 1
key: "semester_4/surveying_ii:gale-table-abcde-2075b"
source: https://www.bctengineer.com/q/semester_4/surveying_ii/gale-table-abcde-2075b
site: BCT Engineering
---

# Gale's table, coordinates of all points

Surveying II · Chapter 1: Traversing

- Asked in: 2075 Baisakh, 8 marks
- Video: [Gale's table coordinate calculations applying correction by Bowditch's rule](https://www.youtube.com/watch?v=oU1wfd1q4Dw) — KLC Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/surveying_ii/gale-table-abcde-2075b
- Whole chapter: https://www.bctengineer.com/md/semester_4/surveying_ii/chapter-1

## Question

Prepare the Gale's Table and find the co-ordinates of all the points if the co-ordinate of C is (1000N, 1500E) from the following data.

| S.No | Line | Length (m) | Bearing (WCB) |
|---|---|---|---|
| 1 | AB | 66.60 | 30°30' |
| 2 | BC | 135.70 | 102°48' |
| 3 | CD | 66.30 | 95°40' |
| 4 | DE | 76.60 | 198°8' |
| 5 | EA | 214.30 | 284°1' |

## Short answer

Using Bowditch rule from C (1000N,1500E), coordinates are: A (972.637N, 1333.995E), B (1030.036N, 1367.756E), C (1000.000N, 1500.000E), D (993.467N, 1565.935E), E (920.688N, 1542.047E). Linear misclosure 0.3657 m, 1/1530.

## Answer

The bearings are given directly, so the Gale's table starts from the latitudes and departures. Bowditch's rule is used to balance the traverse, and the coordinates are then run from C (1000 N, 1500 E).

#### Step 1: Latitude and departure
$$
\text{Lat}=L\cos\theta,\qquad \text{Dep}=L\sin\theta
$$

| Line | Length (m) | Bearing | Latitude | Departure | Corr. lat | Corr. dep |
|---|---|---|---|---|---|---|
| AB | 66.600 | 30°30' | +57.385 | +33.802 | +0.0140 | -0.0412 |
| BC | 135.700 | 102°48' | -30.064 | +132.328 | +0.0285 | -0.0840 |
| CD | 66.300 | 95°40' | -6.547 | +65.976 | +0.0139 | -0.0410 |
| DE | 76.600 | 198°08' | -72.796 | -23.840 | +0.0161 | -0.0474 |
| EA | 214.300 | 284°01' | +51.904 | -207.919 | +0.0450 | -0.1327 |
| **Sum** | 559.500 |  | -0.117 | +0.346 | +0.1174 | -0.3464 |

#### Step 2: Closing error
$$
\begin{aligned}
e_N&=\Sigma\text{Lat}=-0.117\ \text{m},\qquad e_E=\Sigma\text{Dep}=+0.346\ \text{m}\\
e&=\sqrt{e_N^2+e_E^2}=0.3657\ \text{m}\\
\text{Relative error}&=\frac{e}{\Sigma L}=\frac{0.3657}{559.50}=\frac{1}{1530}
\end{aligned}
$$

#### Step 3: Bowditch correction
$$
C_{lat}=-e_N\frac{L}{\Sigma L},\qquad C_{dep}=-e_E\frac{L}{\Sigma L}
$$

The corrections are in the last two columns above (their sums cancel the errors). Adjusted values:

| Line | Adj. lat | Adj. dep | Adj. length (m) | Adj. bearing |
|---|---|---|---|---|
| AB | +57.398 | +33.761 | 66.591 | 30°28' |
| BC | -30.036 | +132.244 | 135.612 | 102°48' |
| CD | -6.533 | +65.935 | 66.258 | 95°39' |
| DE | -72.780 | -23.888 | 76.599 | 198°10' |
| EA | +51.949 | -208.052 | 214.440 | 284°01' |

#### Step 4: Coordinates of all points
Starting from C = (1000.000 N, 1500.000 E), add the adjusted latitude and departure of CD, DE, EA and AB in turn:

| Station | Northing (m) | Easting (m) |
|---|---|---|
| A | 972.637 | 1333.995 |
| B | 1030.036 | 1367.756 |
| C | 1000.000 | 1500.000 |
| D | 993.467 | 1565.935 |
| E | 920.688 | 1542.047 |

Check: B plus the adjusted BC returns exactly to C (1000.000 N, 1500.000 E).

**Answer:** A (972.637 N, 1333.995 E), B (1030.036 N, 1367.756 E), C (1000.000 N, 1500.000 E), D (993.467 N, 1565.935 E), E (920.688 N, 1542.047 E); misclosure 0.3657 m, 1 in 1530.

## Check yourself

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

1. From which station are coordinates run in this problem?
   A. C (1000 N, 1500 E), the station with given coordinates
   B. A, as it is first in the table
   C. The centroid of the traverse
   D. An assumed origin (0,0)
   Answer: A. Known coordinates of C are used and adjusted latitudes and departures are added in sequence. (Key point: Starting point)

2. SigmaLat = -0.117 m and SigmaDep = +0.346 m. What is the total closing error e?
   A. About 0.463 m
   B. About 0.366 m
   C. About 0.229 m
   D. About 0.117 m
   Answer: B. e = sqrt(0.117^2 + 0.346^2) = 0.3657 m. (Key point: Closing error)

3. Which signs do the corrections to latitude and departure have?
   A. Negative for both
   B. Positive for both
   C. Positive for latitudes and negative for departures, opposite to the sums
   D. Negative for latitudes and positive for departures
   Answer: C. Corrections are opposite to the errors; SigmaLat is negative and SigmaDep positive. (Key point: Correction sign)

4. Which line gets the largest Bowditch correction?
   A. BC, the line with the given bearing
   B. AB, the first line
   C. CD, the shortest line
   D. EA, the longest line (214.30 m)
   Answer: D. Correction is proportional to line length. (Key point: Largest correction)

## Related in Surveying II

- [Closed traverse missing EA bearing, BC length](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aclosed-traverse-abcdea-missing-ea-bc) — Surveying II, chapter 1
- [Check Gale's table ABCDEA, D at 2500 N](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Agale-table-abcdea-2081c) — Surveying II, chapter 1
- [Gale's table for traverse ABCDA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Agale-table-abcda-2072a) — Surveying II, chapter 1
- [Link traverse Q to X, Gale's table m1, m2](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Alink-traverse-qx-gale-m1-m2) — Surveying II, chapter 1
- [Gale's table for traverse ABCDEA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Agale-table-abcdea-2078b) — Surveying II, chapter 1
- [Traverse missing length CD, bearing EA](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Atraverse-missing-cd-length-ea-bearing) — Surveying II, chapter 1

## Related in other subjects

- [True length of suspended distance AB (66)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-suspended-ab-114-095) — Surveying I, chapter 2
- [Classify soil, No. 4 70%, No. 200 30%](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclassify-soil-no4-no200-ll33) — Soil Mechanics, chapter 3
- [True length of base line AB (four bays)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atape-base-line-four-bays) — Surveying I, chapter 2
- [Area by coordinates and DMD (AB -370)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aarea-coordinate-and-dmd-minus-370) — Surveying I, chapter 9, asked 4×