---
title: "Level book: profile levelling readings"
subject: "Surveying I"
chapter: 5
key: "semester_3/surveying_i:profile-leveling-readings-3rd-7th-9th"
source: https://www.bctengineer.com/q/semester_3/surveying_i/profile-leveling-readings-3rd-7th-9th
site: BCT Engineering
---

# Level book: profile levelling readings

Surveying I · Chapter 5: Leveling

- Asked in: 2081 Bhadra, 8 marks
- Video: [Longitudinal Levelling Part 3 | Profile Levelling | Plotting Graph for Profile Levelling | Nilesh](https://www.youtube.com/watch?v=_OM_GfTVRGk) — Nilesh Jha Life
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/surveying_i/profile-leveling-readings-3rd-7th-9th
- Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5

## Question

The following readings were successively taken during a levelling operation: 0.320, 0.530, 0.620, 1.780, 1.910, 2.350, 1.750, 0.350, 0.690, 1.240 and (-) 0.980 m. The position of the instrument was changed after the 3rd, 7th and 9th reading. Draw out the form of level book and enter the above readings properly. Assume the R.L. of the 3rd point as 1300.250 m. Calculate the RL of all points by HI method and the gradient between the first and last point if the staff is kept at a constant interval of 20 m.

## Short answer

Using the height of instrument method, the RL of the 3rd point (CP1) is 1300.250 m. Computed RLs of points 1–8: 1300.550, 1300.340, 1300.250, 1300.120, 1299.680, 1300.280, 1299.940, 1302.160 m. The line rises from the first to the last point at a gradient of about 1 in 87 (rise 1.610 m over 140 m).

## Answer

**Arranging the readings.** The instrument was changed after the 3rd, 7th and 9th readings, so there are four set-ups:

- Set-up 1: 0.320 (BS), 0.530 (IS), 0.620 (FS on CP1, which is the 3rd point).
- Set-up 2: 1.780 (BS on CP1), 1.910 and 2.350 (IS), 1.750 (FS on CP2).
- Set-up 3: 0.350 (BS on CP2), 0.690 (FS on CP3).
- Set-up 4: 1.240 (BS on CP3), $-0.980$ (FS on the last point; the negative reading means the staff was held inverted, so the point is above the line of sight).

The 11 readings are on 8 points (the FS and the next BS at a change point are on the same point). The RL of the 3rd point (CP1) is 1300.250 m, so the HI of set-up 1 is $1300.250 + 0.620 = 1300.870$ m and the RLs of points 1 and 2 are found from it.

#### Level field book (height of instrument method)

| Station | BS | IS | FS | HI (m) | RL (m) |
|---|---|---|---|---|---|
| 1 | 0.320 |  |  | 1300.870 | 1300.550 |
| 2 |  | 0.530 |  |  | 1300.340 |
| 3 (CP1) | 1.780 |  | 0.620 | 1302.030 | 1300.250 |
| 4 |  | 1.910 |  |  | 1300.120 |
| 5 |  | 2.350 |  |  | 1299.680 |
| 6 (CP2) | 0.350 |  | 1.750 | 1300.630 | 1300.280 |
| 7 (CP3) | 1.240 |  | 0.690 | 1301.180 | 1299.940 |
| 8 |  |  | -0.980 |  | 1302.160 |

#### Arithmetic check

$\Sigma BS - \Sigma FS = 3.690 - (2.080) = 1.610$ ; last RL $-$ first RL $= 1302.160 - 1300.550 = 1.610$. Both are equal, so the reduction is correct.


#### Gradient between the first and last point

The 8 points are 20 m apart, so the distance between the first and the last point $= 7 \times 20 = 140$ m.

$$
\text{Difference of level} = 1302.160 - 1300.550 = +1.610\ \text{m} \quad (\text{a rise})
$$

$$
\text{Gradient} = \frac{1.610}{140} = \frac{1}{87.0}\ \text{(rising from the first to the last point)}
$$

**Answer:** RLs of points 1 to 8 = 1300.550, 1300.340, 1300.250, 1300.120, 1299.680, 1300.280, 1299.940, 1302.160 m; the line rises from the first to the last point at a gradient of about 1 in 87.

## Check yourself

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

1. The instrument is changed after the 3rd, 7th and 9th readings. How many set-ups, and what is the 3rd reading?
   A. Four set-ups; the 3rd reading is the FS to change point CP1
   B. Three set-ups; the 3rd reading is an IS
   C. Four set-ups; the 3rd reading is a BS
   D. Eleven set-ups, one per reading
   Answer: A. Three changes give four set-ups. The reading just before a shift is the foresight, the next one is the backsight on the same point. (Key point: Set-ups)

2. With RL of the 3rd point = 1300.250 m and FS 0.620 m on it, what are HI and RL of point 1 (BS 0.320 m)?
   A. HI = 1299.630 m; RL = 1299.310 m
   B. HI = 1300.870 m; RL of point 1 = 1300.550 m
   C. HI = 1300.870 m; RL = 1301.190 m
   D. HI = 1300.250 m; RL = 1299.930 m
   Answer: B. HI = RL + reading = 1300.250 + 0.620 = 1300.870 m; RL = HI - 0.320 = 1300.550 m. (Key point: HI)

3. The last reading is -0.980 m. How does it affect the RL?
   A. Staff reading is a mistake and is ignored
   B. RL = HI - 0.980 as for any reading
   C. Staff held inverted; RL = HI + 0.980 = 1302.160 m, point above the line of sight
   D. The point is below the instrument by 0.980 m
   Answer: C. An inverted staff reads negative; RL = HI - (-0.980), so the point lies above the line of sight. (Key point: Negative reading)

4. The first and last points are RL 1300.550 and 1302.160 m, 8 points at 20 m. What is the gradient?
   A. Rising 1.610 m in 160 m, about 1 in 99
   B. Falling 1.610 m in 140 m, about 1 in 87
   C. Rising 1.610 m in 20 m, 1 in 12
   D. Rising 1.610 m in 140 m, about 1 in 87
   Answer: D. 8 points give 7 intervals = 140 m, so gradient = 1.610/140 = 1 in 87. (Key point: Gradient)

## Related in Surveying I

- [Level book, staff readings at B and C (1251.250)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-250) — Surveying I, chapter 5, asked 3×
- [Level book, staff readings at B and C (1251.000)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-1250-800-1251-000) — Surveying I, chapter 5, asked 3×
- [Level book, RL of B 1180.750 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-dumpy-4m-staff-b-1180-750) — Surveying I, chapter 5, asked 2×
- [Level book TBM1 to TBM2 (4th, 7th)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-tbm1-tbm2-1449-870) — Surveying I, chapter 5, asked 4×
- [Level book TBM1-TBM2 with (-)1.685 reading](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-tbm1-tbm2-with-minus-1-685) — Surveying I, chapter 5, asked 4×
- [Level book, RL of 4th point 562.50](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-successive-readings-4th-point-562-50) — Surveying I, chapter 5

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- [Vertical curve +0.5% and -0.7%, IP RL 350.750](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Avertical-curve-pos05-neg07-ip-500) — Surveying II, chapter 6
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