--- title: "Level book, RL of A 380.500, 3.945 on B" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-4m-staff-30m-380-500-minus" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-4m-staff-30m-380-500-minus site: BCT Engineering --- # Level book, RL of A 380.500, 3.945 on B Surveying I · Chapter 5: Leveling - Asked in: 2081 Baisakh, 6 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-4m-staff-30m-380-500-minus - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question The following consecutive readings were taken with a level and a 4 meter levelling staff on a continuously sloping ground at a common interval of 30 meters. -0.855 (on A), 1.545, 2.353, 3.115, 3.825, 0.455, 1.380, 2.055, 2.855, 3.455, 0.585, 1.015, 1.850, 2.755, 3.945 (on B). The R.L. of A was 380.500. Make a level book and apply usual checks. Determine the gradient of the line AB. ## Short answer With rise and fall method, RL of B is 369.460 m. The fall from A (380.500 m) to B is 11.040 m over 360 m (12 intervals of 30 m), giving a falling gradient of 1 in 32.6. ## Answer **Arranging the readings.** The staff is 4 m long, so the instrument must be shifted when the reading nears 4 m: after 3.825 and after 3.455. The first reading ($-0.855$ m) is negative: the staff was held inverted (for example under a beam), so the point A is above the line of sight. The set-ups are: - Set-up 1: BS $-0.855$ on A; IS 1.545, 2.353, 3.115; FS 3.825 on CP1. - Set-up 2: BS 0.455 on CP1; IS 1.380, 2.055, 2.855; FS 3.455 on CP2. - Set-up 3: BS 0.585 on CP2; IS 1.015, 1.850, 2.755; FS 3.945 on B. RL of A $= 380.500$ m. The 15 readings are on 13 points (the FS and BS at a change point are on one point), 30 m apart. #### Level field book (rise and fall method) | Station | BS | IS | FS | Rise | Fall | RL (m) | |---|---|---|---|---|---|---| | A | -0.855 | | | | | 380.500 | | 2 | | 1.545 | | | 2.400 | 378.100 | | 3 | | 2.353 | | | 0.808 | 377.292 | | 4 | | 3.115 | | | 0.762 | 376.530 | | 5 (CP1) | 0.455 | | 3.825 | | 0.710 | 375.820 | | 6 | | 1.380 | | | 0.925 | 374.895 | | 7 | | 2.055 | | | 0.675 | 374.220 | | 8 | | 2.855 | | | 0.800 | 373.420 | | 9 (CP2) | 0.585 | | 3.455 | | 0.600 | 372.820 | | 10 | | 1.015 | | | 0.430 | 372.390 | | 11 | | 1.850 | | | 0.835 | 371.555 | | 12 | | 2.755 | | | 0.905 | 370.650 | | B | | | 3.945 | | 1.190 | 369.460 | #### Arithmetic check $\Sigma BS - \Sigma FS = 0.185 - (11.225) = -11.040$ ; $\Sigma \text{Rise} - \Sigma \text{Fall} = 0.000 - 11.040 = -11.040$ ; last RL $-$ first RL $= 369.460 - 380.500 = -11.040$ All three are equal, so the reduction is correct. #### Gradient of the line AB There are 13 points, so 12 intervals of 30 m: $AB = 12 \times 30 = 360$ m. $$ \text{Fall from A to B} = 380.500 - 369.460 = 11.040\ \text{m} $$ $$ \text{Gradient} = \frac{11.040}{360} = \frac{1}{32.6}\ (\text{falling from A to B}) $$ **Answer:** RL of B = 369.460 m; the line AB falls at a gradient of 1 in 32.6 (about 1 in 33). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. With a 4 m staff, why is the instrument shifted after 3.825 and 3.455? A. The reading nears the staff length, so the next point could not be read from the same set-up B. Those readings contain errors C. Every fourth reading must be a change point D. The staff is inverted there Answer: A. The staff reads only up to 4 m, so a change point is taken when readings approach that. (Key point: Where to shift) 2. What does the first reading of -0.855 m on A mean? A. A is 0.855 m below the instrument B. The staff was held inverted and A is above the line of sight C. It is a booking error D. It is a foresight reading Answer: B. A negative reading means the staff was inverted under an overhead object, so the point is above the line of sight. (Key point: Negative reading) 3. Which three equal quantities verify the rise and fall level book? A. SumBS - SumIS, SumFall, and first RL B. SumFS + SumBS, SumRise + SumFall, and last RL C. SumBS - SumFS, SumRise - SumFall, and last RL - first RL D. SumIS - SumFS only Answer: C. All three equal -11.040 m here, which checks the arithmetic of the reductions. (Key point: Checks) 4. RL of A = 380.500, RL of B = 369.460, 13 points at 30 m. What is the gradient? A. Falling 11.040 m in 390 m, 1 in 35.3 B. Rising 11.040 m in 360 m, 1 in 32.6 C. Falling 11.040 m in 30 m, 1 in 2.7 D. Falling 11.040 m in 360 m, about 1 in 32.6 Answer: D. 13 points give 12 intervals x 30 m = 360 m; 360/11.040 = 32.6. (Key point: Gradient) ## Close variants set in other exams - [Level book, RL of B 1380.500](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-b-1380-500) — Surveying I, chapter 5, asked 3× - [Level book, RL of A 380.500, 3.845 on B](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-4m-staff-a-380-500-3-845) — Surveying I, chapter 5, asked 3× ## 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, 5 m staff, B at 1200.800](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-5m-staff-20m-points-a-b-c-d) — Surveying I, chapter 5, asked 2× - [Level book: profile levelling readings](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprofile-leveling-readings-3rd-7th-9th) — Surveying I, chapter 5 - [Level book, B and C, RL 50.250 base](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Alevel-book-15m-b-c-rl-50-800-51-000) — Surveying I, chapter 5, asked 3×