--- title: "Level book, RL of 4th point 562.50" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:level-book-successive-readings-4th-point-562-50" source: https://www.bctengineer.com/q/semester_3/surveying_i/level-book-successive-readings-4th-point-562-50 site: BCT Engineering --- # Level book, RL of 4th point 562.50 Surveying I · Chapter 5: Leveling - Asked in: 2066 Jestha, 9 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-successive-readings-4th-point-562-50 - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question The following readings were successively taken with a level: 0.35, 0.487, 0.696, 1.675, 1.893, 2.416, 1.823, 0.487, 0.759, 1.350 and 2.057. The instrument was shifted after the fourth and seventh readings. Prepare a level book and calculate the RLs of different points if the RL of the 4th point is 562.50 m. Use both the methods. ## Short answer Using rise and fall and HI methods with instrument shifts after the 4th and 7th readings, the RLs of points 1 to 9 are 563.825, 563.688, 563.479, 562.500, 561.977, 562.570, 562.298, 561.707, and 561.000 m. Checks confirm ΣBS − ΣFS = −2.825 m equals last RL minus first RL. ## Answer **Assumptions:** 11 readings; the instrument is shifted after the 4th and 7th readings, so the 4th and 7th readings are foresights on change points and the 5th and 8th readings are backsights on the same points. Hence there are 9 points (numbered 1 to 9). Set-ups: (0.350, 0.487, 0.696, 1.675), (1.893, 2.416, 1.823), (0.487, 0.759, 1.350, 2.057). RL of point 4 = 562.500 m. #### (a) Rise and fall method | Point | BS | IS | FS | Rise | Fall | RL (m) | |---|---|---|---|---|---|---| | 1 | 0.350 | | | | | 563.825 | | 2 | | 0.487 | | | 0.137 | 563.688 | | 3 | | 0.696 | | | 0.209 | 563.479 | | 4 | 1.893 | | 1.675 | | 0.979 | 562.500 | | 5 | | 2.416 | | | 0.523 | 561.977 | | 6 | 0.487 | | 1.823 | 0.593 | | 562.570 | | 7 | | 0.759 | | | 0.272 | 562.298 | | 8 | | 1.350 | | | 0.591 | 561.707 | | 9 | | | 2.057 | | 0.707 | 561.000 | #### (b) Height of instrument (HI) method HI of set-up 1 = RL of point 4 + FS(4) = 562.500 + 1.675 = 564.175 m, so RL of point 1 = 564.175 - 0.350 = 563.825 m. | Point | BS | IS | FS | HI | RL = HI - reading (m) | |---|---|---|---|---|---| | 1 | 0.350 | | | 564.175 | 563.825 | | 2 | | 0.487 | | | 563.688 | | 3 | | 0.696 | | | 563.479 | | 4 | 1.893 | | 1.675 | 564.393 | 562.500 | | 5 | | 2.416 | | | 561.977 | | 6 | 0.487 | | 1.823 | 563.057 | 562.570 | | 7 | | 0.759 | | | 562.298 | | 8 | | 1.350 | | | 561.707 | | 9 | | | 2.057 | | 561.000 | Both methods give the same RLs. #### Checks $$ \begin{aligned} \Sigma BS - \Sigma FS &= 2.730 - 5.555 = -2.825\\ \Sigma \text{Rise} - \Sigma \text{Fall} &= 0.593 - 3.418 = -2.825\\ \text{Last RL} - \text{first RL} &= 561.000 - 563.825 = -2.825 \end{aligned} $$ **Answer:** RLs of points 1 to 9 = 563.825, 563.688, 563.479, 562.500, 561.977, 562.570, 562.298, 561.707, 561.000 m. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The instrument is shifted after the 4th and 7th readings. How are these treated? A. As FS on change points, with the 5th and 8th readings being BS on the same points B. As BS readings C. As IS readings D. As new points with the 5th and 8th being FS Answer: A. Shifting after a reading means that reading is an FS and the next is a BS on the same point, giving 9 points. (Key point: Change points) 2. What is the HI of the first set-up? A. 562.500 + 0.350 = 562.850 m B. 562.500 + 1.893 = 564.393 m C. 562.500 + 1.675 = 564.175 m D. 562.500 - 1.675 = 560.825 m Answer: C. Point 4 has FS 1.675, so HI = 562.500 + 1.675 = 564.175 m and RL of point 1 = 564.175 - 0.350 = 563.825 m. (Key point: HI of first set-up) 3. Why is there a rise at point 6? A. The instrument was lowered B. FS 1.823 is smaller than the previous reading 2.416 on the same set-up C. IS is larger than BS D. BS is larger than FS Answer: B. A smaller reading than the previous one means a rise: 2.416 - 1.823 = 0.593 m. (Key point: Rise at point 6) 4. What is the check value for this book? A. 0.000 B. -2.825 C. -5.555 D. +2.825 Answer: B. Sum BS - sum FS = 2.730 - 5.555 = -2.825 = sum rise - sum fall = last RL - first RL. 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