--- title: "Principles of levelling; reciprocal levelling" subject: "Surveying I" chapter: 5 key: "semester_3/surveying_i:principles-leveling-and-reciprocal" source: https://www.bctengineer.com/q/semester_3/surveying_i/principles-leveling-and-reciprocal site: BCT Engineering --- # Principles of levelling; reciprocal levelling Surveying I · Chapter 5: Leveling - Asked in: 2078 Bhadra, 3+2 marks; 2070 Chaitra (old course), 10 marks (asked 2 times) - Video: [Reciprocal levelling | Levelling | Type of Levelling | Surveying | By Nadish Pandey](https://www.youtube.com/watch?v=k-eGVDbiWls) — Zero Association - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/principles-leveling-and-reciprocal - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-5 ## Question What are the basic principles of levelling? Describe reciprocal levelling with sketch. ## Answer #### Basic principles of levelling 1. A **horizontal line of sight** is established with a level (the line of collimation is made horizontal by centring the bubble). 2. The vertical distance from this line of sight to the points whose elevations are required is measured with a **graduated levelling staff** held vertically on them. 3. The difference of staff readings gives the difference of level between two points: the point with the **smaller reading is higher**. 4. If the RL of one point is known, the RL of the other is: RL = known RL $\pm$ difference of level, usually found through the **height of instrument** or the **rise and fall** method. 5. When the points are far apart or at different heights, the work is carried out in steps using **change points**; sights are balanced to remove the errors of collimation, curvature and refraction. #### Reciprocal levelling Used when two points A and B are on opposite sides of a river or valley and the level cannot be set at the middle. ```text Set 1: level near A Set 2: level near B A [L] ------------> B A <------------ [L] B a1(near) b1(far) a2(far) b2(near) ``` 1. Set the level near A; read the staff at A ($a_1$) and at B ($b_1$). 2. Move the level near B; read the staff at A ($a_2$) and B ($b_2$). 3. The true difference of level is the mean of the two apparent differences: $$ H = \frac{(a_1 - b_1) + (a_2 - b_2)}{2} $$ The error in the far reading (collimation, curvature, refraction) is $$ e = \frac{(a_2 - b_2) - (a_1 - b_1)}{2} $$ The mean eliminates these errors because the far sight is of the same length in each set. The two sets should be taken at about the same time under the same atmospheric conditions, and the mean of several sets is used for precise work. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Given two staff readings, which point is higher? A. The one with the larger reading B. The one with the smaller reading C. The one nearer the instrument D. The one read first Answer: B. The line of sight is horizontal, so a smaller reading means the point is closer to the line, i.e. higher. (Key point: Staff reading principle) 2. Why are change points used? A. To check the collimation error B. To carry the work in steps when points are far apart or at different heights C. To measure the width of a river D. To avoid using a staff Answer: B. Change points let the instrument be moved while the level is carried forward. (Key point: Use of change points) 3. What is the true difference of level in reciprocal levelling? A. Mean of the two apparent differences B. Difference of the two apparent differences C. Only the first set's difference D. Sum of the near readings Answer: A. H = [(a1 − b1) + (a2 − b2)]/2 cancels the far sight error. (Key point: Reciprocal formula) 4. What does e = [(a2 − b2) − (a1 − b1)]/2 represent? A. The true difference of level B. The error in the far reading from collimation, curvature and refraction C. The river width D. The height of instrument Answer: B. e is the combined error in the far staff reading and is removed by taking the mean. (Key point: Error e) ## Related in Surveying I - [Reciprocal levelling and its significance](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-significance) — Surveying I, chapter 5, asked 3× - [Reciprocal levelling: why and formula](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-derivation) — Surveying I, chapter 5, asked 3× - [Reciprocal levelling: RL of A, B at 1160.18 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-rl-b-1160-18) — Surveying I, chapter 5, asked 2× - [Reciprocal levelling: RL of A, B at 1260.18 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-rl-b-1260-18) — Surveying I, chapter 5, asked 2× - [Reciprocal levelling; RL of closed traverse stations](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-closed-traverse-bcdefgb) — Surveying I, chapter 5 - [Reciprocal levelling across river, 250 m](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Areciprocal-leveling-river-250m-eyepiece-height) — Surveying I, chapter 5 ## Related in other subjects - [Reciprocal trigonometrical levelling formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Areciprocal-trig-leveling-formula) — Surveying II, chapter 3 - [Reciprocal leveling, RL of hill top relation](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Areciprocal-leveling-when-hill-top-relation) — Surveying II, chapter 3 - [Principles of IUH development by Clark's method](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aclark-iuh-principles) — Engineering Hydrology, chapter 7 - [Principles of mix design; factors not in DOE](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Amix-design-principles-doe-omitted) — Concrete Technology and Masonry Structure, chapter 3