--- title: "Reiteration method with VCR, least count 1′" subject: "Surveying I" chapter: 7 key: "semester_3/surveying_i:reiteration-method-oa-ob-oc-least-count-1-min" source: https://www.bctengineer.com/q/semester_3/surveying_i/reiteration-method-oa-ob-oc-least-count-1-min site: BCT Engineering --- # Reiteration method with VCR, least count 1′ Surveying I · Chapter 7: Transit and Theodolite - Asked in: 2078 Kartik, 6+2 marks - Video: [Reiteration method of measuring horizontal angle! Reiteration method by theodolite! Theodolite su...](https://www.youtube.com/watch?v=eeyNc1j73so) — Smart Engineer - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_3/surveying_i/reiteration-method-oa-ob-oc-least-count-1-min - Whole chapter: https://www.bctengineer.com/md/semester_3/surveying_i/chapter-7 ## Question The following angular observations were made during reiteration method of measurement by a theodolite. Compute the horizontal angles included between survey lines OA, OB and OC by mean direction method. Apply necessary check and corrections if the least count of the instrument is 1 minute. Also find the missing data in VCR. | Inst stn | Sighted to | Face | HCR (D M S) | VCR (D M S) | |---|---|---|---|---| | O | A | L | 00 00 00 | 65 45 00 | | | | R | 180 00 00 | ? ? ? | | | B | L | 100 40 40 | ? ? ? | | | | R | 280 39 50 | 268 55 00 | | | C | L | 161 20 40 | ? ? ? | | | | R | 341 20 20 | 300 40 00 | | | A | L | 00 00 20 | | | | | R | 180 00 00 | | ## Short answer Adjusted horizontal angles: AOB=100°40′00″, BOC=60°40′00″, COA=198°40′00″. Missing VCR: A face right=294°15′00″, B face left=91°05′00″, C face left=59°20′00″. ## Answer **Method.** The reiteration (direction) method: all directions are observed from the reference object A, and the horizon is closed on A again. Mean direction = [Face L + (Face R ∓ 180°)]/2. The angles are differences of the mean directions. #### Check on the observations For each target the difference between Face L and (Face R - 180°) should not exceed the least count (1′ = 60″). All differences are below 60″, so the observations are accepted. The closing reading on A must agree with the first reading within the least count. | Stn | Face L | Face R | R - 180° | Difference (L vs R-180°) | Mean direction | Direction from A | |---|---|---|---|---|---|---| | A | 0°00′00″ | 180°00′00″ | 0°00′00″ | 0°00′00″ | 0°00′00″ | 0°00′00″ | | B | 100°40′40″ | 280°39′50″ | 100°39′50″ | 0°00′50″ | 100°40′15″ | 100°40′15″ | | C | 161°20′40″ | 341°20′20″ | 161°20′20″ | 0°00′20″ | 161°20′30″ | 161°20′30″ | | A (closing) | 0°00′20″ | 180°00′00″ | 0°00′00″ | 0°00′20″ | 0°00′10″ | 0°00′10″ | Closing error on A = 0°00′10″, which is less than 1′, so the round is accepted. #### Mean angles and adjustment Sum of the three angles AOB + BOC + COA should be 360°. Distributing the closing error 0°00′10″ equally (correction -0°00′03.33″ per angle): | Angle | Observed | Correction | Adjusted angle | Rounded to least count (1′) | |---|---|---|---|---| | AOB | 100°40′15″ | -0°00′03.33″ | 100°40′11.67″ | 100°40′00″ | | BOC | 60°40′15″ | -0°00′03.33″ | 60°40′11.67″ | 60°40′00″ | | COA | 198°39′40″ | -0°00′03.33″ | 198°39′36.67″ | 198°40′00″ | | Sum | 360°00′10″ | -0°00′10″ | 360°00′00″ | 360°00′00″ | #### Missing VCR FL + FR = 360° for each target. | Observation | VCR Face left | VCR Face right | Vertical angle (90° - Z) | |---|---|---|---| | A (R) | 65°45′00″ | **294°15′00″** | +24°15′00″ | | B (L) | **91°05′00″** | 268°55′00″ | -1°05′00″ | | C (L) | **59°20′00″** | 300°40′00″ | +30°40′00″ | **Answer:** AOB = 100°40′00″, BOC = 60°40′00″, COA = 198°40′00″ (to the least count of 1′); missing VCR: A (face R) = 294°15′00″, B (face L) = 91°05′00″, C (face L) = 59°20′00″. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the reiteration method, what is checked at the end of the round of observations? A. The closing reading on A agrees with the first reading on A within the least count B. The sum of the horizontal angles equals 180° C. Face L and Face R of A are exactly equal D. The vertical angles add to 90° Answer: A. The horizon is closed on the reference object A; the closing error (here 10″) must not exceed the least count (1′). (Key point: Reiteration check) 2. For each target, what difference should not exceed the least count (60″)? A. Face L and Face R B. Face L and (Face R - 180°) C. Mean direction and 360° D. Direct reading of A and of C Answer: B. Both faces observe the same direction, so after removing 180° they must agree within the least count. (Key point: Face check) 3. The angles AOB + BOC + COA total 360°00′10″. What is done with the 10″? A. It is added to AOB only B. It is added equally, +3.33″ to each angle C. It is distributed equally, -3.33″ to each angle D. It is thrown away without any correction Answer: C. The sum must be 360°, so the excess is removed equally from the three angles. (Key point: Distributing closing error) 4. The VCR of A is 65°45′00″ on face left. What is the face right reading? A. 114°15′00″ B. 245°45′00″ C. 24°15′00″ D. 294°15′00″ Answer: D. For a zenith-angle circle FL + FR = 360°, so FR = 360° - 65°45′ = 294°15′. (Key point: Missing VCR) ## Related in Surveying I - [Direction theodolite, least count 6″, station D](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Adirection-theodolite-ls-6-sec-station-d) — Surveying I, chapter 7 - [Mean direction angles with VCR (125°25′20″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Amean-direction-traverse-abcda-vcr-125-25-20) — Surveying I, chapter 7 - [Theodolite traverse ABCDA with missing VCR (68°30′10″)](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-traverse-abcda-hcr-vcr-68-30-10) — Surveying I, chapter 7 - [Theodolite traverse ABCDA, booking format with VCR](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atraverse-abcda-booking-format-vcr-120-14-20) — Surveying I, chapter 7 - [Mean angles; VCR and VA from A](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atraverse-abcdea-vcr-va-from-a-to-e-and-b) — Surveying I, chapter 7 - [Horizontal angles from field notes, triangle ABC](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Atheodolite-field-notes-abc-64-jestha) — Surveying I, chapter 7 ## Related in other subjects - [Distances OA and OC by resection on A, B, C](https://www.bctengineer.com/question.md?key=semester_4%2Fsurveying_ii%3Aresection-abc-sides-oa-oc) — Surveying II, chapter 5 - [8086 ALP: words on lines and word count](https://www.bctengineer.com/question.md?key=semester_4%2Fmicroprocessor%3Aalp-8086-words-lines-count) — Microprocessor, chapter 3