A branch of surveying in which the horizontal and vertical distances of points are obtained by instrumental ob

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A branch of surveying in which the horizontal and vertical distances of points are obtained by instrumental observations is known as

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The correct answer is Option A: Tacheometry surveying. Tacheometry (or Tacheometric Surveying) is a branch of optical surveying in which both horizontal distances and vertical elevations of points are determined using instrumental observations with a tacheometer (a transit theodolite fitted with a stadia diaphragm), eliminating the need for direct chain or tape measurements.

Step-by-Step Solution & Concepts:
Tacheometry (or Tacheometric Surveying) is a branch of optical surveying in which both horizontal distances and vertical elevations of points are determined using instrumental observations with a tacheometer (a transit theodolite fitted with a stadia diaphragm), eliminating the need for direct chain or tape measurements.

Working Principle: It is based on the principle of isosceles triangles, where the ratio of the distance from the vertex to the base and the length of the base remains constant. By measuring the staff intercept (base) using stadia wires in the telescope, the distance from the instrument station can be calculated using stadia constants.

Key Formulas: $D = ks + C$ — Horizontal distance for horizontal line of sight; $D = ks \cos^2	heta + C \cos	heta$ — Horizontal distance for inclined line of sight with vertical staff; $V = \frac{1}{2} ks \sin 2	heta + C \sin	heta$ — Vertical component for inclined line of sight

Key Points: Tacheometer is an ordinary transit theodolite fitted with a stadia diaphragm and an anallatic lens.; The multiplication constant $k = \frac{f}{i}$ is typically kept as $100$.; The additive constant $C = f + d$ is made equal to zero by providing an anallatic lens in the telescope.; Highly preferred for rough, steep, or inaccessible terrains where chaining is difficult or inaccurate.

Advantages: Rapid speed of survey execution compared to conventional chaining.; Ideal for highly undulating, hilly, or marshy land.; Eliminates errors associated with chain dragging and slope corrections.

Disadvantages: Lower precision compared to modern Electronic Distance Measurement (EDM) or chaining on smooth ground.; Limited range, typically up to 100 meters for precise readings with stadia staff.

Applications: Preparation of contour maps and topographic surveys.; Location surveys for roads, railways, and reservoirs.; Checking boundaries and preliminary route surveys.

Additional Info: An anallatic lens is a convex lens fitted between the objective and the diaphragm to make the additive constant zero.. Option B (Hydrographic surveying) is concerned with body of water measurements.. Option C (Chain surveying) uses chain/tape for measuring distances directly along flat ground.. Option D (Plane table surveying) is a graphical method where field work and plotting are done simultaneously.

Answer: A is correct — Tacheometry surveying is the optical branch of surveying where horizontal and vertical distances are computed from instrumental observations.

Exam Tip: Always remember that for a telescope fitted with an anallatic lens, $k = 100$ and $C = 0$, simplifying the distance formula to $D = 100s \cos^2	heta$ for inclined sights.

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Option B: Hydrographic surveying

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Option C: Chain surveying

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Option D: Plane table surveying

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