Prolongation of chain line across an obstruction in chain surveying is done by

🚧 Understanding the Problem: Ranging Across Obstructions

In chain surveying, the goal is to measure linear distances along a straight line. However, obstacles like ponds, buildings, or dense woods often block the line of sight or the path of the chain. Prolongation (or "ranging past an obstacle") refers to the various techniques used to continue the survey line accurately beyond such an obstruction, even when direct measurement is impossible.

🔬 Detailed Analysis of Methods

Surveyors use several geometric and trigonometric methods to bypass obstructions. All the listed options represent valid techniques:

• B. Drawing perpendiculars with a chain: This is a common and purely geometric method. The surveyor can establish two points on the chain line before the obstacle, set out equal perpendiculars from these points (using techniques like the 3-4-5 triangle), run a line parallel to the original chain line past the obstacle, and then set out two more perpendiculars to return to the original alignment.
• C. Solution of triangles: This is a broad category that forms the basis of many techniques. By creating triangles around the obstruction (e.g., equilateral triangles, similar triangles), the surveyor can use the properties of those triangles to calculate the obstructed distance and re-establish the line on the other side.
• A. Making angular measurements: While pure chain survey aims to avoid angular instruments, some methods implicitly or explicitly use angles. For example, one can set out a line at a known angle (e.g., 45° or 60°) from the chain line, measure a certain distance, and then turn back at a calculated angle to bypass the obstacle. More advanced surveys would use instruments like a theodolite for this, but the principle is a valid way to solve the problem.

✅ Conclusion

Since drawing perpendiculars, solving triangles, and making angular measurements are all established methods for prolonging a survey line across an obstruction, all the given options are correct. The specific method chosen in the field depends on the nature of the obstacle, the instruments available, and the required accuracy.

💡 Key Takeaway

When direct measurement in surveying is blocked, the solution is always to use the principles of geometry and trigonometry. Surveyors create shapes with known properties (like right angles and triangles) around the obstacle to indirectly calculate the required distances and directions.