This question was previously asked in

HPPSC AE Civil 2016 (Deputy Manager) Official Paper

Option 4 : In three-point problem, the station is easily located when it falls on the great circle

**Explanation:**

(i) In-Plane table surveying, the **work of taking the measurements and plotting the plan is done in the field only**. It is a quick method of surveying. The advantage of this method is that the plan as plotted in the field can be compared with the actual field plan on the spot. Thus mistakes can be detected at the initial stage itself.

(ii) There are four methods of plane tabling:

1) Radiation:

- In this ray is drawn from the instrument towards the point, then the distance measured is located by plotting to some scale.
- More suitable when the distance is small
**and one instrument can control the points to be detailed.**

2) Intersection/Graphic triangulation:

- Used when the distance between two points is large and cannot be measured accurately due to some field condition.
- The location of the object is determined by sighting at the object from two plane table stations, which were previously plotted and drawing the rays.
- The intersection of these rays gives the location of the object.
- The point of intersection of two rays forms a vertex of a triangle having two rays as two sides and a base as the third side.
- Due to this reason, this is also called graphic triangulation.

3) Traversing:

- Similar to theodolite traversing, the table is set up at each station in succession.
- Foresight is taken to the next station and the required distance is measured to a suitable scale.
- This method is suited when the narrow strip of the terrain is to be surveyed.

4) Resection:

- This method is used when the plane table occupies a position not yet plotted on the drawing sheet.
- It is the process of determining the plotted positions of the station occupied by the plane table, by means of sights taken towards known points, the location of which has been plotted.
- It is done by sighting two points whose positions have earlier been plotted in the two-point problem. alternatively, it can be done by sighting three points whose positions have earlier been plotted in the three point problems.

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iii) The estimation of the location of the plane table depends on its position relative to the well-defined points considered for this purpose. Depending on their relative positions, three cases may arise :

- The position of the plane table is inside the great triangle;
- The position of the plane table is outside the great triangle;
- The position of the plane table lies on or near the circumference of the great circle.

__Important Points__

**If the position of the plane table lies on or near the circumference of the great circle, the solution of the three-point problem becomes indeterminate or unstable.**- But for cases (1) and (2), Lehmann's rules are used to estimate the location of the plane table.