Two-Point Problem in Plane Table Surveying

Introduction:
Plane table is an instrument used for surveying that involves a drawing board and alidade. In plane table surveying, a plane table is set up on a tripod and leveled. Various measurements are made by sighting to known points and sketching the details onto the paper attached to the table.

Orienting a Plane Table:
Orienting a plane table involves setting up the table so that it is aligned with north and the survey area can be accurately drawn onto the paper. There are several methods for orienting a plane table, including:

- Magnetic compass: A magnetic compass is used to align the table with magnetic north.
- True north: The table is oriented with true north using a theodolite or other instrument.
- Resection: The table is oriented by sighting to known points and calculating the orientation based on those observations.
- Two-point problem: The table is oriented by sighting to two inaccessible points and calculating the orientation based on those observations.

Two-Point Problem:
The two-point problem method of orienting a plane table involves sighting to two inaccessible points and using those observations to calculate the orientation of the table. This method is particularly useful when there are no accessible points to sight to or when the accessible points are too far away to be accurate.

The steps for using the two-point problem method are as follows:

1. Set up the plane table and level it.
2. Choose two inaccessible points that are visible from the table. These points should be as far apart as possible and should not be in the same direction from the table.
3. Sight to the first point and mark its location on the paper.
4. Sight to the second point and mark its location on the paper.
5. Draw a line between the two points on the paper.
6. Bisect the line with the alidade and mark the midpoint on the line.
7. Rotate the table until the midpoint is directly under the alidade.
8. Lock the table in place.
9. Draw a line on the paper parallel to the alidade.
10. This line represents the north-south axis of the table, and the table is now oriented.

Conclusion:
The two-point problem method of orienting a plane table is a useful technique for surveying when there are no accessible points to sight to. By sighting to two inaccessible points and using those observations to calculate the orientation of the table, accurate surveying can be achieved.