1.15.6.e. Reciprocal levelling

In levelling, the distance of back sight and distance of fore sight is kept equal, as far as possible. It is done to eliminate the following errors: (a) Error due to non-parallelism of line of collimation and axis of bubble tube, and (b) Errors due to curvature and refraction.

Reciprocal levelling is a technique used in surveying to address specific errors that occur when levelling across large geographical features. The main idea here is to keep the distances for the back sight (BS) and fore sight (FS) as equal as possible. This balance helps eliminate certain errors:

1. Non-parallelism Errors: This occurs when the line of collimation (the line of sight through the telescope) is not perfectly parallel to the axis of the bubble tube, the tool that helps level the instrument. If they are not parallel, the readings can be skewed.

2. Curvature and Refraction Errors: These refer to the bending of light as it passes through different mediums (like air at different temperatures) and the curvature of the Earth itself. If the distances aren't balanced, these effects can lead to inaccuracies in determining the height difference between points.

Think of it like trying to measure the height difference between two buildings using a tape measure. If you're at one building (point A) and you measure up to a particular point on the other building (point B), you might get a different reading compared to if you measure from the second building back to the first. If you measure from both buildings to a mid-point, you can get a more accurate reading of the height difference because you're accounting for any potential errors due to inconsistencies in the ground or atmosphere between the two points.

While doing the levelling across features, like river, big ponds and reservoirs, it is not possible to maintain equal distance for fore sight and back sight distances. In such situations, the reciprocal levelling is used and the height difference between two points is precisely determined by two sets of correlation observations.

The procedure for reciprocal levelling involves a systematic approach where the instrument is set up at one point (Point A) on one side of a valley or body of water. The surveyor takes readings on a staff at Point A and a second staff located at Point B. After completing the measurements from Point A, the instrument is moved to Point B, and the process is repeated. This series of observations allows for a precise determination of height differences, despite the challenging features of the terrain. By comparing the readings, the surveyor can identify and correct any inconsistencies or errors that may arise from the measurement process.

Imagine you want to measure the height difference across a large lake. If you stand on one side and measure towards a stick floating on the other side, your measurement might be affected by waves or wind. Instead, you measure from both sides alternately. First, you take a measurement from your side and then move to the opposite side to take another measurement back to your original position. By averaging these two sets of measurements, you account for any errors introduced by the environment, resulting in a more accurate understanding of the height difference.

In this method, the instrument is set up at a point A on one side of the valley, and readings are taken on the staff held near A and on the staff held at B on the other side of the valley. Let these readings be h_a and h_b, respectively. Reading h_b is considered to be accurate, but reading h_a may have an error ‘e’ due to collimation...

In reciprocal levelling computations, the readings taken at both locations are compared. For example, if the reading from Point A to Point B is given as h_a (which may contain an error), and the reading from Point B back to Point A is h_b (considered accurate), you can use both readings to find the true height difference, h. The formula involving both readings helps to average out any error due to collimation; thus, the final calculated height difference between the two points A and B becomes more reliable.

Picture two friends trying to measure the height of a fence using two different methods. The first friend measures to the top of the fence directly from one side, but the ground is uneven, which affects the accuracy of the measurement. The second friend measures from the other side, which might have a clearer view but can still contain errors. By averaging out their measurements – one from each side, they can determine the fence's height more accurately than either could have done alone.

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