Differential levelling practicle, reduction of level by rise and fall method, arithmetical check

Theory

This method is used in order to find the difference in elevation between two points.

1.      If they are to a far apart.

2.    If the difference in elevation between them is too great.

3.    If these are obstacles intervening.

In such a case it is necessary to set up the level in several positions and to work in series of stages. The method of simple leveling is employed in each of the successive stages. The process is also known as compound of continuous levelling.

Diagram

Procedure

Suppose it is desired to find the difference of levels between two points A and B which are too far apart. Setup the level at O₁ and correctly level it with the bubble in centre take.

The reading on the staff held vertically at A from select a firm point ‘C’ so that its distance from O₁ is approximate equal to that of A form O₁ and with the bubble in the centre fo the tube take the reading on the staff held vertically at ‘C’.

This forms the first stage in the series. Now shift the instrument to set upon level it carefully with the bubble in centre of its turn take the reading on the staff at D. Repeat the procedure until the point B is reached.

The rise and fall system

It consists in determining the difference of levels between commulative point by comparing each point after the first with that immediatlly preceeding it. The difference between their staff reading at the point is smaller or greater than that at the preceeding point. The reduced level of each point is then found by adding the rise of subtracting the fall from the reduced level of the preceeding point.

Arithmetical check

These are three checks on the accuracy of the reductions. The difference between  the sum of the back sign as and sum of sights is equal to the difference between the sum of back sights and sum of the fore sights is equal to the difference between the last reduced level and first reduced level.