Methods of reducing levels

Reduction of levels is the calculation of the reduced level (RL) of each point from the staff readings entered in the level book. Two methods are used.

1. Height of instrument (HI) or height of collimation method

• HI (the RL of the line of collimation) = RL of the BM + BS.
• RL of any point = HI $-$ staff reading (IS or FS) on it.
• At a change point, the new HI = RL of the CP + new BS.

$$\text{HI} = \text{RL} + \text{BS}, \qquad \text{RL} = \text{HI} - \text{IS or FS}$$

Arithmetic check: $\Sigma BS - \Sigma FS = \text{last RL} - \text{first RL}$.

It is quicker and suitable when many intermediate sights are taken (profile and cross-section levelling), but the intermediate sights are not checked.

2. Rise and fall method

• The difference between consecutive staff readings gives a rise or a fall.
• If the second reading is less than the first, it is a rise: rise $=$ previous reading $-$ present reading, and RL $=$ previous RL $+$ rise.
• If it is greater, it is a fall, and RL $=$ previous RL $-$ fall.

Arithmetic check:

$$\Sigma BS - \Sigma FS = \Sigma \text{Rise} - \Sigma \text{Fall} = \text{last RL} - \text{first RL}$$

It checks every reading (including the intermediate sights), but takes more time. It is preferred for precise work, such as fly levelling and check levelling.

Example (HI): BM RL 100.000, BS 1.500 gives HI 101.500; FS 0.800 on point P gives RL 100.700.