What is height of instrument and Rise & fall method of levelling?

To obtain the reduced level of a point in the field from staff readings, we have 2 methods:

1. Height of Instrument or Collimation method
2. Rise and fall method.

Height of instrument method deals with obtaining the RL of the line of collimation by adding BS reading of a point whose RL is known. The RL of line of collimation is called Height of Instrument. From this, the staff readings of all intermediate stations is subtracted to get the RL at those points.

Now, what is the rise and fall method?

Here, instead of calculating the height of instrument, we calculate the difference of staff readings at the two stations. The two stations where staff readings are taken are such that we know the RL of ground of one station and we want to find the RL of other.

A level is set at such a position from where max. no of stations can be visible. Now, the staff is placed at the station whose RL is known and the reading is observed say R1. The staff is then transferred to a station whose RL is to be determined and the reading is observed say R2.

Now, if R1 > R2, it means ground at former station is lower than ground at latter station. So, there is rise in ground surface

Similarly, if R2 > R1, the ground at latter station is deeper / lower than ground at former station. So there is a fall in ground surface

Now that you know what rise and fall is, the question arises how to use this concept to obtain RL of various successive stations?

After taking readings at two stations, the difference of readings i.e. (R1 – R2) is added to the RL of first station to get the RL of second station

=> RL of Station 1 +(R1-R2) = RL of Station 2

Now to find the RL of third station, the staff reading is observed say R3 and (R2-R3) is obtained.

Then,

RL of station 2 + (R2-R3) = RL of station 3

This can be used indefinitely till the last point whose RL is required is reached.

The difference of staff readings is nothing but the rise or fall of ground.

if fore sight reading is greater than back sight reading, there is fall in ground surface. This fall is then subtracted from RL of previous station to obtain RL of next station

This method is a bit laborious as staff reading at each station after the first, is compared with that of the preceding station

There are 3 checks for arithmetical accuracy. These are the “sum of back sight readings minus sum of fore sight readings should be equal to the difference between the sum of rises and sum of falls which in turn should be equal to the difference between first RL and last RL”