Levelling is a branch of surveying, the object of which is to
 Find the elevation of a given point with respect to the given or assumed datum.
 Establish a point at a given elevation with respect to the given or assumed datum.
Levelling is the measurement of geodetic height using an optical levelling instrument and a level staff or rod having a numbered scale. Common levelling instruments include the spirit level, the dumpy level, the digital level, and the laser level
Method Of Levelling :
 Rise and fall method
 Height of collimation method
 Rise and fall method :
In this method, the difference of level between two consecutive points for each setting of the instrument, is obtained by comparing their staff readings. The difference between their staff readings indicates a rise if the back staff reading is more than the fore sight and a fall if it is less than the fore sight. The algebraic sum of rises and falls, gives the difference in level between the starting and closing points.
 Height of collimation method :
In this method height of the instrument is calculated for the first setting of instrument by adding the back sight to the reduced level of the given Bench Mark. The reduced level of the first station is obtained by subtracting its fore sight from the instrument height (H.I.).
Arithmetical checks :
∑ B.S. ∑ F.S. =∑ Rise – ∑ Fall = Last R.L. – First R.L.
Comparison of Line of Collimation Method with Rise and Fall Method :
Height of collimation method  Rise and fall method 
1. It is more rapid and saves a considerable time and labour.
2. It is well adopted for reduction of levels for construction work such as longitudinal or cross section levelling operations. 3. There is no check on reduction of R.L.S. of intermediate stations. 4. There are only two arithmetical check i.e.,, the difference between the sum of the back sights and the sum of the fore sights must be equal to the difference in R.L. of the last station and first station. 5. Errors if any in intermediate sights are not detected. 
1. It is laborious as the staff reading of each station is compared, to get a rise or fall.
2. It is well adopted for determining the difference in levels of two points where precision is required. 3. There is a complete check on the reduction of R.Ls. of intermediate stations. 4. There are three arithmetical checks i.e. the difference between the sum of the back sights and the sum of the fore sights must be equal to the difference between the sum of the rises and the sum of the falls as well as it must be equal to the difference in R.Ls. of the last station and first station. 5. Errors in intermediate sights are noticed as these are used for finding out the rises or falls. 
Sprit level:
The spirit level is on a tripod with sight lines to the two points whose height difference is to be determined. A graduated leveling staff or rod is held vertical on each point; the rod may be graduated in centimetres and fractions or tenths and hundredths of a foot. The observer focuses in turn on each rod and reads the value. Subtracting the “back” and “forward” value provides the height difference.
Refraction and Curvature:
The curvature of the earth means that a line of sight that is horizontal at the instrument will be higher and higher above a spheroid at greater distances. The effect may be significant for some work at distances under 100 meters.
The line of sight is horizontal at the instrument, but is not a straight line because of refraction in the air. The change of air density with elevation causes the line of sight to bend toward the earth.
The combined correction for refraction and curvature is approximately.
Or
For precise work these effects need to be calculated and corrections applied. For most work it is sufficient to keep the foresight and back sight distances approximately equal so that the refraction and curvature effects cancel out. Refraction is generally the greatest source of error in leveling. For short level lines the effects of temperature and pressure are generally insignificant, but the effect of the temperature gradient dT / dh can lead to errors.
Dumpy level :
The dumpy level was developed by English civil engineer William Gravatt, while surveying the route of a proposed railway line form London to Dover. More compact and hence both more robust and easier to transport, it is commonly believed that dumpy levelling is less accurate than other types of levelling, but such is not the case. Dumpy levelling requires shorter and therefore more numerous sights, but this fault is compensated by the practice of making foresights and back sights equal.
Precise level designs were often used for large leveling projects where utmost accuracy was required. They differ from other levels in having a very precise spirit level tube and a micrometer adjustment to raise or lower the line of sight so that the crosshair can be made to coincide with a line on the rod scale and no interpolation is required
Reading the staff :
The staff starts at zero, on the ground. Every 10 cm is a number, showing ( in meters to one decimal) the height of the bottom of what appears to be a stylised E (even numbers) or 3 (odd numbers), 5 cm high. The stems of the E or 3 and the gaps between them are each 10mm high. These 10mm increments continue up to the next 10 cm mark.
To read the staff, take the number shown below the reticle. Count the number of whole 10mm increments between the whole number and the reticle. Then estimate the number of mm between the last whole 10mm block and the center of the reticle. The diagram above shows 4 readings: 1.950, 2.000, 2.035 and 2.087.
The person holding the staff should end heavour to hold it as straight as possible. The leveller can easily see if it is tilted to the left or right, and should correct the staffholder. However, it cannot easily be seen that the staff is tilted towards or away from the leveller. In order to combat this possible source of error, the staff should be slowly rocked towards and away from the leveller. When viewing the staff, the reading will thus vary between a high and low point. The correct reading is the lowest value.
Digital levels electronically read a barcoded scale on the staff. These instruments usually include data recording capability. The automation removes the requirement for the operator to read a scale and write down the value, and so reduces blunders. It may also compute and apply refraction and curvature corrections.
LEVELLING PROCEDURE :
A typical procedure is to set up the instrument within 100 meters (110 yards) of a point of known or assumed elevation. A rod or staff is held vertical on that point and the instrument is used manually or automatically to read the rod scale. This gives the height of the instrument above the starting (backsight) point and allows the height of the instrument (H.I.) above the datum to be computed.
The rod is then held on an unknown point and a reading is taken in the same manner, allowing the elevation of the new (foresight) point to be computed. The procedure is repeated until the destination point is reached. It is usual practice to perform either a complete loop back to the starting point or else close the traverse on a second point whose elevation is already known. The closure check guards against blunders in the operation, and allows residual error to be distributed in the most likely manner among the stations.
Some instruments provide three crosshairs which allow stadia measurement of the foresight and back sight distances. These also allow use of the average of the three readings (3wire leveling) as a check against blunders and for averaging out the error of interpolation between marks on the rod scale.
The two main types of levelling are singlelevelling as already described, and doublelevelling (Doublerodding). In doublelevelling, a surveyor takes two foresights and two back sights and makes sure the difference between the foresights and the difference between the backsights are equal, thereby reducing the amount of error. Doublelevelling costs twice as much as singlelevelling.
Safety and precautions in leveling :
While leveling, the following precautions should be taken:

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