# Double level: Wikis

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# Encyclopedia

(Redirected to Levelling article)

Levelling or leveling is the measurement of geodetic height using a levelling instrument and a level staff. Common levelling instruments include the spirit level, the dumpy level, and the laser level. The two main types of levelling are single-levelling and double-levelling. In double-levelling, a surveyor takes two foresights and two backsights and makes sure the difference between the foresights and the difference between the backsights are equal, thereby reducing the amount of error.[1] Double-levelling costs twice as much as single-levelling.[2]

## Spirit levelling

Spirit levelling employs a spirit level, an instrument consisting of a telescope and a tube level like that used by carpenters, rigidly connected. When the bubble in the tube level is in the middle, the telescope's optical axis (collimation axis) will point exactly in the direction of the local horizontal.

The spirit level is placed on a tripod in the middle between the two points whose height difference is to be determined; the points are marked by markers or benchmarks in the rock or soil. A leveling staff or rod is placed on each point, with measured graduations, usually in centimetres and fractions thereof. The observer focuses in turn on each rod and reads the value from it. Subtracting the "back" and "forward" value provides the height difference.

### Leveling loops

If the Earth's gravity field were completely regular and gravity constant, leveling loops would always close precisely:

$\sum_{i=0}^n \Delta h_i = 0$

around a loop. In the real gravity field of the Earth, this happens only approximately; on small loops, the loop closure is negligible, but on larger loops it is not.

Instead of height differences, geopotential differences do close around loops:

$\sum_{i=0}^n \Delta h_i g_i = 0,$

where gi stands for gravity at the leveling interval i. For precise leveling networks on a national scale, the latter formula should always be used.

$\Delta W_i = \Delta h_i g_i\$

should be used in all computations, producing geopotential values Wi for the benchmarks of the network.

## Dumpy levelling

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 backsights equal.

## Laser levelling

The advantages of laser levelling over other types of levelling is that longer sights can be used and one person can perform the levelling independently while other types of levelling require someone to be stationed at the level and another person to be holding the level staff.[3]

## References

1. ^ Ira Osborn Baker (1887). Leveling: Barometric, Trigonometric and Spirit. D. Van Nostrand. p. 126.
2. ^ Guy Bomford. Geodesy. Clarendon Press. p. 204. ISBN 019851946X.
3. ^ John S. Scott (1992). Dictionary of Civil Engineering. Springer Science+Business Media. p. 252. ISBN 0412984210.