Definitions

# Spirit leveling

Spirit leveling is a technique for determining differences in height between points on the Earth's surface. It works by using 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:

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

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:

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

where $g_i$ 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 $W_i$ for the benchmarks of the network.

See Physical geodesy for details.

## References

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