refraction. 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 backsight 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. Levelling loops and gravity variations Assuming error-free measurements, if the Earth's gravity field were completely regular and gravity constant, leveling loops would always close precisely: around a loop. In the real gravity field of the Earth, this happens only approximately; on small loops typical of engineering projects, the loop closure is negligible, but on larger loops covering regions or continents it is not. Instead of height differences, geopotential differences do close around loops: where stands for gravity at the leveling interval i. For precise leveling networks on a national scale, the latter formula should always be used. should be used in all computations, producing geopotential values for the benchmarks of the network. Instruments Classical instruments The dumpy level was developed by English civil engineer William Gravatt, while surveying the route of a proposed railway line from 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 backsights 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. Automatic level Automatic levels make use of a compensator that ensures that the line of sight remains horizontal once the operator has roughly leveled the instrument (to within maybe 0.05 degree). The surveyor sets the instrument up quickly and does not have to relevel