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A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error. It may be found on many types of instrument measuring linear or angular quantities, but in particular on a vernier caliper which measures internal or external diameter of hollow cylinders. The vernier is a subsidiary scale replacing a single measured-value pointer, and has for instance ten divisions equal in distance to nine divisions on the main scale. The interpolated reading is obtained by observing which of the vernier scale graduations is coincident with a graduation on the main scale, which is easier to perceive than visual estimation between two points. Such an arrangement can go to a higher resolution by using a higher scale ratio, known as the vernier constant. A vernier may be used on circular or straight scales where a simple linear mechanism is adequate. Examples are calipers and micrometers to measure to fine tolerances, on sextants for navigation, on theodolites in surveying, and generally on scientific instruments. The Vernier principle of interpolation is also used for electronic displacement sensors such as absolute encoders to measure linear or rotational movement, as part of an electronic measuring system. Calipers#History and Micrometer (device)#History The first caliper with a secondary scale, which contributed extra precision, was invented in 1631 by French mathematician Pierre Vernier (1580–1637). Its use was described in detail in English in Navigatio Britannica (1750) by mathematician and historian John Barrow. While calipers are the most typical use of vernier scales today, they were originally developed for angle-measuring instruments such as astronomical quadrants. In some languages, the vernier scale is called a nonius after Portuguese mathematician, cosmographer Pedro Nunes (Latin Petrus Nonius, 1502–1578).

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Surveying

Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is called a land surveyor. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designed positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.

Surveying