Vernier scale

A vernier scale is a device that lets the user measure more precisely than could be done unaided when reading a uniformly divided straight or circular measurement scale. It is a scale that indicates where the measurement lies in between two of the marks on the main scale. Verniers are common on sextants used in navigation, scientific instruments used to conduct experiments, machinists' measuring tools (all sorts, but especially calipers and micrometers) used to work materials to fine tolerances, on theodolites used in surveying, and in absolute encoders to measure linear or rotational displacements.

Calipers without a vernier scale originated in ancient China as early as the Qin dynasty (AD 9). The 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. It was also commonly called a nonius in English until the end of the 18th century.Nonius is the Latinised name of the Portuguese mathematician, cosmographer Pedro Nunes (1502-1578). The name "vernier" was popularised by the French astronomer Jérôme Lalande (1732–1807) through his Traité d'astronomie (2 vols) (1764).

In the following, N is the number of divisions the maker wishes to show at a finer level of measure.

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